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Sin function

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Program Information

Name: Sin function
Domain: Numerical program
Functionality: Sin function in math
Input: $x$: A certain Real Number  
Output: $y$: The value of $\sin x$

Reference

 Metamorphic Testing and Beyond https://doi.org/10.1109/STEP.2003.18; 
An Effective Testing Method for End-User Programmers https://doi.org/10.1145/1082983.1083236 ; 
Search-Based Inference of Polynomial Metamorphic Relations https://doi.org/10.1145/2642937.2642994  

MR Information

MR1------

Description:
Property: $\sin x-\sin(x+2\pi)=0$
Source input: $x$
Source output: $\sin x$
Follow-up input: $x+2\pi$
Follow-up output: $\sin (x+2\pi)$
Input relation: $x \Rightarrow (x+2\pi)$
Output relation: $\sin x-\sin(x+2\pi)=0$
Pattern:

MR2------

Description:
Property: $\sin x+\sin(x+\pi)=0$
Source input: $x$
Source output: $\sin x$
Follow-up input: $x+\pi$
Follow-up output: $\sin (x+\pi)$
Input relation: $x \Rightarrow (x+\pi)$
Output relation: $\sin x+\sin(x+\pi)=0$
Pattern:

MR3------

Description:
Property:  $-\sin (-x) -\sin x=0$
Source input: $x$ 
Source output: $\sin x$ 
Follow-up input: $-x$ 
Follow-up output:  $\sin (-x)$
Input relation: $x \Rightarrow (-x)$ 
Output relation: $-\sin (-x) -\sin x=0$ 
Pattern:

MR4------

Description:
Property:   $\sin x-\sin (\pi-x)=0$ 
Source input:  $x$  
Source output:  $\sin x$  
Follow-up input:  $\pi-x$  
Follow-up output:   $\sin (\pi-x)$ 
Input relation:  $x \Rightarrow (\pi-x)$  
Output relation:  $\sin x-\sin (\pi-x)=0$ 
Pattern:

MR5------

Description:
Property:    $\sin x+\sin (2\pi-x)=0$  
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:   $2\pi-x$   
Follow-up output:    $\sin (2\pi-x)$  
Input relation:   $x \Rightarrow (2\pi-x)$   
Output relation:   $\sin x+\sin (2\pi-x)=0$  
Pattern:

MR6------

Description:
Property:    $\sin x+\sin y +\sin z-\sin(x+y+z)-4\sin ((x+y)/2) \sin ((x+z)/2) \sin ((y+z)/2)$  
Source input:  $x,y,z$   
Source output:  $\sin x,\sin y,\sin z$   
Follow-up input:   $x+y+z,(x+y)/2,(x+z)/2,(y+z)/2$   
Follow-up output:    $\sin(x+y+z),\sin((x+y)/2),\sin((x+z)/2),\sin((y+z)/2)$  
Input relation:   $x,y,z \Rightarrow (x+y+z),(x+y)/2,(x+z)/2,(y+z)/2$  
Output relation:   $\sin x+\sin y +\sin z-\sin(x+y+z)-4\sin ((x+y)/2) \sin ((x+z)/2) \sin ((y+z)/2)$ 
Pattern:

MR7------

Description:
Property:    $\sin^2 x+\sin^2 (\pi/2-x)-1=0$  
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:   $\pi/2-x$  
Follow-up output:    $\sin (\pi/2-x)$  
Input relation:   $x \Rightarrow (\pi/2-x)$   
Output relation:   $\sin^2 x+\sin^2 (\pi/2-x)-1=0$  
Pattern:

MR8------

Description:
Property:    $\sin 3x-3\sin x+4\sin^3 x=0$  
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:   $3x$ 
Follow-up output:    $\sin (3x)$  
Input relation:   $x \Rightarrow (3x)$   
Output relation:   $\sin 3x-3\sin x+4\sin^3 x=0$  
Pattern:

MR9------

Description:
Property:    $\sin^2 x-\sin^2 y-\sin (x+y)\sin (x-y)=0$  
Source input:   $x,y$  
Source output:  $\sin x,\sin y$   
Follow-up input:  $x+y, x-y$  
Follow-up output:  $\sin(x+y),\sin(x-y)$   
Input relation:    $x,y \Rightarrow (x+y),(x-y)$ 
Output relation:  $\sin^2 x-\sin^2 y-\sin (x+y)\sin (x-y)=0$
Pattern:

MR10------

Description:
Property:    $\sin 5x-16\sin5x-5\sin 3x+10\sin x=0$  
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:  $5x,3x$ 
Follow-up output:    $\sin (3x),\sin (5x)$ 
Input relation:   $x,y \Rightarrow (3x),(5x)$  
Output relation:  $\sin 5x-16\sin5x-5\sin 3x+10\sin x=0$  
Pattern:

MR11------

Description:
Property:    $\sin^2(x)+\sin^2(-x+0.5\pi)-1=0$  
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:  $-x+0.5\pi$  
Follow-up output:   $\sin(-x+0.5\pi)$  
Input relation:    $x \Rightarrow (-x+0.5\pi)$ 
Output relation:  $\sin^2(x)+\sin^2(-x+0.5\pi)-1=0$ 
Pattern:

MR12------

Description:
Property:    $\sin^2(-0.5x-0.75\pi)+0.5\sin(x)-0.5=0$  
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:  $-0.5x-0.75\pi$  
Follow-up output:   $\sin(-0.5x-0.75\pi)$  
Input relation:  $x \Rightarrow (-0.5x-0.75\pi)$   
Output relation:  $\sin^2(-0.5x-0.75\pi)+0.5\sin(x)-0.5=0$  
Pattern:

MR13------

Description:
Property:   $\sin^2(x)+\sin^2(-x)+2\sin(x)\sin(-x)=0$   
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:  $-x$  
Follow-up output:  $\sin(-x)$   
Input relation:   $x \Rightarrow (-x)$  
Output relation:  $\sin^2(x)+\sin^2(-x)+2\sin(x)\sin(-x)=0$  
Pattern:

MR14------

Description:
Property:   $\sin^2(x)+\sin^2(x-\pi)+2\sin(x)\sin(x-\pi)=0$   
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:  $x-\pi$  
Follow-up output:  $\sin(x-\pi)$   
Input relation:    $x \Rightarrow (x-\pi)$ 
Output relation:  $\sin^2(x)+\sin^2(x-\pi)+2\sin(x)\sin(x-\pi)=0$  
Pattern:

MR15------

Description:
Property:    $\sin^2(x)+\sin^2(x-2.5\pi)-1=0$  
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:  $x-2.5\pi$  
Follow-up output:   $\sin(x-2.5\pi)$  
Input relation:   $x \Rightarrow (x-5.5\pi)$  
Output relation:  $\sin^2(x)+\sin^2(x-2.5\pi)-1=0$  
Pattern:

MR16------

Description:
Property:   $\sin^2(x)+0.5\sin(2x-1.5\pi)-0.5=0$   
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:  $2x-1.5\pi$  
Follow-up output:  $\sin(2x-1.5\pi)$   
Input relation:   $x \Rightarrow (2x-1.5\pi)$  
Output relation:   $\sin^2(x)+0.5\sin(2x-1.5\pi)-0.5=0$ 
Pattern:

MR17------

Description:
Property:   $\sin^2(x)+\sin^2(-x)+2\sin(x)\sin(-x)=0$   
Source input:   $x$   
Source output:   $\sin x$   
Follow-up input:   $-x$ 
Follow-up output:   $\sin(-x)$  
Input relation:   $x \Rightarrow (-x)$  
Output relation:  $\sin^2(x)+\sin^2(-x)+2\sin(x)\sin(-x)=0$  
Pattern:

MR18------

Description:
Property: $\sin(x)-\sin(x-2\pi)=0$  
Source input: $x$   
Source output: $\sin x$   
Follow-up input: $x-2\pi$  
Follow-up output: $\sin(x-2\pi)$  
Input relation:  $x \Rightarrow (x-2\pi)$  
Output relation: $\sin(x)-\sin(x-2\pi)=0$ 
Pattern:

MR19------

Description:
Property: $\sin(x)+\sin(-x-4\pi)=0$ 
Source input:   $x$    
Source output:  $\sin x$    
Follow-up input: $-x-4\pi$ 
Follow-up output: $\sin(-x-4\pi)$ 
Input relation: $x \Rightarrow (-x-4\pi)$  
Output relation: $\sin(x)+\sin(-x-4\pi)=0$ 
Pattern:

MR20------

Description:
Property: $\sin(x)-\sin(-x-\pi)=0$
Source input: $x$     
Source output:  $\sin x$     
Follow-up input: $-x-\pi$  
Follow-up output: $\sin(-x-\pi)$ 
Input relation:   $x \Rightarrow (-x-\pi)$ 
Output relation: $\sin(x)-\sin(-x-\pi)=0$
Pattern:

MR21------

Description:
Property: $\sin(x)-\sin(-x-3\pi)=0$ 
Source input: $x$      
Source output: $\sin x$      
Follow-up input: $-x-3\pi$ 
Follow-up output: $\sin(-x-3\pi)$
Input relation: $x \Rightarrow (-x-3\pi)$  
Output relation: $\sin(x)-\sin(-x-3\pi)=0$ 
Pattern:

MR22------

Description:
Property: $\sin^2(x)-\sin^2(-x-2\pi)-\sin(x)-\sin(-x-2\pi)=0$ 
Source input:  $x$      
Source output: $\sin x$      
Follow-up input: $-x-2\pi$  
Follow-up output: $\sin(-x-2\pi)$  
Input relation: $x \Rightarrow (-x-2\pi)$ 
Output relation: $\sin^2(x)-\sin^2(-x-2\pi)-\sin(x)-\sin(-x-2\pi)=0$ 
Pattern:

MR23------

Description:
Property: $\sin(x)+0.5\sin^2(-x)+1.5\sin(x)\sin(-x)+0.5\sin(x)+0.5\sin(-x)=0$  
Source input: $x$      
Source output: $\sin x$      
Follow-up input: $-x$ 
Follow-up output: $\sin(-x)$ 
Input relation: $x \Rightarrow (-x)$  
Output relation: $\sin(x)+0.5\sin^2(-x)+1.5\sin(x)\sin(-x)+0.5\sin(x)+0.5\sin(-x)=0$ 
Pattern:

MR24------

Description:
Property: $\sin^2(x)-\sin(x)\sin(-x+\pi)+\sin(x)-\sin(-x+\pi)=0$ 
Source input: $x$       
Source output: $\sin x$       
Follow-up input: $-x+\pi$    
Follow-up output: $\sin(-x+\pi)$   
Input relation: $x \Rightarrow (-x+\pi)$   
Output relation: $\sin^2(x)-\sin(x)\sin(-x+\pi)+\sin(x)-\sin(-x+\pi)=0$ 
Pattern:

MR25------

Description:
Property: $\sin^2(x)+\sin^2(-x)-2\sin(x)\sin(-x)=0$ 
Source input: $x$        
Source output: $\sin x$        
Follow-up input: $-x$   
Follow-up output: $\sin(-x)$   
Input relation: $x \Rightarrow (-x)$  
Output relation: $\sin^2(x)+\sin^2(-x)-2\sin(x)\sin(-x)=0$  
Pattern:

MR26------

Description:
Property: $\sin^2(x)+\sin^2(-x-\pi)-2\sin(x)\sin(-x-\pi)=0$  
Source input: $x$         
Source output: $\sin x$         
Follow-up input: $-x-\pi$    
Follow-up output: $\sin(-x-\pi)$    
Input relation: $x \Rightarrow (-x-\pi)$   
Output relation: $\sin^2(x)+\sin^2(-x-\pi)-2\sin(x)\sin(-x-\pi)=0$   
Pattern:

MR27------

Description:
Property: $\sin^2(x)+\sin(x)\sin(x-\pi)+2\sin(x)+2\sin(x-\pi)=0$  
Source input: $x$         
Source output: $\sin x$         
Follow-up input: $x-\pi$    
Follow-up output: $\sin(x-\pi)$    
Input relation: $x \Rightarrow (x-\pi)$   
Output relation: $\sin^2(x)+\sin(x)\sin(x-\pi)+2\sin(x)+2\sin(x-\pi)=0$   
Pattern:

MR28------

Description:
Property:  $\sin^2(x)+0.5\sin(2x+0.5\pi)-0.5=0$  
Source input: $x$ 
Source output: $\sin x$ 
Follow-up input: $2x+0.5\pi$ 
Follow-up output: $\sin(2x+0.5\pi)$ 
Input relation: $x \Rightarrow (2x+0.5\pi)$ 
Output relation: $\sin^2(x)+0.5\sin(2x+0.5\pi)-0.5=0$ 
Pattern:
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