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Tan function

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Program Information

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

Reference

 Metamorphic Testing of Programs on Partial Differential Equations: a Case Study https://doi.org/10.1109/CMPSAC.2002.1045022; 
Search-Based Inference of Polynomial Metamorphic Relations https://doi.org/10.1145/2642937.2642994; 

MR Information

MR1------

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

MR2------

Description:
Property: $\tan^2(x)-2\tan(x)\tan(2x-3\pi /2)-1=0$
Source input: $x$
Source output: $\tan(x)$
Follow-up input: $2x-3\pi /2$
Follow-up output: $\tan(2x-3\pi /2)$
Input relation: $x \Rightarrow (2x-3\pi /2)$
Output relation: $\tan^2(x)-2\tan(x)\tan(2x-3\pi /2)-1=0$
Pattern:

MR3------

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

MR4------

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

MR5------

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

MR6------

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

MR7------

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

MR8------

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

MR9------

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

MR10------

Description:
Property: $\tan^2(0.5x+1.25\pi)-2\tan(x)\tan(0.5x+1.25\pi)-1=0$ 
Source input: $x$ 
Source output: $\tan(x)$ 
Follow-up input:  $0.5x+1.25\pi$
Follow-up output:  $\tan(0.5x+1.25\pi)$
Input relation: $x \Rightarrow (0.5x+1.25\pi)$ 
Output relation: $\tan^2(0.5x+1.25\pi)-2\tan(x)\tan(0.5x+1.25\pi)-1=0$ 
Pattern:

MR11------

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

MR12------

Description:
Property: $\tan^2(x)+\tan^2(x+3\pi)-2\tan(x)\tan(x+3\pi)=0$ 
Source input: $x$ 
Source output: $\tan(x)$ 
Follow-up input:  $x+3\pi$
Follow-up output:  $\tan(x+3\pi)$
Input relation: $x \Rightarrow (x+3\pi)$ 
Output relation: $\tan^2(x)+\tan^2(x+3\pi)-2\tan(x)\tan(x+3\pi)=0$ 
Pattern:

MR13------

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

MR14------

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

MR15------

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

MR16------

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

MR17------

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

MR18------

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

MR19------

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

MR20------

Description:
Property: $\tan^2(0.5x-1.75\pi)-2\tan(x)\tan(0.5x-1.75\pi)-1=0$ 
Source input: $x$ 
Source output: $\tan(x)$ 
Follow-up input:  $0.5x-1.75\pi$
Follow-up output: $\tan(0.5x-1.75\pi)$ 
Input relation: $x \Rightarrow (0.5x-1.75\pi)$ 
Output relation: $\tan^2(0.5x-1.75\pi)-2\tan(x)\tan(0.5x-1.75\pi)-1=0$ 
Pattern:
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