math.log/1 on complex, imaginary part

Percentage Accurate: 100.0% → 100.0%

Time: 964.0ms

Precision: binary64

Cost: 6528

Math

\[\tan^{-1}_* \frac{im}{re} \]

↓

\[\tan^{-1}_* \frac{im}{re} \]

FPCore

(FPCore (re im) :precision binary64 (atan2 im re))

↓

(FPCore (re im) :precision binary64 (atan2 im re))

C

double code(double re, double im) {
	return atan2(im, re);
}

↓

double code(double re, double im) {
	return atan2(im, re);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = atan2(im, re)
end function

↓

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = atan2(im, re)
end function

Java

public static double code(double re, double im) {
	return Math.atan2(im, re);
}

↓

public static double code(double re, double im) {
	return Math.atan2(im, re);
}

Python

def code(re, im):
	return math.atan2(im, re)

↓

def code(re, im):
	return math.atan2(im, re)

Julia

function code(re, im)
	return atan(im, re)
end

↓

function code(re, im)
	return atan(im, re)
end

MATLAB

function tmp = code(re, im)
	tmp = atan2(im, re);
end

↓

function tmp = code(re, im)
	tmp = atan2(im, re);
end

Wolfram

code[re_, im_] := N[ArcTan[im / re], $MachinePrecision]

↓

code[re_, im_] := N[ArcTan[im / re], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\tan^{-1}_* \frac{im}{re} \]

2. Final simplification 100.0%

   \[\leadsto \tan^{-1}_* \frac{im}{re} \]

Reproduce

herbie shell --seed 2023160 
(FPCore (re im)
  :name "math.log/1 on complex, imaginary part"
  :precision binary64
  (atan2 im re))