math.log10 on complex, imaginary part

Average Accuracy: 98.7% → 99.9%

Time: 20.0s

Precision: binary64

Math

\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10} \]

↓

\[\frac{\tan^{-1}_* \frac{im}{re} \cdot {\log 10}^{3}}{{\log 10}^{4}} \]

FPCore

(FPCore (re im) :precision binary64 (/ (atan2 im re) (log 10.0)))

↓

(FPCore (re im)
 :precision binary64
 (/ (* (atan2 im re) (pow (log 10.0) 3.0)) (pow (log 10.0) 4.0)))

C

double code(double re, double im) {
	return atan2(im, re) / log(10.0);
}

↓

double code(double re, double im) {
	return (atan2(im, re) * pow(log(10.0), 3.0)) / pow(log(10.0), 4.0);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = atan2(im, re) / log(10.0d0)
end function

↓

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (atan2(im, re) * (log(10.0d0) ** 3.0d0)) / (log(10.0d0) ** 4.0d0)
end function

Java

public static double code(double re, double im) {
	return Math.atan2(im, re) / Math.log(10.0);
}

↓

public static double code(double re, double im) {
	return (Math.atan2(im, re) * Math.pow(Math.log(10.0), 3.0)) / Math.pow(Math.log(10.0), 4.0);
}

Python

def code(re, im):
	return math.atan2(im, re) / math.log(10.0)

↓

def code(re, im):
	return (math.atan2(im, re) * math.pow(math.log(10.0), 3.0)) / math.pow(math.log(10.0), 4.0)

Julia

function code(re, im)
	return Float64(atan(im, re) / log(10.0))
end

↓

function code(re, im)
	return Float64(Float64(atan(im, re) * (log(10.0) ^ 3.0)) / (log(10.0) ^ 4.0))
end

MATLAB

function tmp = code(re, im)
	tmp = atan2(im, re) / log(10.0);
end

↓

function tmp = code(re, im)
	tmp = (atan2(im, re) * (log(10.0) ^ 3.0)) / (log(10.0) ^ 4.0);
end

Wolfram

code[re_, im_] := N[(N[ArcTan[im / re], $MachinePrecision] / N[Log[10.0], $MachinePrecision]), $MachinePrecision]

↓

code[re_, im_] := N[(N[(N[ArcTan[im / re], $MachinePrecision] * N[Power[N[Log[10.0], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision] / N[Power[N[Log[10.0], $MachinePrecision], 4.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.7%

   \[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10} \]

2. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{im}{re} \cdot {\log 10}^{3}}{{\log 10}^{4}}} \]

Reproduce

herbie shell --seed 2023151 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  :precision binary64
  (/ (atan2 im re) (log 10.0)))