math.log10 on complex, imaginary part

Average Error: 0.8 → 0.1

Time: 11.2s

Precision: binary64

Cost: 13312

Math

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

↓

\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 0.1 \cdot -3} \cdot 3 \]

FPCore

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

↓

(FPCore (re im)
 :precision binary64
 (* (/ (atan2 im re) (* (log 0.1) -3.0)) 3.0))

C

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

↓

double code(double re, double im) {
	return (atan2(im, re) / (log(0.1) * -3.0)) * 3.0;
}

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(0.1d0) * (-3.0d0))) * 3.0d0
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.log(0.1) * -3.0)) * 3.0;
}

Python

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

↓

def code(re, im):
	return (math.atan2(im, re) / (math.log(0.1) * -3.0)) * 3.0

Julia

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

↓

function code(re, im)
	return Float64(Float64(atan(im, re) / Float64(log(0.1) * -3.0)) * 3.0)
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(0.1) * -3.0)) * 3.0;
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[(N[Log[0.1], $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision]

Derivation

1. Initial program 0.8

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

2. Applied egg-rr 1.3

   \[\leadsto \color{blue}{\frac{\frac{-1}{\log 10}}{0.3333333333333333} \cdot \frac{-\tan^{-1}_* \frac{im}{re}}{3}} \]

3. Applied egg-rr 0.1

   \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{im}{re}}{\log 0.1 \cdot -3} \cdot 3} \]

Alternatives

Alternative 1
Error	0.1
Cost	13120

\[\frac{-\tan^{-1}_* \frac{im}{re}}{\log 0.1} \]

Alternative 2
Error	0.8
Cost	13056

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

Reproduce

herbie shell --seed 2023010 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  :precision binary64
  (/ (atan2 im re) (log 10.0)))