math.exp on complex, imaginary part

Average Error: 100.0% → 100.0%

Time: 10.4s

Precision: binary64

Cost: 12992.00

Math

\[e^{re} \cdot \sin im \]

↓

\[e^{re} \cdot \sin im \]

FPCore

(FPCore (re im) :precision binary64 (* (exp re) (sin im)))

↓

(FPCore (re im) :precision binary64 (* (exp re) (sin im)))

C

double code(double re, double im) {
	return exp(re) * sin(im);
}

↓

double code(double re, double im) {
	return exp(re) * sin(im);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = exp(re) * sin(im)
end function

↓

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = exp(re) * sin(im)
end function

Java

public static double code(double re, double im) {
	return Math.exp(re) * Math.sin(im);
}

↓

public static double code(double re, double im) {
	return Math.exp(re) * Math.sin(im);
}

Python

def code(re, im):
	return math.exp(re) * math.sin(im)

↓

def code(re, im):
	return math.exp(re) * math.sin(im)

Julia

function code(re, im)
	return Float64(exp(re) * sin(im))
end

↓

function code(re, im)
	return Float64(exp(re) * sin(im))
end

MATLAB

function tmp = code(re, im)
	tmp = exp(re) * sin(im);
end

↓

function tmp = code(re, im)
	tmp = exp(re) * sin(im);
end

Wolfram

code[re_, im_] := N[(N[Exp[re], $MachinePrecision] * N[Sin[im], $MachinePrecision]), $MachinePrecision]

↓

code[re_, im_] := N[(N[Exp[re], $MachinePrecision] * N[Sin[im], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0

   \[e^{re} \cdot \sin im \]

2. Final simplification 100.0

   \[\leadsto e^{re} \cdot \sin im \]

Alternatives

Alternative 1
Error	99.2%
Cost	14532.00

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0.95:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(\frac{re \cdot re}{re + -1} + \left(\left(re \cdot re\right) \cdot \left(re \cdot 0.16666666666666666 + 0.5\right) + \frac{-1}{re + -1}\right)\right)\\ \end{array} \]

Alternative 2
Error	99.2%
Cost	13892.00

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0.95:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(\left(re \cdot re\right) \cdot \left(0.5 - re \cdot -0.16666666666666666\right) + \left(re + 1\right)\right)\\ \end{array} \]

Alternative 3
Error	99.1%
Cost	13636.00

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0.95:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(\left(re + 1\right) + re \cdot \left(re \cdot 0.5\right)\right)\\ \end{array} \]

Alternative 4
Error	99.1%
Cost	13636.00

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0.95:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(1 + \left(re + re \cdot \left(re \cdot 0.5\right)\right)\right)\\ \end{array} \]

Alternative 5
Error	98.8%
Cost	13252.00

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0.95:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(re + 1\right)\\ \end{array} \]

Alternative 6
Error	66.7%
Cost	13124.00

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 1:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im\\ \end{array} \]

Alternative 7
Error	66.1%
Cost	12996.00

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0.5:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;im + im \cdot \left(re - \left(re \cdot re\right) \cdot -0.5\right)\\ \end{array} \]

Alternative 8
Error	97.9%
Cost	12996.00

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0.5:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\sin im\\ \end{array} \]

Alternative 9
Error	45.9%
Cost	968.00

\[\begin{array}{l} \mathbf{if}\;re \leq -1 \cdot 10^{+139}:\\ \;\;\;\;\frac{im}{1 - re}\\ \mathbf{elif}\;re \leq -0.86:\\ \;\;\;\;-1 + \left(1 + \left(im + re \cdot im\right)\right)\\ \mathbf{else}:\\ \;\;\;\;im + im \cdot \left(re - \left(re \cdot re\right) \cdot -0.5\right)\\ \end{array} \]

Alternative 10
Error	45.8%
Cost	840.00

\[\begin{array}{l} t_0 := im + re \cdot im\\ \mathbf{if}\;re \leq -8.2 \cdot 10^{+138}:\\ \;\;\;\;\frac{im}{1 - re}\\ \mathbf{elif}\;re \leq -1:\\ \;\;\;\;-1 + \left(1 + t_0\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	34.1%
Cost	320.00

\[im \cdot \left(re + 1\right) \]

Alternative 12
Error	34.1%
Cost	320.00

\[im + re \cdot im \]

Alternative 13
Error	42.4%
Cost	320.00

\[\frac{im}{1 - re} \]

Alternative 14
Error	34.3%
Cost	64.00

\[im \]

Reproduce

herbie shell --seed 2023097 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))