math.exp on complex, imaginary part

Average Accuracy: 100.0% → 100.0%

Time: 10.2s

Precision: binary64

Cost: 12992

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
Accuracy	99.2%
Cost	13892

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 5 \cdot 10^{-42}:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(\left(re + 1\right) + \left(re \cdot re\right) \cdot \left(0.5 + re \cdot 0.16666666666666666\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	99.0%
Cost	13700

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 5 \cdot 10^{-42}:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sin im}{re - \left(1 + re \cdot \left(re \cdot 0.5\right)\right)}\\ \end{array} \]

Alternative 3
Accuracy	99.0%
Cost	13636

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 5 \cdot 10^{-42}:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(\left(re + 1\right) + re \cdot \left(re \cdot 0.5\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	98.7%
Cost	13316

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 5 \cdot 10^{-42}:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\frac{-\sin im}{re + -1}\\ \end{array} \]

Alternative 5
Accuracy	98.7%
Cost	13252

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 5 \cdot 10^{-42}:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(re + 1\right)\\ \end{array} \]

Alternative 6
Accuracy	66.6%
Cost	13124

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

Alternative 7
Accuracy	73.2%
Cost	6596

\[\begin{array}{l} \mathbf{if}\;re \leq -62:\\ \;\;\;\;\left(1 + \left(im + re \cdot im\right)\right) + -1\\ \mathbf{else}:\\ \;\;\;\;\sin im\\ \end{array} \]

Alternative 8
Accuracy	41.4%
Cost	964

\[\begin{array}{l} \mathbf{if}\;re \leq -0.00085:\\ \;\;\;\;\left(1 + \left(im + re \cdot im\right)\right) + -1\\ \mathbf{else}:\\ \;\;\;\;re \cdot im + \left(im + 0.5 \cdot \left(im \cdot \left(re \cdot re\right)\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	41.3%
Cost	836

\[\begin{array}{l} \mathbf{if}\;re \leq -31:\\ \;\;\;\;\left(1 + \left(im + re \cdot im\right)\right) + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{im - im \cdot \left(re \cdot re\right)}{1 - re}\\ \end{array} \]

Alternative 10
Accuracy	41.3%
Cost	708

\[\begin{array}{l} t_0 := im + re \cdot im\\ \mathbf{if}\;re \leq -31:\\ \;\;\;\;\left(1 + t_0\right) + -1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Accuracy	34.5%
Cost	320

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

Alternative 12
Accuracy	34.5%
Cost	320

\[im + re \cdot im \]

Alternative 13
Accuracy	34.7%
Cost	64

\[im \]

Reproduce

herbie shell --seed 2023133 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))