math.exp on complex, imaginary part

Percentage Accurate: 100.0% → 100.0%

Time: 8.6s

Precision: binary64

Cost: 12992

• 24.4% of points produce a very large (infinite) output. You may want to add a precondition.

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	100.0%
Cost	12992

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

Alternative 2
Accuracy	95.8%
Cost	7368

\[\begin{array}{l} t_0 := 0.5 \cdot \left(re \cdot re\right)\\ t_1 := e^{re} \cdot im\\ \mathbf{if}\;re \leq -0.06:\\ \;\;\;\;t_1\\ \mathbf{elif}\;re \leq 1000000000000:\\ \;\;\;\;\sin im \cdot \left(\left(re + 1\right) + t_0\right)\\ \mathbf{elif}\;re \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot t_0\\ \end{array} \]

Alternative 3
Accuracy	95.7%
Cost	7244

\[\begin{array}{l} t_0 := e^{re} \cdot im\\ \mathbf{if}\;re \leq -0.06:\\ \;\;\;\;t_0\\ \mathbf{elif}\;re \leq 1000000000000:\\ \;\;\;\;\sin im \cdot \left(re + 1\right)\\ \mathbf{elif}\;re \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(0.5 \cdot \left(re \cdot re\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	92.2%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;re \leq -0.06 \lor \neg \left(re \leq 1000000000000\right):\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(re + 1\right)\\ \end{array} \]

Alternative 5
Accuracy	92.6%
Cost	6857

\[\begin{array}{l} \mathbf{if}\;re \leq -0.06 \lor \neg \left(re \leq 3.5 \cdot 10^{-9}\right):\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im\\ \end{array} \]

Alternative 6
Accuracy	60.6%
Cost	6596

\[\begin{array}{l} \mathbf{if}\;re \leq 8.8 \cdot 10^{+46}:\\ \;\;\;\;\sin im\\ \mathbf{else}:\\ \;\;\;\;im \cdot \left(0.5 \cdot \left(re \cdot re\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	36.3%
Cost	580

\[\begin{array}{l} \mathbf{if}\;re \leq 1000000000000:\\ \;\;\;\;im\\ \mathbf{else}:\\ \;\;\;\;im \cdot \left(0.5 \cdot \left(re \cdot re\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	29.0%
Cost	324

\[\begin{array}{l} \mathbf{if}\;re \leq 1000000000000:\\ \;\;\;\;im\\ \mathbf{else}:\\ \;\;\;\;re \cdot im\\ \end{array} \]

Alternative 9
Accuracy	29.0%
Cost	320

\[im + re \cdot im \]

Alternative 10
Accuracy	26.2%
Cost	64

\[im \]

Reproduce

herbie shell --seed 2023269 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))