math.exp on complex, imaginary part

Average Error: 0.0 → 0.0

Time: 14.4s

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 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.7
Cost	13252

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0.99999:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\left(re + 1\right) \cdot \sin im\\ \end{array} \]

Alternative 2
Error	1.1
Cost	13124

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0.99999:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im\\ \end{array} \]

Alternative 3
Error	9.0
Cost	6992

\[\begin{array}{l} t_0 := im \cdot \left(re + 2\right)\\ t_1 := t_0 + t_0\\ t_2 := \frac{1}{\frac{1}{\left(1 + re\right) \cdot im} + \left(-0.16666666666666666 \cdot \left(re \cdot im\right) + 0.16666666666666666 \cdot im\right)}\\ t_3 := \left(t_1 + \left(t_0 + 2 \cdot im\right)\right) - \left(t_1 + \left(im + t_0\right)\right)\\ \mathbf{if}\;re \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;re \leq -1.18 \cdot 10^{+170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;re \leq -8.5 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;re \leq -1.9 \cdot 10^{+15}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\sin im\\ \end{array} \]

Alternative 4
Error	25.3
Cost	2888

\[\begin{array}{l} t_0 := \frac{1}{\frac{1}{\left(1 + re\right) \cdot im} + \left(-0.16666666666666666 \cdot \left(re \cdot im\right) + 0.16666666666666666 \cdot im\right)}\\ t_1 := im \cdot \left(re + 2\right)\\ t_2 := t_1 + t_1\\ \mathbf{if}\;im \leq -8.5 \cdot 10^{+112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;im \leq 10^{+88}:\\ \;\;\;\;\left(t_2 + \left(t_1 + 2 \cdot im\right)\right) - \left(t_2 + \left(im + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	32.3
Cost	1480

\[\begin{array}{l} t_0 := \frac{1}{\frac{1}{\left(1 + re\right) \cdot im} + \left(-0.16666666666666666 \cdot \left(re \cdot im\right) + 0.16666666666666666 \cdot im\right)}\\ \mathbf{if}\;re \leq -9.5 \cdot 10^{+162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;re \leq -1.4:\\ \;\;\;\;re + \left(\left(im + im \cdot re\right) - re\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	31.8
Cost	836

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

Alternative 7
Error	32.0
Cost	708

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

Alternative 8
Error	32.0
Cost	708

\[\begin{array}{l} \mathbf{if}\;re \leq -220:\\ \;\;\;\;re + \left(\left(im + im \cdot re\right) - re\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{im} + im \cdot 0.16666666666666666}\\ \end{array} \]

Alternative 9
Error	36.2
Cost	448

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

Alternative 10
Error	41.8
Cost	64

\[im \]

Reproduce

herbie shell --seed 2023066 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))