math.exp on complex, imaginary part

Average Error: 0.0 → 0.0

Time: 10.6s

Precision: binary64

Cost: 13056

Math

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

↓

\[\frac{\sin im}{e^{-re}} \]

FPCore

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

↓

(FPCore (re im) :precision binary64 (/ (sin im) (exp (- re))))

C

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

↓

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

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 = sin(im) / exp(-re)
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.sin(im) / Math.exp(-re);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 1.0

   \[\leadsto \color{blue}{{\left(\sqrt[3]{e^{re} \cdot \sin im}\right)}^{3}} \]

3. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\frac{\sin im}{\frac{1}{e^{re}}}} \]

4. Simplified 0.0

   \[\leadsto \color{blue}{\frac{\sin im}{e^{-re}}} \]
   Proof

Alternatives

Alternative 1
Error	0.9
Cost	13252

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\left(re + 1\right) \cdot \sin im\\ \end{array} \]

Alternative 2
Error	1.4
Cost	13124

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im\\ \end{array} \]

Alternative 3
Error	0.0
Cost	12992

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

Alternative 4
Error	21.3
Cost	6464

\[\sin im \]

Alternative 5
Error	41.7
Cost	64

\[im \]

Reproduce

herbie shell --seed 2023010 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))