math.exp on complex, real part

Average Error: 0.0 → 0.0

Time: 9.5s

Precision: binary64

Cost: 12992

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.6
Cost	13636

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 10^{-8}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(\left(re + 1\right) + 0.5 \cdot \left(re \cdot re\right)\right)\\ \end{array} \]

Alternative 2
Error	0.8
Cost	13252

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 10^{-8}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(re + 1\right)\\ \end{array} \]

Alternative 3
Error	1.3
Cost	12996

\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 10^{-8}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im\\ \end{array} \]

Alternative 4
Error	1.7
Cost	6728

\[\begin{array}{l} t_0 := \left(re + -1\right) + \left(re \cdot re\right) \cdot -0.5\\ \mathbf{if}\;re \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{-1}{t_0}\\ \mathbf{elif}\;re \leq -9.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{re \cdot re + \left(-1 - re \cdot re\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\cos im\\ \end{array} \]

Alternative 5
Error	20.1
Cost	1348

\[\begin{array}{l} t_0 := \left(re + -1\right) + \left(re \cdot re\right) \cdot -0.5\\ \mathbf{if}\;re \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{-1}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{re \cdot re + \left(-1 - re \cdot re\right)}{t_0}\\ \end{array} \]

Alternative 6
Error	29.4
Cost	704

\[\frac{-1}{\left(re + -1\right) + \left(re \cdot re\right) \cdot -0.5} \]

Alternative 7
Error	40.6
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022340 
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))