math.exp on complex, real part

?

Percentage Accurate: 100.0% → 100.0%
Time: 8.5s
Precision: binary64
Cost: 12992

?

\[e^{re} \cdot \cos im \]
↓
\[e^{re} \cdot \cos im \]
(FPCore (re im) :precision binary64 (* (exp re) (cos im)))
↓
(FPCore (re im) :precision binary64 (* (exp re) (cos im)))
double code(double re, double im) {
	return exp(re) * cos(im);
}
↓
double code(double re, double im) {
	return exp(re) * cos(im);
}

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

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);
}

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

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

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

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]

e^{re} \cdot \cos im
↓
e^{re} \cdot \cos im

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 16 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 100.0%

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

  2. Final simplification100.0%

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

Alternatives

Alternative 1
Accuracy100.0%
Cost12992
\[e^{re} \cdot \cos im \]
Alternative 2
Accuracy71.1%
Cost19528
\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 1:\\ \;\;\;\;e^{re}\\ \mathbf{elif}\;e^{re} \leq 5 \cdot 10^{+91}:\\ \;\;\;\;\cos im\\ \mathbf{else}:\\ \;\;\;\;e^{re}\\ \end{array} \]
Alternative 3
Accuracy96.0%
Cost7368
\[\begin{array}{l} \mathbf{if}\;re \leq -7.2 \cdot 10^{-5}:\\ \;\;\;\;e^{re}\\ \mathbf{elif}\;re \leq 215:\\ \;\;\;\;\cos im \cdot \left(0.5 \cdot \left(re \cdot re\right) + \left(re + 1\right)\right)\\ \mathbf{elif}\;re \leq 1.9 \cdot 10^{+154}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(re \cdot \left(re \cdot 0.5\right)\right)\\ \end{array} \]
Alternative 4
Accuracy95.9%
Cost7244
\[\begin{array}{l} \mathbf{if}\;re \leq -5.7 \cdot 10^{-5}:\\ \;\;\;\;e^{re}\\ \mathbf{elif}\;re \leq 215:\\ \;\;\;\;\cos im \cdot \left(re + 1\right)\\ \mathbf{elif}\;re \leq 1.9 \cdot 10^{+154}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(re \cdot \left(re \cdot 0.5\right)\right)\\ \end{array} \]
Alternative 5
Accuracy93.0%
Cost6984
\[\begin{array}{l} \mathbf{if}\;re \leq -6.6 \cdot 10^{-5}:\\ \;\;\;\;e^{re}\\ \mathbf{elif}\;re \leq 215:\\ \;\;\;\;\cos im \cdot \left(re + 1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{re}\\ \end{array} \]
Alternative 6
Accuracy66.9%
Cost6728
\[\begin{array}{l} t_0 := 1 + -0.5 \cdot \left(im \cdot im\right)\\ t_1 := re \cdot \left(re \cdot 0.5\right)\\ \mathbf{if}\;re \leq -9500000:\\ \;\;\;\;re \cdot \left(im \cdot \left(im \cdot -0.5\right)\right)\\ \mathbf{elif}\;re \leq 520:\\ \;\;\;\;\cos im\\ \mathbf{elif}\;re \leq 5.8 \cdot 10^{+145}:\\ \;\;\;\;t_0 \cdot \left(0.5 \cdot \left(re \cdot re\right) + \left(re + 1\right)\right)\\ \mathbf{elif}\;re \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot t_0\\ \end{array} \]
Alternative 7
Accuracy45.5%
Cost1484
\[\begin{array}{l} t_0 := 0.5 \cdot \left(re \cdot re\right) + \left(re + 1\right)\\ \mathbf{if}\;re \leq -9500000:\\ \;\;\;\;re \cdot \left(im \cdot \left(im \cdot -0.5\right)\right)\\ \mathbf{elif}\;re \leq 180:\\ \;\;\;\;t_0\\ \mathbf{elif}\;re \leq 5.8 \cdot 10^{+145}:\\ \;\;\;\;\left(1 + -0.5 \cdot \left(im \cdot im\right)\right) \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 8
Accuracy45.5%
Cost1228
\[\begin{array}{l} t_0 := re \cdot \left(re \cdot 0.5\right)\\ \mathbf{if}\;re \leq -11500000:\\ \;\;\;\;re \cdot \left(im \cdot \left(im \cdot -0.5\right)\right)\\ \mathbf{elif}\;re \leq 210:\\ \;\;\;\;0.5 \cdot \left(re \cdot re\right) + \left(re + 1\right)\\ \mathbf{elif}\;re \leq 5.8 \cdot 10^{+145}:\\ \;\;\;\;t_0 \cdot \left(1 + -0.5 \cdot \left(im \cdot im\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 9
Accuracy45.2%
Cost972
\[\begin{array}{l} \mathbf{if}\;re \leq -2.35:\\ \;\;\;\;re \cdot \left(im \cdot \left(im \cdot -0.5\right)\right)\\ \mathbf{elif}\;re \leq 210:\\ \;\;\;\;re + 1\\ \mathbf{elif}\;re \leq 5.8 \cdot 10^{+145}:\\ \;\;\;\;im \cdot \left(im \cdot \left(re \cdot \left(re \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 10
Accuracy45.2%
Cost972
\[\begin{array}{l} \mathbf{if}\;re \leq -4.6:\\ \;\;\;\;re \cdot \left(im \cdot \left(im \cdot -0.5\right)\right)\\ \mathbf{elif}\;re \leq 210:\\ \;\;\;\;re + 1\\ \mathbf{elif}\;re \leq 5.8 \cdot 10^{+145}:\\ \;\;\;\;\left(im \cdot im\right) \cdot \left(\left(re \cdot re\right) \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 11
Accuracy45.2%
Cost972
\[\begin{array}{l} \mathbf{if}\;re \leq -9500000:\\ \;\;\;\;re \cdot \left(im \cdot \left(im \cdot -0.5\right)\right)\\ \mathbf{elif}\;re \leq 210:\\ \;\;\;\;0.5 \cdot \left(re \cdot re\right) + \left(re + 1\right)\\ \mathbf{elif}\;re \leq 4.7 \cdot 10^{+145}:\\ \;\;\;\;\left(im \cdot im\right) \cdot \left(\left(re \cdot re\right) \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 12
Accuracy41.9%
Cost844
\[\begin{array}{l} t_0 := -0.5 \cdot \left(im \cdot \left(re \cdot im\right)\right)\\ \mathbf{if}\;re \leq -7.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;re \leq 210:\\ \;\;\;\;re + 1\\ \mathbf{elif}\;re \leq 5.5 \cdot 10^{+145}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 13
Accuracy44.8%
Cost844
\[\begin{array}{l} \mathbf{if}\;re \leq -3.8:\\ \;\;\;\;re \cdot \left(im \cdot \left(im \cdot -0.5\right)\right)\\ \mathbf{elif}\;re \leq 210:\\ \;\;\;\;re + 1\\ \mathbf{elif}\;re \leq 1.05 \cdot 10^{+144}:\\ \;\;\;\;-0.5 \cdot \left(im \cdot \left(re \cdot im\right)\right)\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 14
Accuracy37.1%
Cost452
\[\begin{array}{l} \mathbf{if}\;re \leq 215:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 15
Accuracy28.6%
Cost192
\[re + 1 \]
Alternative 16
Accuracy28.2%
Cost64
\[1 \]

Reproduce?

herbie shell --seed 2023178 
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))