math.exp on complex, real part

?

Percentage Accurate: 100.0% → 100.0%
Time: 13.1s
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?

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.

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
Accuracy98.3%
Cost8268
\[\begin{array}{l} t_0 := 0.5 + re \cdot -0.16666666666666666\\ \mathbf{if}\;re \leq -0.000205:\\ \;\;\;\;e^{re}\\ \mathbf{elif}\;re \leq 0.22:\\ \;\;\;\;\cos im \cdot \left(\left(re + 1\right) + \frac{re \cdot \left(re \cdot 0.25\right)}{t_0}\right)\\ \mathbf{elif}\;re \leq 2.8 \cdot 10^{+77}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(\left(re + 1\right) + \frac{\left(re \cdot re\right) \cdot \left(0.25 - \left(re \cdot re\right) \cdot 0.027777777777777776\right)}{t_0}\right)\\ \end{array} \]
Alternative 2
Accuracy97.8%
Cost7757
\[\begin{array}{l} \mathbf{if}\;re \leq -0.0031 \lor \neg \left(re \leq 0.36\right) \land re \leq 1.05 \cdot 10^{+103}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(\left(re + 1\right) + \left(re \cdot re\right) \cdot \left(0.5 + re \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
Alternative 3
Accuracy97.7%
Cost7756
\[\begin{array}{l} \mathbf{if}\;re \leq -0.000205:\\ \;\;\;\;e^{re}\\ \mathbf{elif}\;re \leq 0.22:\\ \;\;\;\;\cos im \cdot \left(\left(re + 1\right) + \frac{re \cdot \left(re \cdot 0.25\right)}{0.5 + re \cdot -0.16666666666666666}\right)\\ \mathbf{elif}\;re \leq 1.05 \cdot 10^{+103}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(\left(re + 1\right) + \left(re \cdot re\right) \cdot \left(0.5 + re \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
Alternative 4
Accuracy96.7%
Cost7368
\[\begin{array}{l} \mathbf{if}\;re \leq -0.000205:\\ \;\;\;\;e^{re}\\ \mathbf{elif}\;re \leq 0.27:\\ \;\;\;\;\cos im \cdot \left(\left(re + 1\right) + re \cdot \left(re \cdot 0.5\right)\right)\\ \mathbf{elif}\;re \leq 2.3 \cdot 10^{+154}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\left(re \cdot \cos im\right) \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 5
Accuracy96.6%
Cost7244
\[\begin{array}{l} \mathbf{if}\;re \leq -0.0002:\\ \;\;\;\;e^{re}\\ \mathbf{elif}\;re \leq 0.22:\\ \;\;\;\;\cos im \cdot \left(re + 1\right)\\ \mathbf{elif}\;re \leq 1.9 \cdot 10^{+154}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\left(re \cdot \cos im\right) \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 6
Accuracy93.3%
Cost6984
\[\begin{array}{l} \mathbf{if}\;re \leq -0.000205:\\ \;\;\;\;e^{re}\\ \mathbf{elif}\;re \leq 0.22:\\ \;\;\;\;\cos im \cdot \left(re + 1\right)\\ \mathbf{elif}\;re \leq 8.6 \cdot 10^{+219}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\left(re \cdot re\right) \cdot \left(0.5 + \left(im \cdot im\right) \cdot -0.25\right)\\ \end{array} \]
Alternative 7
Accuracy92.8%
Cost6860
\[\begin{array}{l} \mathbf{if}\;re \leq -2.15 \cdot 10^{-7}:\\ \;\;\;\;e^{re}\\ \mathbf{elif}\;re \leq 0.22:\\ \;\;\;\;\cos im\\ \mathbf{elif}\;re \leq 10^{+220}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\left(re \cdot re\right) \cdot \left(0.5 + \left(im \cdot im\right) \cdot -0.25\right)\\ \end{array} \]
Alternative 8
Accuracy64.3%
Cost6728
\[\begin{array}{l} \mathbf{if}\;re \leq -530:\\ \;\;\;\;\left(im \cdot im\right) \cdot \left(re \cdot \left(re \cdot -0.25\right)\right)\\ \mathbf{elif}\;re \leq 500:\\ \;\;\;\;\cos im\\ \mathbf{else}:\\ \;\;\;\;\left(re \cdot re\right) \cdot \left(0.5 + \left(im \cdot im\right) \cdot -0.25\right)\\ \end{array} \]
Alternative 9
Accuracy42.4%
Cost972
\[\begin{array}{l} t_0 := \left(im \cdot im\right) \cdot \left(re \cdot \left(re \cdot -0.25\right)\right)\\ \mathbf{if}\;re \leq -170:\\ \;\;\;\;t_0\\ \mathbf{elif}\;re \leq 3.2 \cdot 10^{-12}:\\ \;\;\;\;re + 1\\ \mathbf{elif}\;re \leq 1.65 \cdot 10^{+140}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 10
Accuracy42.8%
Cost968
\[\begin{array}{l} \mathbf{if}\;re \leq -125:\\ \;\;\;\;\left(im \cdot im\right) \cdot \left(re \cdot \left(re \cdot -0.25\right)\right)\\ \mathbf{elif}\;re \leq 3.2 \cdot 10^{-12}:\\ \;\;\;\;re + 1\\ \mathbf{else}:\\ \;\;\;\;\left(re \cdot re\right) \cdot \left(0.5 + \left(im \cdot im\right) \cdot -0.25\right)\\ \end{array} \]
Alternative 11
Accuracy39.3%
Cost840
\[\begin{array}{l} \mathbf{if}\;re \leq 3.2 \cdot 10^{-12}:\\ \;\;\;\;re + 1\\ \mathbf{elif}\;re \leq 1.7 \cdot 10^{+140}:\\ \;\;\;\;re \cdot \left(1 + \left(im \cdot im\right) \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 12
Accuracy38.9%
Cost712
\[\begin{array}{l} \mathbf{if}\;re \leq 1.55 \cdot 10^{-34}:\\ \;\;\;\;re + 1\\ \mathbf{elif}\;re \leq 1.65 \cdot 10^{+140}:\\ \;\;\;\;1 + \left(im \cdot im\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 13
Accuracy37.9%
Cost452
\[\begin{array}{l} \mathbf{if}\;re \leq 3.2 \cdot 10^{-12}:\\ \;\;\;\;re + 1\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(re \cdot 0.5\right)\\ \end{array} \]
Alternative 14
Accuracy29.2%
Cost192
\[re + 1 \]

Error

Reproduce?

herbie shell --seed 2023160 
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))