math.exp on complex, imaginary part

?

Percentage Accurate: 100.0% → 100.0%
Time: 8.4s
Precision: binary64
Cost: 12992

?

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

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

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);
}

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

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

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

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]

e^{re} \cdot \sin im
↓
e^{re} \cdot \sin 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 12 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%

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

  2. Final simplification100.0%

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

Alternatives

Alternative 1
Accuracy100.0%
Cost12992
\[e^{re} \cdot \sin im \]
Alternative 2
Accuracy92.6%
Cost19657
\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0 \lor \neg \left(e^{re} \leq 1.00000000002\right):\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im\\ \end{array} \]
Alternative 3
Accuracy97.2%
Cost7757
\[\begin{array}{l} \mathbf{if}\;re \leq -0.0285 \lor \neg \left(re \leq 2.4 \cdot 10^{-11}\right) \land re \leq 10^{+103}:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(\left(re + 1\right) + \left(re \cdot re\right) \cdot \left(re \cdot 0.16666666666666666 + 0.5\right)\right)\\ \end{array} \]
Alternative 4
Accuracy95.7%
Cost7501
\[\begin{array}{l} \mathbf{if}\;re \leq -2.05 \lor \neg \left(re \leq 2.4 \cdot 10^{-11}\right) \land re \leq 6.8 \cdot 10^{+142}:\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(\left(re + 1\right) + re \cdot \left(re \cdot 0.5\right)\right)\\ \end{array} \]
Alternative 5
Accuracy95.6%
Cost7244
\[\begin{array}{l} t_0 := e^{re} \cdot im\\ \mathbf{if}\;re \leq -0.00046:\\ \;\;\;\;t_0\\ \mathbf{elif}\;re \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;\sin im \cdot \left(re + 1\right)\\ \mathbf{elif}\;re \leq 6.8 \cdot 10^{+142}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(re \cdot \left(re \cdot 0.5\right)\right)\\ \end{array} \]
Alternative 6
Accuracy93.1%
Cost6985
\[\begin{array}{l} \mathbf{if}\;re \leq -0.00084 \lor \neg \left(re \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;e^{re} \cdot im\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(re + 1\right)\\ \end{array} \]
Alternative 7
Accuracy61.7%
Cost6728
\[\begin{array}{l} \mathbf{if}\;re \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{im}{1 - re} \cdot \left(1 - re \cdot re\right)\\ \mathbf{elif}\;re \leq 1.65 \cdot 10^{+23}:\\ \;\;\;\;\sin im\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(im \cdot \left(re \cdot re\right)\right)\\ \end{array} \]
Alternative 8
Accuracy38.5%
Cost836
\[\begin{array}{l} \mathbf{if}\;re \leq 1.1 \cdot 10^{+23}:\\ \;\;\;\;\frac{im}{1 - re} \cdot \left(1 - re \cdot re\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(im \cdot \left(re \cdot re\right)\right)\\ \end{array} \]
Alternative 9
Accuracy37.5%
Cost580
\[\begin{array}{l} \mathbf{if}\;re \leq 1.1 \cdot 10^{+23}:\\ \;\;\;\;im\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(im \cdot \left(re \cdot re\right)\right)\\ \end{array} \]
Alternative 10
Accuracy30.0%
Cost324
\[\begin{array}{l} \mathbf{if}\;re \leq 1.1 \cdot 10^{+23}:\\ \;\;\;\;im\\ \mathbf{else}:\\ \;\;\;\;re \cdot im\\ \end{array} \]
Alternative 11
Accuracy30.0%
Cost320
\[im + re \cdot im \]
Alternative 12
Accuracy27.1%
Cost64
\[im \]

Reproduce?

herbie shell --seed 2023272 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))