Average Error: 0.0 → 0.0
Time: 2.9s
Precision: binary64
Cost: 12992
\[e^{re} \cdot \sin im\]
↓
\[e^{re} \cdot \sin im\]
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);
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.5
Cost13825
\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(re + \left(1 + 0.5 \cdot \left(re \cdot re\right)\right)\right)\\ \end{array}\]
Alternative 2
Error0.7
Cost13441
\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 9.434857144439931 \cdot 10^{-60}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\sin im \cdot \left(re + 1\right)\\ \end{array}\]
Alternative 3
Error1.1
Cost13185
\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 8.806710028269764 \cdot 10^{-60}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\sin im\\ \end{array}\]
Alternative 4
Error38.7
Cost6464
\[e^{re}\]
Alternative 5
Error38.7
Cost385
\[\begin{array}{l} \mathbf{if}\;re \leq -8.147025997709781 \cdot 10^{-07}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 6
Error60.1
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))