Average Error: 0.0 → 0.0
Time: 2.6s
Precision: binary64
Cost: 12992
\[e^{re} \cdot \cos im\]
↓
\[e^{re} \cdot \cos im\]
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);
}

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
Error0.6
Cost13825
\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 9.434857144439931 \cdot 10^{-60}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(re + \left(1 + 0.5 \cdot \left(re \cdot re\right)\right)\right)\\ \end{array}\]
Alternative 2
Error0.8
Cost13441
\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 9.434857144439931 \cdot 10^{-60}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(re + 1\right)\\ \end{array}\]
Alternative 3
Error1.1
Cost13185
\[\begin{array}{l} \mathbf{if}\;e^{re} \leq 0.9880301012453675:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im\\ \end{array}\]
Alternative 4
Error19.0
Cost6464
\[e^{re}\]
Alternative 5
Error19.7
Cost385
\[\begin{array}{l} \mathbf{if}\;re \leq -328.042577655251:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 6
Error40.8
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

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