Average Error: 0.0 → 0.0
Time: 7.7s
Precision: binary64
\[e^{re} \cdot \cos im \]
↓
\[\cos im \cdot e^{re} \]
e^{re} \cdot \cos im
↓
\cos im \cdot e^{re}

(FPCore (re im) :precision binary64 (* (exp re) (cos im)))
↓
(FPCore (re im) :precision binary64 (* (cos im) (exp re)))
double code(double re, double im) {
	return exp(re) * cos(im);
}
↓
double code(double re, double im) {
	return cos(im) * exp(re);
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Applied *-commutative_binary640.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021340 
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))