Average Error: 0.0 → 0.0
Time: 7.5s
Precision: binary64
\[e^{re} \cdot \cos im \]
↓
\[\begin{array}{l} t_0 := \sqrt{e^{re}}\\ t_0 \cdot \left(t_0 \cdot \cos im\right) \end{array} \]
e^{re} \cdot \cos im
↓
\begin{array}{l}
t_0 := \sqrt{e^{re}}\\
t_0 \cdot \left(t_0 \cdot \cos im\right)
\end{array}

(FPCore (re im) :precision binary64 (* (exp re) (cos im)))
↓
(FPCore (re im)
 :precision binary64
 (let* ((t_0 (sqrt (exp re)))) (* t_0 (* t_0 (cos im)))))
double code(double re, double im) {
	return exp(re) * cos(im);
}
↓
double code(double re, double im) {
	double t_0 = sqrt(exp(re));
	return t_0 * (t_0 * 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

Derivation

  1. Initial program 0.0

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

  2. Applied add-sqr-sqrt_binary640.0

    \[\leadsto \color{blue}{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right)} \cdot \cos im \]

  3. Applied associate-*l*_binary640.0

    \[\leadsto \color{blue}{\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)} \]

  4. Final simplification0.0

    \[\leadsto \sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right) \]

Reproduce

herbie shell --seed 2021357 
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))