Average Error: 0.0 → 0.0
Time: 20.3s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)\]
e^{re} \cdot \cos im
↓
\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)
double f(double re, double im) {
        double r3252755 = re;
        double r3252756 = exp(r3252755);
        double r3252757 = im;
        double r3252758 = cos(r3252757);
        double r3252759 = r3252756 * r3252758;
        return r3252759;
}
↓
double f(double re, double im) {
        double r3252760 = re;
        double r3252761 = exp(r3252760);
        double r3252762 = sqrt(r3252761);
        double r3252763 = im;
        double r3252764 = cos(r3252763);
        double r3252765 = r3252762 * r3252764;
        double r3252766 = r3252762 * r3252765;
        return r3252766;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*l*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))