Average Error: 0.0 → 0.0
Time: 5.2s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[\sqrt{e^{re}} \cdot \left(\sin im \cdot \sqrt{e^{re}}\right)\]
e^{re} \cdot \sin im
↓
\sqrt{e^{re}} \cdot \left(\sin im \cdot \sqrt{e^{re}}\right)
double f(double re, double im) {
        double r1628702 = re;
        double r1628703 = exp(r1628702);
        double r1628704 = im;
        double r1628705 = sin(r1628704);
        double r1628706 = r1628703 * r1628705;
        return r1628706;
}
↓
double f(double re, double im) {
        double r1628707 = re;
        double r1628708 = exp(r1628707);
        double r1628709 = sqrt(r1628708);
        double r1628710 = im;
        double r1628711 = sin(r1628710);
        double r1628712 = r1628711 * r1628709;
        double r1628713 = r1628709 * r1628712;
        return r1628713;
}

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

    \[e^{re} \cdot \sin im\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*l*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))