Average Error: 0.0 → 0.0
Time: 23.4s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)\]
e^{re} \cdot \sin im
↓
\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)
double f(double re, double im) {
        double r6869478 = re;
        double r6869479 = exp(r6869478);
        double r6869480 = im;
        double r6869481 = sin(r6869480);
        double r6869482 = r6869479 * r6869481;
        return r6869482;
}
↓
double f(double re, double im) {
        double r6869483 = re;
        double r6869484 = exp(r6869483);
        double r6869485 = sqrt(r6869484);
        double r6869486 = im;
        double r6869487 = sin(r6869486);
        double r6869488 = r6869485 * r6869487;
        double r6869489 = r6869485 * r6869488;
        return r6869489;
}

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

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

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))