Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[\sqrt{e^{re}} \cdot \left(e^{\frac{1}{2} \cdot re} \cdot \sin im\right)\]
e^{re} \cdot \sin im
↓
\sqrt{e^{re}} \cdot \left(e^{\frac{1}{2} \cdot re} \cdot \sin im\right)
double f(double re, double im) {
        double r49592 = re;
        double r49593 = exp(r49592);
        double r49594 = im;
        double r49595 = sin(r49594);
        double r49596 = r49593 * r49595;
        return r49596;
}
↓
double f(double re, double im) {
        double r49597 = re;
        double r49598 = exp(r49597);
        double r49599 = sqrt(r49598);
        double r49600 = 0.5;
        double r49601 = r49600 * r49597;
        double r49602 = exp(r49601);
        double r49603 = im;
        double r49604 = sin(r49603);
        double r49605 = r49602 * r49604;
        double r49606 = r49599 * r49605;
        return r49606;
}

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. Using strategy rm

  6. Applied add-exp-log0.0

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

  7. Simplified0.0

    \[\leadsto \sqrt{e^{re}} \cdot \left(e^{\color{blue}{\frac{1}{2} \cdot re}} \cdot \sin im\right)\]

  8. Final simplification0.0

    \[\leadsto \sqrt{e^{re}} \cdot \left(e^{\frac{1}{2} \cdot re} \cdot \sin im\right)\]

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))