Average Error: 0.0 → 0.0
Time: 21.6s
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 r3100451 = re;
        double r3100452 = exp(r3100451);
        double r3100453 = im;
        double r3100454 = sin(r3100453);
        double r3100455 = r3100452 * r3100454;
        return r3100455;
}
↓
double f(double re, double im) {
        double r3100456 = re;
        double r3100457 = exp(r3100456);
        double r3100458 = sqrt(r3100457);
        double r3100459 = im;
        double r3100460 = sin(r3100459);
        double r3100461 = r3100458 * r3100460;
        double r3100462 = r3100458 * r3100461;
        return r3100462;
}

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 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))