Average Error: 0.0 → 0.0
Time: 10.8s
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 r48101 = re;
        double r48102 = exp(r48101);
        double r48103 = im;
        double r48104 = sin(r48103);
        double r48105 = r48102 * r48104;
        return r48105;
}
↓
double f(double re, double im) {
        double r48106 = re;
        double r48107 = exp(r48106);
        double r48108 = sqrt(r48107);
        double r48109 = im;
        double r48110 = sin(r48109);
        double r48111 = r48108 * r48110;
        double r48112 = r48108 * r48111;
        return r48112;
}

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 2020042 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))