Average Error: 0.0 → 0.1
Time: 3.4s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[\sqrt[3]{{\left(e^{re}\right)}^{2}} \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)\]
e^{re} \cdot \sin im
↓
\sqrt[3]{{\left(e^{re}\right)}^{2}} \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)
double f(double re, double im) {
        double r39013 = re;
        double r39014 = exp(r39013);
        double r39015 = im;
        double r39016 = sin(r39015);
        double r39017 = r39014 * r39016;
        return r39017;
}
↓
double f(double re, double im) {
        double r39018 = re;
        double r39019 = exp(r39018);
        double r39020 = 2.0;
        double r39021 = pow(r39019, r39020);
        double r39022 = cbrt(r39021);
        double r39023 = cbrt(r39019);
        double r39024 = im;
        double r39025 = sin(r39024);
        double r39026 = r39023 * r39025;
        double r39027 = r39022 * r39026;
        return r39027;
}

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-cube-cbrt0.0

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{e^{re}} \cdot \sqrt[3]{e^{re}}\right) \cdot \sqrt[3]{e^{re}}\right)} \cdot \sin im\]

  4. Applied associate-*l*0.0

    \[\leadsto \color{blue}{\left(\sqrt[3]{e^{re}} \cdot \sqrt[3]{e^{re}}\right) \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)}\]
  5. Using strategy rm

  6. Applied cbrt-unprod0.1

    \[\leadsto \color{blue}{\sqrt[3]{e^{re} \cdot e^{re}}} \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)\]

  7. Simplified0.1

    \[\leadsto \sqrt[3]{\color{blue}{{\left(e^{re}\right)}^{2}}} \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)\]

  8. Final simplification0.1

    \[\leadsto \sqrt[3]{{\left(e^{re}\right)}^{2}} \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))