Average Error: 0.0 → 0.0
Time: 12.9s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\left(\sqrt{e^{re}} \cdot \cos im\right) \cdot \left(\left|\sqrt[3]{e^{re}}\right| \cdot \sqrt{\sqrt[3]{e^{re}}}\right)\]
e^{re} \cdot \cos im
↓
\left(\sqrt{e^{re}} \cdot \cos im\right) \cdot \left(\left|\sqrt[3]{e^{re}}\right| \cdot \sqrt{\sqrt[3]{e^{re}}}\right)
double f(double re, double im) {
        double r1717015 = re;
        double r1717016 = exp(r1717015);
        double r1717017 = im;
        double r1717018 = cos(r1717017);
        double r1717019 = r1717016 * r1717018;
        return r1717019;
}
↓
double f(double re, double im) {
        double r1717020 = re;
        double r1717021 = exp(r1717020);
        double r1717022 = sqrt(r1717021);
        double r1717023 = im;
        double r1717024 = cos(r1717023);
        double r1717025 = r1717022 * r1717024;
        double r1717026 = cbrt(r1717021);
        double r1717027 = fabs(r1717026);
        double r1717028 = sqrt(r1717026);
        double r1717029 = r1717027 * r1717028;
        double r1717030 = r1717025 * r1717029;
        return r1717030;
}

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

    \[e^{re} \cdot \cos im\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*l*0.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Applied sqrt-prod0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))