Average Error: 0.0 → 0.0
Time: 12.3s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\left(\cos im \cdot e^{\log \left(\sqrt{e^{re}}\right)}\right) \cdot \sqrt{e^{re}}\]
e^{re} \cdot \cos im
↓
\left(\cos im \cdot e^{\log \left(\sqrt{e^{re}}\right)}\right) \cdot \sqrt{e^{re}}
double f(double re, double im) {
        double r1587421 = re;
        double r1587422 = exp(r1587421);
        double r1587423 = im;
        double r1587424 = cos(r1587423);
        double r1587425 = r1587422 * r1587424;
        return r1587425;
}
↓
double f(double re, double im) {
        double r1587426 = im;
        double r1587427 = cos(r1587426);
        double r1587428 = re;
        double r1587429 = exp(r1587428);
        double r1587430 = sqrt(r1587429);
        double r1587431 = log(r1587430);
        double r1587432 = exp(r1587431);
        double r1587433 = r1587427 * r1587432;
        double r1587434 = r1587433 * r1587430;
        return r1587434;
}

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-exp-log0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019125 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))