Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)\]
e^{re} \cdot \cos im
↓
\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)
double f(double re, double im) {
        double r50324 = re;
        double r50325 = exp(r50324);
        double r50326 = im;
        double r50327 = cos(r50326);
        double r50328 = r50325 * r50327;
        return r50328;
}
↓
double f(double re, double im) {
        double r50329 = re;
        double r50330 = exp(r50329);
        double r50331 = sqrt(r50330);
        double r50332 = im;
        double r50333 = cos(r50332);
        double r50334 = r50331 * r50333;
        double r50335 = r50331 * r50334;
        return r50335;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))