Average Error: 0.0 → 0.0
Time: 2.9s
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 r97042 = re;
        double r97043 = exp(r97042);
        double r97044 = im;
        double r97045 = cos(r97044);
        double r97046 = r97043 * r97045;
        return r97046;
}
↓
double f(double re, double im) {
        double r97047 = re;
        double r97048 = exp(r97047);
        double r97049 = sqrt(r97048);
        double r97050 = im;
        double r97051 = cos(r97050);
        double r97052 = r97049 * r97051;
        double r97053 = r97049 * r97052;
        return r97053;
}

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 2020001 
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))