Average Error: 0.0 → 0.0
Time: 18.8s
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 r35409 = re;
        double r35410 = exp(r35409);
        double r35411 = im;
        double r35412 = cos(r35411);
        double r35413 = r35410 * r35412;
        return r35413;
}
↓
double f(double re, double im) {
        double r35414 = re;
        double r35415 = exp(r35414);
        double r35416 = sqrt(r35415);
        double r35417 = im;
        double r35418 = cos(r35417);
        double r35419 = r35416 * r35418;
        double r35420 = r35416 * r35419;
        return r35420;
}

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 2019326 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))