Average Error: 0.0 → 0.0
Time: 16.2s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[e^{\log \left(\frac{1}{e^{im}} + e^{im}\right)} \cdot \left(0.5 \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
e^{\log \left(\frac{1}{e^{im}} + e^{im}\right)} \cdot \left(0.5 \cdot \cos re\right)
double f(double re, double im) {
        double r1698188 = 0.5;
        double r1698189 = re;
        double r1698190 = cos(r1698189);
        double r1698191 = r1698188 * r1698190;
        double r1698192 = im;
        double r1698193 = -r1698192;
        double r1698194 = exp(r1698193);
        double r1698195 = exp(r1698192);
        double r1698196 = r1698194 + r1698195;
        double r1698197 = r1698191 * r1698196;
        return r1698197;
}
↓
double f(double re, double im) {
        double r1698198 = 1.0;
        double r1698199 = im;
        double r1698200 = exp(r1698199);
        double r1698201 = r1698198 / r1698200;
        double r1698202 = r1698201 + r1698200;
        double r1698203 = log(r1698202);
        double r1698204 = exp(r1698203);
        double r1698205 = 0.5;
        double r1698206 = re;
        double r1698207 = cos(r1698206);
        double r1698208 = r1698205 * r1698207;
        double r1698209 = r1698204 * r1698208;
        return r1698209;
}

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

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied add-exp-log0.0

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \color{blue}{e^{\log \left(e^{-im} + e^{im}\right)}}\]

  4. Simplified0.0

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot e^{\color{blue}{\log \left(\frac{1}{e^{im}} + e^{im}\right)}}\]

  5. Final simplification0.0

    \[\leadsto e^{\log \left(\frac{1}{e^{im}} + e^{im}\right)} \cdot \left(0.5 \cdot \cos re\right)\]

Reproduce

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