Average Error: 0.0 → 0.0
Time: 13.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \frac{0.5}{e^{im}} + \left(\cos re \cdot e^{im}\right) \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \frac{0.5}{e^{im}} + \left(\cos re \cdot e^{im}\right) \cdot 0.5
double f(double re, double im) {
        double r34228 = 0.5;
        double r34229 = re;
        double r34230 = cos(r34229);
        double r34231 = r34228 * r34230;
        double r34232 = im;
        double r34233 = -r34232;
        double r34234 = exp(r34233);
        double r34235 = exp(r34232);
        double r34236 = r34234 + r34235;
        double r34237 = r34231 * r34236;
        return r34237;
}
↓
double f(double re, double im) {
        double r34238 = re;
        double r34239 = cos(r34238);
        double r34240 = 0.5;
        double r34241 = im;
        double r34242 = exp(r34241);
        double r34243 = r34240 / r34242;
        double r34244 = r34239 * r34243;
        double r34245 = r34239 * r34242;
        double r34246 = r34245 * r34240;
        double r34247 = r34244 + r34246;
        return r34247;
}

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. Simplified0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))