Average Error: 0.0 → 0.0
Time: 22.6s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{\cos re \cdot 0.5}{e^{im}} + \left(\cos re \cdot 0.5\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{\cos re \cdot 0.5}{e^{im}} + \left(\cos re \cdot 0.5\right) \cdot e^{im}
double f(double re, double im) {
        double r2035449 = 0.5;
        double r2035450 = re;
        double r2035451 = cos(r2035450);
        double r2035452 = r2035449 * r2035451;
        double r2035453 = im;
        double r2035454 = -r2035453;
        double r2035455 = exp(r2035454);
        double r2035456 = exp(r2035453);
        double r2035457 = r2035455 + r2035456;
        double r2035458 = r2035452 * r2035457;
        return r2035458;
}
↓
double f(double re, double im) {
        double r2035459 = re;
        double r2035460 = cos(r2035459);
        double r2035461 = 0.5;
        double r2035462 = r2035460 * r2035461;
        double r2035463 = im;
        double r2035464 = exp(r2035463);
        double r2035465 = r2035462 / r2035464;
        double r2035466 = r2035462 * r2035464;
        double r2035467 = r2035465 + r2035466;
        return r2035467;
}

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

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

  4. Applied fma-udef0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))