Average Error: 0.0 → 0.0
Time: 10.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)
double f(double re, double im) {
        double r740559 = 0.5;
        double r740560 = re;
        double r740561 = cos(r740560);
        double r740562 = r740559 * r740561;
        double r740563 = im;
        double r740564 = -r740563;
        double r740565 = exp(r740564);
        double r740566 = exp(r740563);
        double r740567 = r740565 + r740566;
        double r740568 = r740562 * r740567;
        return r740568;
}
↓
double f(double re, double im) {
        double r740569 = im;
        double r740570 = exp(r740569);
        double r740571 = -r740569;
        double r740572 = exp(r740571);
        double r740573 = r740570 + r740572;
        double r740574 = 0.5;
        double r740575 = re;
        double r740576 = cos(r740575);
        double r740577 = r740574 * r740576;
        double r740578 = r740573 * r740577;
        return r740578;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))