Average Error: 0.0 → 0.0
Time: 11.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r26588 = 0.5;
        double r26589 = re;
        double r26590 = cos(r26589);
        double r26591 = r26588 * r26590;
        double r26592 = im;
        double r26593 = -r26592;
        double r26594 = exp(r26593);
        double r26595 = exp(r26592);
        double r26596 = r26594 + r26595;
        double r26597 = r26591 * r26596;
        return r26597;
}
↓
double f(double re, double im) {
        double r26598 = 0.5;
        double r26599 = re;
        double r26600 = cos(r26599);
        double r26601 = r26598 * r26600;
        double r26602 = im;
        double r26603 = -r26602;
        double r26604 = exp(r26603);
        double r26605 = exp(r26602);
        double r26606 = r26604 + r26605;
        double r26607 = r26601 * r26606;
        return r26607;
}

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

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

Reproduce

herbie shell --seed 2019326 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))