Average Error: 0.0 → 0.0
Time: 12.3s
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 r103413 = 0.5;
        double r103414 = re;
        double r103415 = cos(r103414);
        double r103416 = r103413 * r103415;
        double r103417 = im;
        double r103418 = -r103417;
        double r103419 = exp(r103418);
        double r103420 = exp(r103417);
        double r103421 = r103419 + r103420;
        double r103422 = r103416 * r103421;
        return r103422;
}
↓
double f(double re, double im) {
        double r103423 = 0.5;
        double r103424 = re;
        double r103425 = cos(r103424);
        double r103426 = r103423 * r103425;
        double r103427 = im;
        double r103428 = -r103427;
        double r103429 = exp(r103428);
        double r103430 = exp(r103427);
        double r103431 = r103429 + r103430;
        double r103432 = r103426 * r103431;
        return r103432;
}

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 2020042 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))