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 r103412 = 0.5;
        double r103413 = re;
        double r103414 = cos(r103413);
        double r103415 = r103412 * r103414;
        double r103416 = im;
        double r103417 = -r103416;
        double r103418 = exp(r103417);
        double r103419 = exp(r103416);
        double r103420 = r103418 + r103419;
        double r103421 = r103415 * r103420;
        return r103421;
}
↓
double f(double re, double im) {
        double r103422 = 0.5;
        double r103423 = re;
        double r103424 = cos(r103423);
        double r103425 = r103422 * r103424;
        double r103426 = im;
        double r103427 = -r103426;
        double r103428 = exp(r103427);
        double r103429 = exp(r103426);
        double r103430 = r103428 + r103429;
        double r103431 = r103425 * r103430;
        return r103431;
}

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))))