Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
double f(double re, double im) {
        double r61714 = 0.5;
        double r61715 = re;
        double r61716 = sin(r61715);
        double r61717 = r61714 * r61716;
        double r61718 = 0.0;
        double r61719 = im;
        double r61720 = r61718 - r61719;
        double r61721 = exp(r61720);
        double r61722 = exp(r61719);
        double r61723 = r61721 + r61722;
        double r61724 = r61717 * r61723;
        return r61724;
}
↓
double f(double re, double im) {
        double r61725 = 0.5;
        double r61726 = re;
        double r61727 = sin(r61726);
        double r61728 = r61725 * r61727;
        double r61729 = 0.0;
        double r61730 = im;
        double r61731 = r61729 - r61730;
        double r61732 = exp(r61731);
        double r61733 = exp(r61730);
        double r61734 = r61732 + r61733;
        double r61735 = r61728 * r61734;
        return r61735;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]

  2. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]

Reproduce

herbie shell --seed 2019353 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))