Average Error: 0.0 → 0.0
Time: 24.6s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \frac{\sin re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \frac{\sin re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r14579 = 0.5;
        double r14580 = re;
        double r14581 = sin(r14580);
        double r14582 = r14579 * r14581;
        double r14583 = 0.0;
        double r14584 = im;
        double r14585 = r14583 - r14584;
        double r14586 = exp(r14585);
        double r14587 = exp(r14584);
        double r14588 = r14586 + r14587;
        double r14589 = r14582 * r14588;
        return r14589;
}
↓
double f(double re, double im) {
        double r14590 = 0.5;
        double r14591 = re;
        double r14592 = sin(r14591);
        double r14593 = im;
        double r14594 = exp(r14593);
        double r14595 = r14592 / r14594;
        double r14596 = r14590 * r14595;
        double r14597 = r14590 * r14592;
        double r14598 = r14597 * r14594;
        double r14599 = r14596 + r14598;
        return r14599;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Taylor expanded around inf 0.0

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

  5. Simplified0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{\sin re}{e^{im}}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))