Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{\left(0.5 \cdot \sin re\right) \cdot e^{0.0}}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{\left(0.5 \cdot \sin re\right) \cdot e^{0.0}}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r29615 = 0.5;
        double r29616 = re;
        double r29617 = sin(r29616);
        double r29618 = r29615 * r29617;
        double r29619 = 0.0;
        double r29620 = im;
        double r29621 = r29619 - r29620;
        double r29622 = exp(r29621);
        double r29623 = exp(r29620);
        double r29624 = r29622 + r29623;
        double r29625 = r29618 * r29624;
        return r29625;
}
↓
double f(double re, double im) {
        double r29626 = 0.5;
        double r29627 = re;
        double r29628 = sin(r29627);
        double r29629 = r29626 * r29628;
        double r29630 = 0.0;
        double r29631 = exp(r29630);
        double r29632 = r29629 * r29631;
        double r29633 = im;
        double r29634 = exp(r29633);
        double r29635 = r29632 / r29634;
        double r29636 = r29629 * r29634;
        double r29637 = r29635 + r29636;
        return r29637;
}

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. Using strategy rm

  5. Applied exp-diff0.0

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

  6. Applied associate-*r/0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))