Average Error: 0.1 → 0.0
Time: 36.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\frac{\sin re \cdot 0.5}{e^{im}} + \left(\sin re \cdot 0.5\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\frac{\sin re \cdot 0.5}{e^{im}} + \left(\sin re \cdot 0.5\right) \cdot e^{im}
double f(double re, double im) {
        double r1697745 = 0.5;
        double r1697746 = re;
        double r1697747 = sin(r1697746);
        double r1697748 = r1697745 * r1697747;
        double r1697749 = 0.0;
        double r1697750 = im;
        double r1697751 = r1697749 - r1697750;
        double r1697752 = exp(r1697751);
        double r1697753 = exp(r1697750);
        double r1697754 = r1697752 + r1697753;
        double r1697755 = r1697748 * r1697754;
        return r1697755;
}
↓
double f(double re, double im) {
        double r1697756 = re;
        double r1697757 = sin(r1697756);
        double r1697758 = 0.5;
        double r1697759 = r1697757 * r1697758;
        double r1697760 = im;
        double r1697761 = exp(r1697760);
        double r1697762 = r1697759 / r1697761;
        double r1697763 = r1697759 * r1697761;
        double r1697764 = r1697762 + r1697763;
        return r1697764;
}

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 0.1

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019125 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))