Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r23643 = 0.5;
        double r23644 = re;
        double r23645 = sin(r23644);
        double r23646 = r23643 * r23645;
        double r23647 = 0.0;
        double r23648 = im;
        double r23649 = r23647 - r23648;
        double r23650 = exp(r23649);
        double r23651 = exp(r23648);
        double r23652 = r23650 + r23651;
        double r23653 = r23646 * r23652;
        return r23653;
}
↓
double f(double re, double im) {
        double r23654 = 0.5;
        double r23655 = re;
        double r23656 = sin(r23655);
        double r23657 = r23654 * r23656;
        double r23658 = 0.0;
        double r23659 = im;
        double r23660 = r23658 - r23659;
        double r23661 = exp(r23660);
        double r23662 = r23657 * r23661;
        double r23663 = exp(r23659);
        double r23664 = r23657 * r23663;
        double r23665 = r23662 + r23664;
        return r23665;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019347 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))