Average Error: 0.0 → 0.0
Time: 14.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
\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 r72532 = 0.5;
        double r72533 = re;
        double r72534 = sin(r72533);
        double r72535 = r72532 * r72534;
        double r72536 = 0.0;
        double r72537 = im;
        double r72538 = r72536 - r72537;
        double r72539 = exp(r72538);
        double r72540 = exp(r72537);
        double r72541 = r72539 + r72540;
        double r72542 = r72535 * r72541;
        return r72542;
}
↓
double f(double re, double im) {
        double r72543 = 0.5;
        double r72544 = re;
        double r72545 = sin(r72544);
        double r72546 = r72543 * r72545;
        double r72547 = 0.0;
        double r72548 = im;
        double r72549 = r72547 - r72548;
        double r72550 = exp(r72549);
        double r72551 = exp(r72548);
        double r72552 = r72550 + r72551;
        double r72553 = r72546 * r72552;
        return r72553;
}

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 2019351 +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))))