Average Error: 0.0 → 0.0
Time: 15.3s
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 r16523 = 0.5;
        double r16524 = re;
        double r16525 = sin(r16524);
        double r16526 = r16523 * r16525;
        double r16527 = 0.0;
        double r16528 = im;
        double r16529 = r16527 - r16528;
        double r16530 = exp(r16529);
        double r16531 = exp(r16528);
        double r16532 = r16530 + r16531;
        double r16533 = r16526 * r16532;
        return r16533;
}
↓
double f(double re, double im) {
        double r16534 = 0.5;
        double r16535 = re;
        double r16536 = sin(r16535);
        double r16537 = r16534 * r16536;
        double r16538 = 0.0;
        double r16539 = im;
        double r16540 = r16538 - r16539;
        double r16541 = exp(r16540);
        double r16542 = exp(r16539);
        double r16543 = r16541 + r16542;
        double r16544 = r16537 * r16543;
        return r16544;
}

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

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

Reproduce

herbie shell --seed 2019298 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))