Average Error: 0.0 → 0.0
Time: 4.1s
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 r20573 = 0.5;
        double r20574 = re;
        double r20575 = sin(r20574);
        double r20576 = r20573 * r20575;
        double r20577 = 0.0;
        double r20578 = im;
        double r20579 = r20577 - r20578;
        double r20580 = exp(r20579);
        double r20581 = exp(r20578);
        double r20582 = r20580 + r20581;
        double r20583 = r20576 * r20582;
        return r20583;
}
↓
double f(double re, double im) {
        double r20584 = 0.5;
        double r20585 = re;
        double r20586 = sin(r20585);
        double r20587 = r20584 * r20586;
        double r20588 = 0.0;
        double r20589 = im;
        double r20590 = r20588 - r20589;
        double r20591 = exp(r20590);
        double r20592 = exp(r20589);
        double r20593 = r20591 + r20592;
        double r20594 = r20587 * r20593;
        return r20594;
}

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 2020003 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))