Average Error: 0.0 → 0.0
Time: 23.9s
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 r16593 = 0.5;
        double r16594 = re;
        double r16595 = sin(r16594);
        double r16596 = r16593 * r16595;
        double r16597 = 0.0;
        double r16598 = im;
        double r16599 = r16597 - r16598;
        double r16600 = exp(r16599);
        double r16601 = exp(r16598);
        double r16602 = r16600 + r16601;
        double r16603 = r16596 * r16602;
        return r16603;
}
↓
double f(double re, double im) {
        double r16604 = 0.5;
        double r16605 = re;
        double r16606 = sin(r16605);
        double r16607 = r16604 * r16606;
        double r16608 = 0.0;
        double r16609 = im;
        double r16610 = r16608 - r16609;
        double r16611 = exp(r16610);
        double r16612 = exp(r16609);
        double r16613 = r16611 + r16612;
        double r16614 = r16607 * r16613;
        return r16614;
}

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 2019306 +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))))