Average Error: 0.0 → 0.0
Time: 19.7s
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 r23561 = 0.5;
        double r23562 = re;
        double r23563 = sin(r23562);
        double r23564 = r23561 * r23563;
        double r23565 = 0.0;
        double r23566 = im;
        double r23567 = r23565 - r23566;
        double r23568 = exp(r23567);
        double r23569 = exp(r23566);
        double r23570 = r23568 + r23569;
        double r23571 = r23564 * r23570;
        return r23571;
}
↓
double f(double re, double im) {
        double r23572 = 0.5;
        double r23573 = re;
        double r23574 = sin(r23573);
        double r23575 = r23572 * r23574;
        double r23576 = 0.0;
        double r23577 = im;
        double r23578 = r23576 - r23577;
        double r23579 = exp(r23578);
        double r23580 = exp(r23577);
        double r23581 = r23579 + r23580;
        double r23582 = r23575 * r23581;
        return r23582;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))