Average Error: 0.0 → 0.0
Time: 25.3s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \frac{\sin re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \frac{\sin re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r14568 = 0.5;
        double r14569 = re;
        double r14570 = sin(r14569);
        double r14571 = r14568 * r14570;
        double r14572 = 0.0;
        double r14573 = im;
        double r14574 = r14572 - r14573;
        double r14575 = exp(r14574);
        double r14576 = exp(r14573);
        double r14577 = r14575 + r14576;
        double r14578 = r14571 * r14577;
        return r14578;
}
↓
double f(double re, double im) {
        double r14579 = 0.5;
        double r14580 = re;
        double r14581 = sin(r14580);
        double r14582 = im;
        double r14583 = exp(r14582);
        double r14584 = r14581 / r14583;
        double r14585 = r14579 * r14584;
        double r14586 = r14579 * r14581;
        double r14587 = r14586 * r14583;
        double r14588 = r14585 + r14587;
        return r14588;
}

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. Taylor expanded around inf 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 +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))))