Average Error: 0.0 → 0.0
Time: 28.4s
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 r19447 = 0.5;
        double r19448 = re;
        double r19449 = sin(r19448);
        double r19450 = r19447 * r19449;
        double r19451 = 0.0;
        double r19452 = im;
        double r19453 = r19451 - r19452;
        double r19454 = exp(r19453);
        double r19455 = exp(r19452);
        double r19456 = r19454 + r19455;
        double r19457 = r19450 * r19456;
        return r19457;
}
↓
double f(double re, double im) {
        double r19458 = 0.5;
        double r19459 = re;
        double r19460 = sin(r19459);
        double r19461 = im;
        double r19462 = exp(r19461);
        double r19463 = r19460 / r19462;
        double r19464 = r19458 * r19463;
        double r19465 = r19458 * r19460;
        double r19466 = r19465 * r19462;
        double r19467 = r19464 + r19466;
        return r19467;
}

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 2019304 +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))))