Average Error: 0.0 → 0.0
Time: 24.1s
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 r33380 = 0.5;
        double r33381 = re;
        double r33382 = sin(r33381);
        double r33383 = r33380 * r33382;
        double r33384 = 0.0;
        double r33385 = im;
        double r33386 = r33384 - r33385;
        double r33387 = exp(r33386);
        double r33388 = exp(r33385);
        double r33389 = r33387 + r33388;
        double r33390 = r33383 * r33389;
        return r33390;
}
↓
double f(double re, double im) {
        double r33391 = 0.5;
        double r33392 = re;
        double r33393 = sin(r33392);
        double r33394 = r33391 * r33393;
        double r33395 = 0.0;
        double r33396 = im;
        double r33397 = r33395 - r33396;
        double r33398 = exp(r33397);
        double r33399 = exp(r33396);
        double r33400 = r33398 + r33399;
        double r33401 = r33394 * r33400;
        return r33401;
}

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 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))