Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r18331 = 0.5;
        double r18332 = re;
        double r18333 = sin(r18332);
        double r18334 = r18331 * r18333;
        double r18335 = 0.0;
        double r18336 = im;
        double r18337 = r18335 - r18336;
        double r18338 = exp(r18337);
        double r18339 = exp(r18336);
        double r18340 = r18338 + r18339;
        double r18341 = r18334 * r18340;
        return r18341;
}
↓
double f(double re, double im) {
        double r18342 = 0.5;
        double r18343 = re;
        double r18344 = sin(r18343);
        double r18345 = r18342 * r18344;
        double r18346 = 0.0;
        double r18347 = im;
        double r18348 = r18346 - r18347;
        double r18349 = exp(r18348);
        double r18350 = r18345 * r18349;
        double r18351 = exp(r18347);
        double r18352 = r18345 * r18351;
        double r18353 = r18350 + r18352;
        return r18353;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))