Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)
double f(double re, double im) {
        double r12403 = 0.5;
        double r12404 = re;
        double r12405 = sin(r12404);
        double r12406 = r12403 * r12405;
        double r12407 = 0.0;
        double r12408 = im;
        double r12409 = r12407 - r12408;
        double r12410 = exp(r12409);
        double r12411 = exp(r12408);
        double r12412 = r12410 + r12411;
        double r12413 = r12406 * r12412;
        return r12413;
}
↓
double f(double re, double im) {
        double r12414 = 0.0;
        double r12415 = im;
        double r12416 = r12414 - r12415;
        double r12417 = exp(r12416);
        double r12418 = 0.5;
        double r12419 = re;
        double r12420 = sin(r12419);
        double r12421 = r12418 * r12420;
        double r12422 = r12417 * r12421;
        double r12423 = exp(r12415);
        double r12424 = r12423 * r12421;
        double r12425 = r12422 + r12424;
        return r12425;
}

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. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))