Average Error: 0.0 → 0.0
Time: 17.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(\left(0.5 \cdot \sin re\right) \cdot \sqrt{e^{0.0 - im}}\right) \cdot \sqrt{e^{0.0 - im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(\left(0.5 \cdot \sin re\right) \cdot \sqrt{e^{0.0 - im}}\right) \cdot \sqrt{e^{0.0 - im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r29405 = 0.5;
        double r29406 = re;
        double r29407 = sin(r29406);
        double r29408 = r29405 * r29407;
        double r29409 = 0.0;
        double r29410 = im;
        double r29411 = r29409 - r29410;
        double r29412 = exp(r29411);
        double r29413 = exp(r29410);
        double r29414 = r29412 + r29413;
        double r29415 = r29408 * r29414;
        return r29415;
}
↓
double f(double re, double im) {
        double r29416 = 0.5;
        double r29417 = re;
        double r29418 = sin(r29417);
        double r29419 = r29416 * r29418;
        double r29420 = 0.0;
        double r29421 = im;
        double r29422 = r29420 - r29421;
        double r29423 = exp(r29422);
        double r29424 = sqrt(r29423);
        double r29425 = r29419 * r29424;
        double r29426 = r29425 * r29424;
        double r29427 = exp(r29421);
        double r29428 = r29419 * r29427;
        double r29429 = r29426 + r29428;
        return r29429;
}

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. Using strategy rm

  5. Applied add-sqr-sqrt0.0

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

  6. Applied associate-*r*0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 +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))))