Average Error: 0.5 → 0.5
Time: 1.9m
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{\sqrt{2}}\right)\right)\right) \cdot \left(\cos x - \cos y\right) + 2}{3 \cdot e^{\log \left(\cos y \cdot \frac{3 - \sqrt{5}}{2} + \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right)}}\]
\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}
↓
\frac{\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{\sqrt{2}}\right)\right)\right) \cdot \left(\cos x - \cos y\right) + 2}{3 \cdot e^{\log \left(\cos y \cdot \frac{3 - \sqrt{5}}{2} + \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right)}}
double f(double x, double y) {
        double r9461511 = 2.0;
        double r9461512 = sqrt(r9461511);
        double r9461513 = x;
        double r9461514 = sin(r9461513);
        double r9461515 = y;
        double r9461516 = sin(r9461515);
        double r9461517 = 16.0;
        double r9461518 = r9461516 / r9461517;
        double r9461519 = r9461514 - r9461518;
        double r9461520 = r9461512 * r9461519;
        double r9461521 = r9461514 / r9461517;
        double r9461522 = r9461516 - r9461521;
        double r9461523 = r9461520 * r9461522;
        double r9461524 = cos(r9461513);
        double r9461525 = cos(r9461515);
        double r9461526 = r9461524 - r9461525;
        double r9461527 = r9461523 * r9461526;
        double r9461528 = r9461511 + r9461527;
        double r9461529 = 3.0;
        double r9461530 = 1.0;
        double r9461531 = 5.0;
        double r9461532 = sqrt(r9461531);
        double r9461533 = r9461532 - r9461530;
        double r9461534 = r9461533 / r9461511;
        double r9461535 = r9461534 * r9461524;
        double r9461536 = r9461530 + r9461535;
        double r9461537 = r9461529 - r9461532;
        double r9461538 = r9461537 / r9461511;
        double r9461539 = r9461538 * r9461525;
        double r9461540 = r9461536 + r9461539;
        double r9461541 = r9461529 * r9461540;
        double r9461542 = r9461528 / r9461541;
        return r9461542;
}
↓
double f(double x, double y) {
        double r9461543 = y;
        double r9461544 = sin(r9461543);
        double r9461545 = x;
        double r9461546 = sin(r9461545);
        double r9461547 = 16.0;
        double r9461548 = r9461546 / r9461547;
        double r9461549 = r9461544 - r9461548;
        double r9461550 = 2.0;
        double r9461551 = sqrt(r9461550);
        double r9461552 = sqrt(r9461551);
        double r9461553 = r9461544 / r9461547;
        double r9461554 = r9461546 - r9461553;
        double r9461555 = r9461554 * r9461552;
        double r9461556 = r9461552 * r9461555;
        double r9461557 = r9461549 * r9461556;
        double r9461558 = cos(r9461545);
        double r9461559 = cos(r9461543);
        double r9461560 = r9461558 - r9461559;
        double r9461561 = r9461557 * r9461560;
        double r9461562 = r9461561 + r9461550;
        double r9461563 = 3.0;
        double r9461564 = 5.0;
        double r9461565 = sqrt(r9461564);
        double r9461566 = r9461563 - r9461565;
        double r9461567 = r9461566 / r9461550;
        double r9461568 = r9461559 * r9461567;
        double r9461569 = 1.0;
        double r9461570 = r9461565 - r9461569;
        double r9461571 = r9461570 / r9461550;
        double r9461572 = r9461571 * r9461558;
        double r9461573 = r9461569 + r9461572;
        double r9461574 = r9461568 + r9461573;
        double r9461575 = log(r9461574);
        double r9461576 = exp(r9461575);
        double r9461577 = r9461563 * r9461576;
        double r9461578 = r9461562 / r9461577;
        return r9461578;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{\color{blue}{\sqrt{2} \cdot \sqrt{2}}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

  4. Applied sqrt-prod0.5

    \[\leadsto \frac{2 + \left(\left(\color{blue}{\left(\sqrt{\sqrt{2}} \cdot \sqrt{\sqrt{2}}\right)} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

  5. Applied associate-*l*0.5

    \[\leadsto \frac{2 + \left(\color{blue}{\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right)} \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
  6. Using strategy rm

  7. Applied add-exp-log0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \color{blue}{e^{\log \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}}}\]

  8. Final simplification0.5

    \[\leadsto \frac{\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{\sqrt{2}}\right)\right)\right) \cdot \left(\cos x - \cos y\right) + 2}{3 \cdot e^{\log \left(\cos y \cdot \frac{3 - \sqrt{5}}{2} + \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right)}}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x y)
  :name "Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5"
  (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y))))))