Average Error: 0.0 → 0.7
Time: 5.7s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot e^{\sqrt[3]{\sqrt{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}}} \cdot \sqrt[3]{\sqrt{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}}}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot e^{\sqrt[3]{\sqrt{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}}} \cdot \sqrt[3]{\sqrt{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}}}}
double f(double x, double y) {
        double r154536 = x;
        double r154537 = sin(r154536);
        double r154538 = y;
        double r154539 = sinh(r154538);
        double r154540 = r154539 / r154538;
        double r154541 = r154537 * r154540;
        return r154541;
}
↓
double f(double x, double y) {
        double r154542 = x;
        double r154543 = sin(r154542);
        double r154544 = 0.16666666666666666;
        double r154545 = y;
        double r154546 = 2.0;
        double r154547 = pow(r154545, r154546);
        double r154548 = r154544 * r154547;
        double r154549 = 0.008333333333333333;
        double r154550 = 4.0;
        double r154551 = pow(r154545, r154550);
        double r154552 = r154549 * r154551;
        double r154553 = 1.0;
        double r154554 = r154552 + r154553;
        double r154555 = r154548 + r154554;
        double r154556 = log(r154555);
        double r154557 = 3.0;
        double r154558 = pow(r154556, r154557);
        double r154559 = sqrt(r154558);
        double r154560 = cbrt(r154559);
        double r154561 = r154560 * r154560;
        double r154562 = exp(r154561);
        double r154563 = r154543 * r154562;
        return r154563;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\sin x \cdot \frac{\sinh y}{y}\]

  2. Taylor expanded around 0 0.7

    \[\leadsto \sin x \cdot \color{blue}{\left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)}\]
  3. Using strategy rm

  4. Applied add-exp-log0.7

    \[\leadsto \sin x \cdot \color{blue}{e^{\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)}}\]
  5. Using strategy rm

  6. Applied add-cbrt-cube0.7

    \[\leadsto \sin x \cdot e^{\color{blue}{\sqrt[3]{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right) \cdot \log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right) \cdot \log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)}}}\]

  7. Simplified0.7

    \[\leadsto \sin x \cdot e^{\sqrt[3]{\color{blue}{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}}}}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.7

    \[\leadsto \sin x \cdot e^{\sqrt[3]{\color{blue}{\sqrt{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}} \cdot \sqrt{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}}}}}\]

  10. Applied cbrt-prod0.7

    \[\leadsto \sin x \cdot e^{\color{blue}{\sqrt[3]{\sqrt{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}}} \cdot \sqrt[3]{\sqrt{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}}}}}\]

  11. Final simplification0.7

    \[\leadsto \sin x \cdot e^{\sqrt[3]{\sqrt{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}}} \cdot \sqrt[3]{\sqrt{{\left(\log \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\right)}^{3}}}}\]

Reproduce

herbie shell --seed 2020034 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))