Average Error: 14.1 → 1.1
Time: 22.9s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \frac{\frac{\sinh y}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{x}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \frac{\frac{\sinh y}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{x}}
double f(double x, double y) {
        double r16790453 = x;
        double r16790454 = sin(r16790453);
        double r16790455 = y;
        double r16790456 = sinh(r16790455);
        double r16790457 = r16790454 * r16790456;
        double r16790458 = r16790457 / r16790453;
        return r16790458;
}
↓
double f(double x, double y) {
        double r16790459 = x;
        double r16790460 = sin(r16790459);
        double r16790461 = y;
        double r16790462 = sinh(r16790461);
        double r16790463 = cbrt(r16790459);
        double r16790464 = r16790463 * r16790463;
        double r16790465 = r16790462 / r16790464;
        double r16790466 = r16790465 / r16790463;
        double r16790467 = r16790460 * r16790466;
        return r16790467;
}

Error

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Bits error versus y

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Results

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Target

Original14.1
Target0.2
Herbie1.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.1

    \[\frac{\sin x \cdot \sinh y}{x}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity14.1

    \[\leadsto \frac{\sin x \cdot \sinh y}{\color{blue}{1 \cdot x}}\]

  4. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{\sin x}{1} \cdot \frac{\sinh y}{x}}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{\sin x} \cdot \frac{\sinh y}{x}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt1.1

    \[\leadsto \sin x \cdot \frac{\sinh y}{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}\]

  8. Applied associate-/r*1.1

    \[\leadsto \sin x \cdot \color{blue}{\frac{\frac{\sinh y}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{x}}}\]

  9. Final simplification1.1

    \[\leadsto \sin x \cdot \frac{\frac{\sinh y}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\sqrt[3]{x}}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))