Average Error: 0.0 → 0.1
Time: 26.9s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{{\left(\sqrt{\frac{\sinh y}{y}}\right)}^{3}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{{\left(\sqrt{\frac{\sinh y}{y}}\right)}^{3}}
double f(double x, double y) {
        double r162371 = x;
        double r162372 = sin(r162371);
        double r162373 = y;
        double r162374 = sinh(r162373);
        double r162375 = r162374 / r162373;
        double r162376 = r162372 * r162375;
        return r162376;
}
↓
double f(double x, double y) {
        double r162377 = x;
        double r162378 = sin(r162377);
        double r162379 = y;
        double r162380 = sinh(r162379);
        double r162381 = r162380 / r162379;
        double r162382 = sqrt(r162381);
        double r162383 = r162378 * r162382;
        double r162384 = 3.0;
        double r162385 = pow(r162382, r162384);
        double r162386 = cbrt(r162385);
        double r162387 = r162383 * r162386;
        return r162387;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}}\]
  5. Using strategy rm

  6. Applied add-cbrt-cube0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))