Average Error: 0.0 → 0.1
Time: 6.0s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \left(\left|\sqrt[3]{\frac{\sinh y}{y}}\right| \cdot \sqrt{\sqrt[3]{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \left(\left|\sqrt[3]{\frac{\sinh y}{y}}\right| \cdot \sqrt{\sqrt[3]{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r136101 = x;
        double r136102 = sin(r136101);
        double r136103 = y;
        double r136104 = sinh(r136103);
        double r136105 = r136104 / r136103;
        double r136106 = r136102 * r136105;
        return r136106;
}
↓
double f(double x, double y) {
        double r136107 = x;
        double r136108 = sin(r136107);
        double r136109 = y;
        double r136110 = sinh(r136109);
        double r136111 = r136110 / r136109;
        double r136112 = cbrt(r136111);
        double r136113 = fabs(r136112);
        double r136114 = sqrt(r136112);
        double r136115 = r136113 * r136114;
        double r136116 = r136108 * r136115;
        double r136117 = sqrt(r136111);
        double r136118 = r136116 * r136117;
        return r136118;
}

Error

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Bits error versus y

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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-cube-cbrt0.1

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

  7. Applied sqrt-prod0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))