Average Error: 0.0 → 0.0
Time: 16.7s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\left(\sin x \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\left(\sin x \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r121463 = x;
        double r121464 = sin(r121463);
        double r121465 = y;
        double r121466 = sinh(r121465);
        double r121467 = r121466 / r121465;
        double r121468 = r121464 * r121467;
        return r121468;
}
↓
double f(double x, double y) {
        double r121469 = x;
        double r121470 = sin(r121469);
        double r121471 = y;
        double r121472 = sinh(r121471);
        double r121473 = r121472 / r121471;
        double r121474 = sqrt(r121473);
        double r121475 = sqrt(r121474);
        double r121476 = r121470 * r121475;
        double r121477 = r121476 * r121475;
        double r121478 = r121477 * r121474;
        return r121478;
}

Error

Bits error versus x

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-sqr-sqrt0.0

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

  7. Applied sqrt-prod0.0

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

  8. Applied associate-*r*0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))