Average Error: 0.0 → 0.0
Time: 28.3s
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 r140462 = x;
        double r140463 = sin(r140462);
        double r140464 = y;
        double r140465 = sinh(r140464);
        double r140466 = r140465 / r140464;
        double r140467 = r140463 * r140466;
        return r140467;
}
↓
double f(double x, double y) {
        double r140468 = x;
        double r140469 = sin(r140468);
        double r140470 = y;
        double r140471 = sinh(r140470);
        double r140472 = r140471 / r140470;
        double r140473 = sqrt(r140472);
        double r140474 = sqrt(r140473);
        double r140475 = r140469 * r140474;
        double r140476 = r140475 * r140474;
        double r140477 = r140476 * r140473;
        return r140477;
}

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