Average Error: 0.0 → 0.0
Time: 13.5s
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 r153835 = x;
        double r153836 = sin(r153835);
        double r153837 = y;
        double r153838 = sinh(r153837);
        double r153839 = r153838 / r153837;
        double r153840 = r153836 * r153839;
        return r153840;
}
↓
double f(double x, double y) {
        double r153841 = x;
        double r153842 = sin(r153841);
        double r153843 = y;
        double r153844 = sinh(r153843);
        double r153845 = r153844 / r153843;
        double r153846 = sqrt(r153845);
        double r153847 = sqrt(r153846);
        double r153848 = r153842 * r153847;
        double r153849 = r153848 * r153847;
        double r153850 = r153849 * r153846;
        return r153850;
}

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-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)))