Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sin x\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sin x\right)
double f(double x, double y) {
        double r6320734 = x;
        double r6320735 = sin(r6320734);
        double r6320736 = y;
        double r6320737 = sinh(r6320736);
        double r6320738 = r6320737 / r6320736;
        double r6320739 = r6320735 * r6320738;
        return r6320739;
}
↓
double f(double x, double y) {
        double r6320740 = y;
        double r6320741 = sinh(r6320740);
        double r6320742 = r6320741 / r6320740;
        double r6320743 = sqrt(r6320742);
        double r6320744 = x;
        double r6320745 = sin(r6320744);
        double r6320746 = r6320743 * r6320745;
        double r6320747 = r6320743 * r6320746;
        return r6320747;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))