Average Error: 0.0 → 0.0
Time: 17.4s
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 r8032641 = x;
        double r8032642 = sin(r8032641);
        double r8032643 = y;
        double r8032644 = sinh(r8032643);
        double r8032645 = r8032644 / r8032643;
        double r8032646 = r8032642 * r8032645;
        return r8032646;
}
↓
double f(double x, double y) {
        double r8032647 = y;
        double r8032648 = sinh(r8032647);
        double r8032649 = r8032648 / r8032647;
        double r8032650 = sqrt(r8032649);
        double r8032651 = x;
        double r8032652 = sin(r8032651);
        double r8032653 = r8032650 * r8032652;
        double r8032654 = r8032650 * r8032653;
        return r8032654;
}

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