Average Error: 0.0 → 0.0
Time: 25.3s
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 r5546746 = x;
        double r5546747 = sin(r5546746);
        double r5546748 = y;
        double r5546749 = sinh(r5546748);
        double r5546750 = r5546749 / r5546748;
        double r5546751 = r5546747 * r5546750;
        return r5546751;
}
↓
double f(double x, double y) {
        double r5546752 = y;
        double r5546753 = sinh(r5546752);
        double r5546754 = r5546753 / r5546752;
        double r5546755 = sqrt(r5546754);
        double r5546756 = x;
        double r5546757 = sin(r5546756);
        double r5546758 = r5546755 * r5546757;
        double r5546759 = r5546755 * r5546758;
        return r5546759;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019163 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))