Average Error: 14.2 → 0.1
Time: 18.2s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sinh y \cdot \frac{\sin x}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sinh y \cdot \frac{\sin x}{x}
double f(double x, double y) {
        double r21098113 = x;
        double r21098114 = sin(r21098113);
        double r21098115 = y;
        double r21098116 = sinh(r21098115);
        double r21098117 = r21098114 * r21098116;
        double r21098118 = r21098117 / r21098113;
        return r21098118;
}
↓
double f(double x, double y) {
        double r21098119 = y;
        double r21098120 = sinh(r21098119);
        double r21098121 = x;
        double r21098122 = sin(r21098121);
        double r21098123 = r21098122 / r21098121;
        double r21098124 = r21098120 * r21098123;
        return r21098124;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.2
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.2

    \[\frac{\sin x \cdot \sinh y}{x}\]
  2. Using strategy rm

  3. Applied associate-/l*0.8

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.1

    \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y}\]

  6. Final simplification0.1

    \[\leadsto \sinh y \cdot \frac{\sin x}{x}\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))