Average Error: 14.5 → 0.1
Time: 3.9s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sin x}{x} \cdot \sinh y\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sin x}{x} \cdot \sinh y
double f(double x, double y) {
        double r437205 = x;
        double r437206 = sin(r437205);
        double r437207 = y;
        double r437208 = sinh(r437207);
        double r437209 = r437206 * r437208;
        double r437210 = r437209 / r437205;
        return r437210;
}
↓
double f(double x, double y) {
        double r437211 = x;
        double r437212 = sin(r437211);
        double r437213 = r437212 / r437211;
        double r437214 = y;
        double r437215 = sinh(r437214);
        double r437216 = r437213 * r437215;
        return r437216;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.5
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.5

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

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

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

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

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