Average Error: 13.3 → 0.1
Time: 14.9s
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 r274203 = x;
        double r274204 = sin(r274203);
        double r274205 = y;
        double r274206 = sinh(r274205);
        double r274207 = r274204 * r274206;
        double r274208 = r274207 / r274203;
        return r274208;
}
↓
double f(double x, double y) {
        double r274209 = x;
        double r274210 = sin(r274209);
        double r274211 = r274210 / r274209;
        double r274212 = y;
        double r274213 = sinh(r274212);
        double r274214 = r274211 * r274213;
        return r274214;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.3
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.3

    \[\frac{\sin x \cdot \sinh y}{x}\]
  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 2019208 +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))