Average Error: 13.9 → 0.8
Time: 16.7s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sin x}{\frac{x}{\sinh y}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sin x}{\frac{x}{\sinh y}}
double f(double x, double y) {
        double r26241158 = x;
        double r26241159 = sin(r26241158);
        double r26241160 = y;
        double r26241161 = sinh(r26241160);
        double r26241162 = r26241159 * r26241161;
        double r26241163 = r26241162 / r26241158;
        return r26241163;
}
↓
double f(double x, double y) {
        double r26241164 = x;
        double r26241165 = sin(r26241164);
        double r26241166 = y;
        double r26241167 = sinh(r26241166);
        double r26241168 = r26241164 / r26241167;
        double r26241169 = r26241165 / r26241168;
        return r26241169;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.9
Target0.2
Herbie0.8
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.9

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

  3. Applied associate-/l*0.8

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

  4. Final simplification0.8

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

Reproduce

herbie shell --seed 2019174 
(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))