Average Error: 13.8 → 0.1
Time: 4.2s
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 r411004 = x;
        double r411005 = sin(r411004);
        double r411006 = y;
        double r411007 = sinh(r411006);
        double r411008 = r411005 * r411007;
        double r411009 = r411008 / r411004;
        return r411009;
}
↓
double f(double x, double y) {
        double r411010 = x;
        double r411011 = sin(r411010);
        double r411012 = r411011 / r411010;
        double r411013 = y;
        double r411014 = sinh(r411013);
        double r411015 = r411012 * r411014;
        return r411015;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.8
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.8

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

  3. Applied associate-/l*0.7

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  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 2020035 
(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))