Average Error: 14.2 → 0.3
Time: 38.5s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \frac{\sinh y}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \frac{\sinh y}{x}
double f(double x, double y) {
        double r380669 = x;
        double r380670 = sin(r380669);
        double r380671 = y;
        double r380672 = sinh(r380671);
        double r380673 = r380670 * r380672;
        double r380674 = r380673 / r380669;
        return r380674;
}
↓
double f(double x, double y) {
        double r380675 = x;
        double r380676 = sin(r380675);
        double r380677 = y;
        double r380678 = sinh(r380677);
        double r380679 = r380678 / r380675;
        double r380680 = r380676 * r380679;
        return r380680;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.2
Target0.3
Herbie0.3
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.2

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

  3. Applied *-un-lft-identity14.2

    \[\leadsto \frac{\sin x \cdot \sinh y}{\color{blue}{1 \cdot x}}\]

  4. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{\sin x}{1} \cdot \frac{\sinh y}{x}}\]

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019304 
(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))