Average Error: 14.0 → 0.2
Time: 4.7s
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 r624200 = x;
        double r624201 = sin(r624200);
        double r624202 = y;
        double r624203 = sinh(r624202);
        double r624204 = r624201 * r624203;
        double r624205 = r624204 / r624200;
        return r624205;
}
↓
double f(double x, double y) {
        double r624206 = x;
        double r624207 = sin(r624206);
        double r624208 = y;
        double r624209 = sinh(r624208);
        double r624210 = r624209 / r624206;
        double r624211 = r624207 * r624210;
        return r624211;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.0
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.0

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

  3. Applied *-un-lft-identity14.0

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

  4. Applied times-frac0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020057 
(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))