Average Error: 14.0 → 0.1
Time: 16.1s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sinh y \cdot \frac{1}{\frac{x}{\sin x}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sinh y \cdot \frac{1}{\frac{x}{\sin x}}
double f(double x, double y) {
        double r428010 = x;
        double r428011 = sin(r428010);
        double r428012 = y;
        double r428013 = sinh(r428012);
        double r428014 = r428011 * r428013;
        double r428015 = r428014 / r428010;
        return r428015;
}
↓
double f(double x, double y) {
        double r428016 = y;
        double r428017 = sinh(r428016);
        double r428018 = 1.0;
        double r428019 = x;
        double r428020 = sin(r428019);
        double r428021 = r428019 / r428020;
        double r428022 = r428018 / r428021;
        double r428023 = r428017 * r428022;
        return r428023;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.0
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.0

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

  2. Simplified0.8

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.8

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

  5. Applied *-un-lft-identity0.8

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

  6. Applied times-frac0.8

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

  7. Applied *-un-lft-identity0.8

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

  8. Applied times-frac0.8

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

  9. Simplified0.8

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

  10. Simplified0.1

    \[\leadsto 1 \cdot \color{blue}{\left(\frac{\sin x}{x} \cdot \sinh y\right)}\]
  11. Using strategy rm

  12. Applied clear-num0.1

    \[\leadsto 1 \cdot \left(\color{blue}{\frac{1}{\frac{x}{\sin x}}} \cdot \sinh y\right)\]

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(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))