Average Error: 0.1 → 0.2
Time: 13.8s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}
double f(double x, double y) {
        double r426449 = x;
        double r426450 = cosh(r426449);
        double r426451 = y;
        double r426452 = sin(r426451);
        double r426453 = r426452 / r426451;
        double r426454 = r426450 * r426453;
        return r426454;
}
↓
double f(double x, double y) {
        double r426455 = x;
        double r426456 = cosh(r426455);
        double r426457 = 1.0;
        double r426458 = y;
        double r426459 = r426457 / r426458;
        double r426460 = sin(r426458);
        double r426461 = r426457 / r426460;
        double r426462 = r426459 / r426461;
        double r426463 = r426456 * r426462;
        return r426463;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

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

  3. Applied clear-num0.2

    \[\leadsto \cosh x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\]
  4. Using strategy rm

  5. Applied div-inv0.4

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

  6. Applied associate-/r*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))