Average Error: 0.2 → 0.2
Time: 5.2s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{1}{\frac{y}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{1}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r491489 = x;
        double r491490 = cosh(r491489);
        double r491491 = y;
        double r491492 = sin(r491491);
        double r491493 = r491492 / r491491;
        double r491494 = r491490 * r491493;
        return r491494;
}
↓
double f(double x, double y) {
        double r491495 = x;
        double r491496 = cosh(r491495);
        double r491497 = 1.0;
        double r491498 = y;
        double r491499 = sin(r491498);
        double r491500 = r491498 / r491499;
        double r491501 = r491497 / r491500;
        double r491502 = r491496 * r491501;
        return r491502;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.2

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

  3. Applied clear-num0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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)))