Average Error: 0.2 → 0.2
Time: 5.7s
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 r510500 = x;
        double r510501 = cosh(r510500);
        double r510502 = y;
        double r510503 = sin(r510502);
        double r510504 = r510503 / r510502;
        double r510505 = r510501 * r510504;
        return r510505;
}
↓
double f(double x, double y) {
        double r510506 = x;
        double r510507 = cosh(r510506);
        double r510508 = 1.0;
        double r510509 = y;
        double r510510 = sin(r510509);
        double r510511 = r510509 / r510510;
        double r510512 = r510508 / r510511;
        double r510513 = r510507 * r510512;
        return r510513;
}

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 2020062 +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)))