Average Error: 0.1 → 0.1
Time: 6.1s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{\sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r510548 = x;
        double r510549 = cosh(r510548);
        double r510550 = y;
        double r510551 = sin(r510550);
        double r510552 = r510551 / r510550;
        double r510553 = r510549 * r510552;
        return r510553;
}
↓
double f(double x, double y) {
        double r510554 = x;
        double r510555 = cosh(r510554);
        double r510556 = y;
        double r510557 = sin(r510556);
        double r510558 = r510557 / r510556;
        double r510559 = r510555 * r510558;
        return r510559;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2020089 +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)))