Average Error: 0.2 → 0.2
Time: 4.7s
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 r500141 = x;
        double r500142 = cosh(r500141);
        double r500143 = y;
        double r500144 = sin(r500143);
        double r500145 = r500144 / r500143;
        double r500146 = r500142 * r500145;
        return r500146;
}
↓
double f(double x, double y) {
        double r500147 = x;
        double r500148 = cosh(r500147);
        double r500149 = y;
        double r500150 = sin(r500149);
        double r500151 = r500150 / r500149;
        double r500152 = r500148 * r500151;
        return r500152;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020064 +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)))