Average Error: 0.1 → 0.1
Time: 52.4s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\sin y}{y} \cdot \cosh x\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\sin y}{y} \cdot \cosh x
double f(double x, double y) {
        double r15635538 = x;
        double r15635539 = cosh(r15635538);
        double r15635540 = y;
        double r15635541 = sin(r15635540);
        double r15635542 = r15635541 / r15635540;
        double r15635543 = r15635539 * r15635542;
        return r15635543;
}
↓
double f(double x, double y) {
        double r15635544 = y;
        double r15635545 = sin(r15635544);
        double r15635546 = r15635545 / r15635544;
        double r15635547 = x;
        double r15635548 = cosh(r15635547);
        double r15635549 = r15635546 * r15635548;
        return r15635549;
}

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

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"

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

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