Average Error: 0.2 → 0.2
Time: 27.5s
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 r398954 = x;
        double r398955 = cosh(r398954);
        double r398956 = y;
        double r398957 = sin(r398956);
        double r398958 = r398957 / r398956;
        double r398959 = r398955 * r398958;
        return r398959;
}
↓
double f(double x, double y) {
        double r398960 = y;
        double r398961 = sin(r398960);
        double r398962 = r398961 / r398960;
        double r398963 = x;
        double r398964 = cosh(r398963);
        double r398965 = r398962 * r398964;
        return r398965;
}

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 *-commutative0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 +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)))