Average Error: 0.1 → 0.2
Time: 18.0s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{1}{\frac{y}{\sin y}} \cdot \cosh x\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{1}{\frac{y}{\sin y}} \cdot \cosh x
double f(double x, double y) {
        double r21477702 = x;
        double r21477703 = cosh(r21477702);
        double r21477704 = y;
        double r21477705 = sin(r21477704);
        double r21477706 = r21477705 / r21477704;
        double r21477707 = r21477703 * r21477706;
        return r21477707;
}
↓
double f(double x, double y) {
        double r21477708 = 1.0;
        double r21477709 = y;
        double r21477710 = sin(r21477709);
        double r21477711 = r21477709 / r21477710;
        double r21477712 = r21477708 / r21477711;
        double r21477713 = x;
        double r21477714 = cosh(r21477713);
        double r21477715 = r21477712 * r21477714;
        return r21477715;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

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

    \[\leadsto \frac{1}{\frac{y}{\sin y}} \cdot \cosh x\]

Reproduce

herbie shell --seed 2019192 +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)))