Average Error: 0.1 → 0.2
Time: 24.6s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\left(e^{x} + e^{-x}\right) \cdot \sin y}{2 \cdot y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\left(e^{x} + e^{-x}\right) \cdot \sin y}{2 \cdot y}
double f(double x, double y) {
        double r378694 = x;
        double r378695 = cosh(r378694);
        double r378696 = y;
        double r378697 = sin(r378696);
        double r378698 = r378697 / r378696;
        double r378699 = r378695 * r378698;
        return r378699;
}
↓
double f(double x, double y) {
        double r378700 = x;
        double r378701 = exp(r378700);
        double r378702 = -r378700;
        double r378703 = exp(r378702);
        double r378704 = r378701 + r378703;
        double r378705 = y;
        double r378706 = sin(r378705);
        double r378707 = r378704 * r378706;
        double r378708 = 2.0;
        double r378709 = r378708 * r378705;
        double r378710 = r378707 / r378709;
        return r378710;
}

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 cosh-def0.1

    \[\leadsto \color{blue}{\frac{e^{x} + e^{-x}}{2}} \cdot \frac{\sin y}{y}\]

  4. Applied frac-times0.2

    \[\leadsto \color{blue}{\frac{\left(e^{x} + e^{-x}\right) \cdot \sin y}{2 \cdot y}}\]

  5. Final simplification0.2

    \[\leadsto \frac{\left(e^{x} + e^{-x}\right) \cdot \sin y}{2 \cdot y}\]

Reproduce

herbie shell --seed 2019306 
(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)))