Average Error: 0.2 → 0.2
Time: 17.5s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\frac{e^{x} \cdot \sin y + \frac{\sin y}{e^{x}}}{y}}{2}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\frac{e^{x} \cdot \sin y + \frac{\sin y}{e^{x}}}{y}}{2}
double f(double x, double y) {
        double r26236449 = x;
        double r26236450 = cosh(r26236449);
        double r26236451 = y;
        double r26236452 = sin(r26236451);
        double r26236453 = r26236452 / r26236451;
        double r26236454 = r26236450 * r26236453;
        return r26236454;
}
↓
double f(double x, double y) {
        double r26236455 = x;
        double r26236456 = exp(r26236455);
        double r26236457 = y;
        double r26236458 = sin(r26236457);
        double r26236459 = r26236456 * r26236458;
        double r26236460 = r26236458 / r26236456;
        double r26236461 = r26236459 + r26236460;
        double r26236462 = r26236461 / r26236457;
        double r26236463 = 2.0;
        double r26236464 = r26236462 / r26236463;
        return r26236464;
}

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 cosh-def0.2

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

  4. Applied associate-*l/0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019165 
(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)))