Average Error: 0.2 → 0.2
Time: 49.1s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{e^{x} \cdot \sin y + \frac{\sin y}{e^{x}}}{2 \cdot y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{e^{x} \cdot \sin y + \frac{\sin y}{e^{x}}}{2 \cdot y}
double f(double x, double y) {
        double r26994513 = x;
        double r26994514 = cosh(r26994513);
        double r26994515 = y;
        double r26994516 = sin(r26994515);
        double r26994517 = r26994516 / r26994515;
        double r26994518 = r26994514 * r26994517;
        return r26994518;
}
↓
double f(double x, double y) {
        double r26994519 = x;
        double r26994520 = exp(r26994519);
        double r26994521 = y;
        double r26994522 = sin(r26994521);
        double r26994523 = r26994520 * r26994522;
        double r26994524 = r26994522 / r26994520;
        double r26994525 = r26994523 + r26994524;
        double r26994526 = 2.0;
        double r26994527 = r26994526 * r26994521;
        double r26994528 = r26994525 / r26994527;
        return r26994528;
}

Error

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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 frac-times0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

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)))