Average Error: 0.1 → 0.1
Time: 21.8s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\frac{\frac{\sin y}{y}}{e^{x}} + e^{x} \cdot \frac{\sin y}{y}}{2}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\frac{\frac{\sin y}{y}}{e^{x}} + e^{x} \cdot \frac{\sin y}{y}}{2}
double f(double x, double y) {
        double r26749009 = x;
        double r26749010 = cosh(r26749009);
        double r26749011 = y;
        double r26749012 = sin(r26749011);
        double r26749013 = r26749012 / r26749011;
        double r26749014 = r26749010 * r26749013;
        return r26749014;
}
↓
double f(double x, double y) {
        double r26749015 = y;
        double r26749016 = sin(r26749015);
        double r26749017 = r26749016 / r26749015;
        double r26749018 = x;
        double r26749019 = exp(r26749018);
        double r26749020 = r26749017 / r26749019;
        double r26749021 = r26749019 * r26749017;
        double r26749022 = r26749020 + r26749021;
        double r26749023 = 2.0;
        double r26749024 = r26749022 / r26749023;
        return r26749024;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

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 associate-*l/0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(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)))