Average Error: 0.1 → 0.2
Time: 22.8s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{e^{\log \left(e^{x} + e^{-x}\right)} \cdot \sin y}{2 \cdot y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{e^{\log \left(e^{x} + e^{-x}\right)} \cdot \sin y}{2 \cdot y}
double f(double x, double y) {
        double r343394 = x;
        double r343395 = cosh(r343394);
        double r343396 = y;
        double r343397 = sin(r343396);
        double r343398 = r343397 / r343396;
        double r343399 = r343395 * r343398;
        return r343399;
}
↓
double f(double x, double y) {
        double r343400 = x;
        double r343401 = exp(r343400);
        double r343402 = -r343400;
        double r343403 = exp(r343402);
        double r343404 = r343401 + r343403;
        double r343405 = log(r343404);
        double r343406 = exp(r343405);
        double r343407 = y;
        double r343408 = sin(r343407);
        double r343409 = r343406 * r343408;
        double r343410 = 2.0;
        double r343411 = r343410 * r343407;
        double r343412 = r343409 / r343411;
        return r343412;
}

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. Using strategy rm

  6. Applied add-exp-log0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(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)))