Average Error: 0.0 → 0.0
Time: 17.9s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sin x}{\frac{y}{\sinh y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x}{\frac{y}{\sinh y}}
double f(double x, double y) {
        double r97349 = x;
        double r97350 = sin(r97349);
        double r97351 = y;
        double r97352 = sinh(r97351);
        double r97353 = r97352 / r97351;
        double r97354 = r97350 * r97353;
        return r97354;
}
↓
double f(double x, double y) {
        double r97355 = x;
        double r97356 = sin(r97355);
        double r97357 = y;
        double r97358 = sinh(r97357);
        double r97359 = r97357 / r97358;
        double r97360 = r97356 / r97359;
        return r97360;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

    \[\sin x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto \sin x \cdot \color{blue}{\frac{1}{\frac{y}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied pow10.0

    \[\leadsto \sin x \cdot \color{blue}{{\left(\frac{1}{\frac{y}{\sinh y}}\right)}^{1}}\]

  6. Applied pow10.0

    \[\leadsto \color{blue}{{\left(\sin x\right)}^{1}} \cdot {\left(\frac{1}{\frac{y}{\sinh y}}\right)}^{1}\]

  7. Applied pow-prod-down0.0

    \[\leadsto \color{blue}{{\left(\sin x \cdot \frac{1}{\frac{y}{\sinh y}}\right)}^{1}}\]

  8. Simplified0.0

    \[\leadsto {\color{blue}{\left(\frac{\sin x}{\frac{y}{\sinh y}}\right)}}^{1}\]

  9. Final simplification0.0

    \[\leadsto \frac{\sin x}{\frac{y}{\sinh y}}\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))