Average Error: 0.0 → 0.0
Time: 5.7s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\cos x}{\frac{y}{\sinh y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\frac{\cos x}{\frac{y}{\sinh y}}
double f(double x, double y) {
        double r109448 = x;
        double r109449 = cos(r109448);
        double r109450 = y;
        double r109451 = sinh(r109450);
        double r109452 = r109451 / r109450;
        double r109453 = r109449 * r109452;
        return r109453;
}
↓
double f(double x, double y) {
        double r109454 = x;
        double r109455 = cos(r109454);
        double r109456 = y;
        double r109457 = sinh(r109456);
        double r109458 = r109456 / r109457;
        double r109459 = r109455 / r109458;
        return r109459;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied clear-num0.0

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

  5. Applied pow10.0

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

  6. Applied pow10.0

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

  7. Applied pow-prod-down0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))