Average Error: 0.1 → 0.1
Time: 4.5s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[\frac{x}{\frac{y}{\sin y}}\]
x \cdot \frac{\sin y}{y}
↓
\frac{x}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r137474 = x;
        double r137475 = y;
        double r137476 = sin(r137475);
        double r137477 = r137476 / r137475;
        double r137478 = r137474 * r137477;
        return r137478;
}
↓
double f(double x, double y) {
        double r137479 = x;
        double r137480 = y;
        double r137481 = sin(r137480);
        double r137482 = r137480 / r137481;
        double r137483 = r137479 / r137482;
        return r137483;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied div-inv0.2

    \[\leadsto x \cdot \color{blue}{\left(\sin y \cdot \frac{1}{y}\right)}\]
  4. Using strategy rm

  5. Applied pow10.2

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

  6. Applied pow10.2

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

  7. Applied pow-prod-down0.2

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

  8. Applied pow10.2

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

  9. Applied pow-prod-down0.2

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

  10. Simplified7.2

    \[\leadsto {\color{blue}{\left(\frac{x \cdot \sin y}{y}\right)}}^{1}\]
  11. Using strategy rm

  12. Applied associate-/l*0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))