Average Error: 0.1 → 0.1
Time: 3.3s
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 r145696 = x;
        double r145697 = y;
        double r145698 = sin(r145697);
        double r145699 = r145698 / r145697;
        double r145700 = r145696 * r145699;
        return r145700;
}
↓
double f(double x, double y) {
        double r145701 = x;
        double r145702 = y;
        double r145703 = sin(r145702);
        double r145704 = r145702 / r145703;
        double r145705 = r145701 / r145704;
        return r145705;
}

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 add-cube-cbrt1.3

    \[\leadsto x \cdot \frac{\sin y}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\]

  4. Applied *-un-lft-identity1.3

    \[\leadsto x \cdot \frac{\color{blue}{1 \cdot \sin y}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}\]

  5. Applied times-frac1.3

    \[\leadsto x \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sin y}{\sqrt[3]{y}}\right)}\]

  6. Applied associate-*r*6.5

    \[\leadsto \color{blue}{\left(x \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sin y}{\sqrt[3]{y}}}\]

  7. Simplified6.5

    \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \frac{\sin y}{\sqrt[3]{y}}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity6.5

    \[\leadsto \color{blue}{\left(1 \cdot \frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)} \cdot \frac{\sin y}{\sqrt[3]{y}}\]

  10. Applied associate-*l*6.5

    \[\leadsto \color{blue}{1 \cdot \left(\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sin y}{\sqrt[3]{y}}\right)}\]

  11. Simplified7.0

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

  13. Applied associate-/l*0.1

    \[\leadsto 1 \cdot \color{blue}{\frac{x}{\frac{y}{\sin y}}}\]

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020027 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))