Average Error: 5.6 → 0.1
Time: 3.0s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \left(1 - \frac{x}{3}\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \left(1 - \frac{x}{3}\right)
double f(double x, double y) {
        double r553653 = 1.0;
        double r553654 = x;
        double r553655 = r553653 - r553654;
        double r553656 = 3.0;
        double r553657 = r553656 - r553654;
        double r553658 = r553655 * r553657;
        double r553659 = y;
        double r553660 = r553659 * r553656;
        double r553661 = r553658 / r553660;
        return r553661;
}
↓
double f(double x, double y) {
        double r553662 = 1.0;
        double r553663 = x;
        double r553664 = r553662 - r553663;
        double r553665 = y;
        double r553666 = r553664 / r553665;
        double r553667 = 1.0;
        double r553668 = 3.0;
        double r553669 = r553663 / r553668;
        double r553670 = r553667 - r553669;
        double r553671 = r553666 * r553670;
        return r553671;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.6
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.6

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}}\]
  4. Using strategy rm

  5. Applied div-sub0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

    \[\leadsto \frac{1 - x}{y} \cdot \left(1 - \frac{x}{3}\right)\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1 x) y) (/ (- 3 x) 3))

  (/ (* (- 1 x) (- 3 x)) (* y 3)))