Average Error: 5.4 → 0.1
Time: 42.0s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - \frac{x}{3}\right) \cdot \frac{1 - x}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - \frac{x}{3}\right) \cdot \frac{1 - x}{y}
double f(double x, double y) {
        double r30749595 = 1.0;
        double r30749596 = x;
        double r30749597 = r30749595 - r30749596;
        double r30749598 = 3.0;
        double r30749599 = r30749598 - r30749596;
        double r30749600 = r30749597 * r30749599;
        double r30749601 = y;
        double r30749602 = r30749601 * r30749598;
        double r30749603 = r30749600 / r30749602;
        return r30749603;
}
↓
double f(double x, double y) {
        double r30749604 = 1.0;
        double r30749605 = x;
        double r30749606 = 3.0;
        double r30749607 = r30749605 / r30749606;
        double r30749608 = r30749604 - r30749607;
        double r30749609 = 1.0;
        double r30749610 = r30749609 - r30749605;
        double r30749611 = y;
        double r30749612 = r30749610 / r30749611;
        double r30749613 = r30749608 * r30749612;
        return r30749613;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.4
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.4

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

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))