Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3

Average Error: 5.6 → 0.2

Time: 16.5s

Precision: 64

Math

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

↓

\[\frac{1}{\frac{y}{1 - x}} \cdot \frac{3 - x}{3}\]

C

double f(double x, double y) {
        double r432533 = 1.0;
        double r432534 = x;
        double r432535 = r432533 - r432534;
        double r432536 = 3.0;
        double r432537 = r432536 - r432534;
        double r432538 = r432535 * r432537;
        double r432539 = y;
        double r432540 = r432539 * r432536;
        double r432541 = r432538 / r432540;
        return r432541;
}

↓

double f(double x, double y) {
        double r432542 = 1.0;
        double r432543 = y;
        double r432544 = 1.0;
        double r432545 = x;
        double r432546 = r432544 - r432545;
        double r432547 = r432543 / r432546;
        double r432548 = r432542 / r432547;
        double r432549 = 3.0;
        double r432550 = r432549 - r432545;
        double r432551 = r432550 / r432549;
        double r432552 = r432548 * r432551;
        return r432552;
}

Error

Bits error versus x

Bits error versus y

Target

Original	5.6
Target	0.1
Herbie	0.2

\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

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-frac 0.1

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

5. Applied clear-num 0.2

   \[\leadsto \color{blue}{\frac{1}{\frac{y}{1 - x}}} \cdot \frac{3 - x}{3}\]

6. Final simplification 0.2

   \[\leadsto \frac{1}{\frac{y}{1 - x}} \cdot \frac{3 - x}{3}\]

Reproduce

herbie shell --seed 2019323 +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)))