Average Error: 5.5 → 0.1
Time: 16.9s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{3 - x}{3} \cdot \frac{1 - x}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{3 - x}{3} \cdot \frac{1 - x}{y}
double f(double x, double y) {
        double r555523 = 1.0;
        double r555524 = x;
        double r555525 = r555523 - r555524;
        double r555526 = 3.0;
        double r555527 = r555526 - r555524;
        double r555528 = r555525 * r555527;
        double r555529 = y;
        double r555530 = r555529 * r555526;
        double r555531 = r555528 / r555530;
        return r555531;
}
↓
double f(double x, double y) {
        double r555532 = 3.0;
        double r555533 = x;
        double r555534 = r555532 - r555533;
        double r555535 = r555534 / r555532;
        double r555536 = 1.0;
        double r555537 = r555536 - r555533;
        double r555538 = y;
        double r555539 = r555537 / r555538;
        double r555540 = r555535 * r555539;
        return r555540;
}

Error

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Bits error versus y

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Results

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Target

Original5.5
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.5

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 +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)))