Average Error: 5.8 → 0.1
Time: 15.4s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{\frac{3 - x}{3}}{y} \cdot \left(1 - x\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{\frac{3 - x}{3}}{y} \cdot \left(1 - x\right)
double f(double x, double y) {
        double r33559106 = 1.0;
        double r33559107 = x;
        double r33559108 = r33559106 - r33559107;
        double r33559109 = 3.0;
        double r33559110 = r33559109 - r33559107;
        double r33559111 = r33559108 * r33559110;
        double r33559112 = y;
        double r33559113 = r33559112 * r33559109;
        double r33559114 = r33559111 / r33559113;
        return r33559114;
}
↓
double f(double x, double y) {
        double r33559115 = 3.0;
        double r33559116 = x;
        double r33559117 = r33559115 - r33559116;
        double r33559118 = r33559117 / r33559115;
        double r33559119 = y;
        double r33559120 = r33559118 / r33559119;
        double r33559121 = 1.0;
        double r33559122 = r33559121 - r33559116;
        double r33559123 = r33559120 * r33559122;
        return r33559123;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.8
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.8

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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-inv0.2

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

  7. Applied associate-*l*0.2

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 +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)))