Average Error: 5.4 → 0.2
Time: 23.9s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{3 - x}{3} \cdot \left(\frac{1}{y} \cdot \left(1 - x\right)\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{3 - x}{3} \cdot \left(\frac{1}{y} \cdot \left(1 - x\right)\right)
double f(double x, double y) {
        double r30901237 = 1.0;
        double r30901238 = x;
        double r30901239 = r30901237 - r30901238;
        double r30901240 = 3.0;
        double r30901241 = r30901240 - r30901238;
        double r30901242 = r30901239 * r30901241;
        double r30901243 = y;
        double r30901244 = r30901243 * r30901240;
        double r30901245 = r30901242 / r30901244;
        return r30901245;
}
↓
double f(double x, double y) {
        double r30901246 = 3.0;
        double r30901247 = x;
        double r30901248 = r30901246 - r30901247;
        double r30901249 = r30901248 / r30901246;
        double r30901250 = 1.0;
        double r30901251 = y;
        double r30901252 = r30901250 / r30901251;
        double r30901253 = 1.0;
        double r30901254 = r30901253 - r30901247;
        double r30901255 = r30901252 * r30901254;
        double r30901256 = r30901249 * r30901255;
        return r30901256;
}

Error

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Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

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-inv0.2

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

  6. Final simplification0.2

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

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)))