Average Error: 5.7 → 0.1
Time: 15.0s
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 r29781330 = 1.0;
        double r29781331 = x;
        double r29781332 = r29781330 - r29781331;
        double r29781333 = 3.0;
        double r29781334 = r29781333 - r29781331;
        double r29781335 = r29781332 * r29781334;
        double r29781336 = y;
        double r29781337 = r29781336 * r29781333;
        double r29781338 = r29781335 / r29781337;
        return r29781338;
}
↓
double f(double x, double y) {
        double r29781339 = 3.0;
        double r29781340 = x;
        double r29781341 = r29781339 - r29781340;
        double r29781342 = r29781341 / r29781339;
        double r29781343 = y;
        double r29781344 = r29781342 / r29781343;
        double r29781345 = 1.0;
        double r29781346 = r29781345 - r29781340;
        double r29781347 = r29781344 * r29781346;
        return r29781347;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.7
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.7

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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. Applied associate-*l*0.2

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 +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)))