Average Error: 5.3 → 0.1
Time: 7.8s
Precision: 64
\[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
↓
\[\frac{\frac{3.0 - x}{3.0}}{y} \cdot \left(1.0 - x\right)\]
\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}
↓
\frac{\frac{3.0 - x}{3.0}}{y} \cdot \left(1.0 - x\right)
double f(double x, double y) {
        double r13672989 = 1.0;
        double r13672990 = x;
        double r13672991 = r13672989 - r13672990;
        double r13672992 = 3.0;
        double r13672993 = r13672992 - r13672990;
        double r13672994 = r13672991 * r13672993;
        double r13672995 = y;
        double r13672996 = r13672995 * r13672992;
        double r13672997 = r13672994 / r13672996;
        return r13672997;
}
↓
double f(double x, double y) {
        double r13672998 = 3.0;
        double r13672999 = x;
        double r13673000 = r13672998 - r13672999;
        double r13673001 = r13673000 / r13672998;
        double r13673002 = y;
        double r13673003 = r13673001 / r13673002;
        double r13673004 = 1.0;
        double r13673005 = r13673004 - r13672999;
        double r13673006 = r13673003 * r13673005;
        return r13673006;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.3
Target0.1
Herbie0.1
\[\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}\]

Derivation

  1. Initial program 5.3

    \[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
  2. Using strategy rm

  3. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

    \[\leadsto \color{blue}{\left(\left(1.0 - x\right) \cdot \frac{1}{y}\right)} \cdot \frac{3.0 - x}{3.0}\]
  6. Using strategy rm

  7. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\left(1.0 - x\right) \cdot \left(\frac{1}{y} \cdot \frac{3.0 - x}{3.0}\right)}\]

  8. Simplified0.1

    \[\leadsto \left(1.0 - x\right) \cdot \color{blue}{\frac{\frac{3.0 - x}{3.0}}{y}}\]

  9. Final simplification0.1

    \[\leadsto \frac{\frac{3.0 - x}{3.0}}{y} \cdot \left(1.0 - x\right)\]

Reproduce

herbie shell --seed 2019156 
(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)))