Average Error: 5.9 → 0.1
Time: 15.8s
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 r363922 = 1.0;
        double r363923 = x;
        double r363924 = r363922 - r363923;
        double r363925 = 3.0;
        double r363926 = r363925 - r363923;
        double r363927 = r363924 * r363926;
        double r363928 = y;
        double r363929 = r363928 * r363925;
        double r363930 = r363927 / r363929;
        return r363930;
}
↓
double f(double x, double y) {
        double r363931 = 3.0;
        double r363932 = x;
        double r363933 = r363931 - r363932;
        double r363934 = r363933 / r363931;
        double r363935 = 1.0;
        double r363936 = r363935 - r363932;
        double r363937 = y;
        double r363938 = r363936 / r363937;
        double r363939 = r363934 * r363938;
        return r363939;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.9
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.9

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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 *-un-lft-identity0.1

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

  6. Applied *-un-lft-identity0.1

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

  7. Applied times-frac0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1 x) y) (/ (- 3 x) 3))

  (/ (* (- 1 x) (- 3 x)) (* y 3)))