Average Error: 5.9 → 0.1
Time: 10.3s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y \cdot \frac{3}{3 - x}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y \cdot \frac{3}{3 - x}}
double f(double x, double y) {
        double r445951 = 1.0;
        double r445952 = x;
        double r445953 = r445951 - r445952;
        double r445954 = 3.0;
        double r445955 = r445954 - r445952;
        double r445956 = r445953 * r445955;
        double r445957 = y;
        double r445958 = r445957 * r445954;
        double r445959 = r445956 / r445958;
        return r445959;
}
↓
double f(double x, double y) {
        double r445960 = 1.0;
        double r445961 = x;
        double r445962 = r445960 - r445961;
        double r445963 = y;
        double r445964 = 3.0;
        double r445965 = r445964 - r445961;
        double r445966 = r445964 / r445965;
        double r445967 = r445963 * r445966;
        double r445968 = r445962 / r445967;
        return r445968;
}

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 clear-num0.2

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

  7. Applied frac-times0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019209 
(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)))