Average Error: 5.7 → 0.2
Time: 10.2s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{\frac{1 - x}{y}}{3} \cdot \left(3 - x\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{\frac{1 - x}{y}}{3} \cdot \left(3 - x\right)
double f(double x, double y) {
        double r541120 = 1.0;
        double r541121 = x;
        double r541122 = r541120 - r541121;
        double r541123 = 3.0;
        double r541124 = r541123 - r541121;
        double r541125 = r541122 * r541124;
        double r541126 = y;
        double r541127 = r541126 * r541123;
        double r541128 = r541125 / r541127;
        return r541128;
}
↓
double f(double x, double y) {
        double r541129 = 1.0;
        double r541130 = x;
        double r541131 = r541129 - r541130;
        double r541132 = y;
        double r541133 = r541131 / r541132;
        double r541134 = 3.0;
        double r541135 = r541133 / r541134;
        double r541136 = r541134 - r541130;
        double r541137 = r541135 * r541136;
        return r541137;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.7
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.7

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

  2. Simplified0.3

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

  4. Applied div-inv0.4

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

  5. Applied associate-*l*0.4

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(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)))