Average Error: 5.2 → 0.1
Time: 2.7s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \frac{3 - x}{3}
double f(double x, double y) {
        double r818204 = 1.0;
        double r818205 = x;
        double r818206 = r818204 - r818205;
        double r818207 = 3.0;
        double r818208 = r818207 - r818205;
        double r818209 = r818206 * r818208;
        double r818210 = y;
        double r818211 = r818210 * r818207;
        double r818212 = r818209 / r818211;
        return r818212;
}
↓
double f(double x, double y) {
        double r818213 = 1.0;
        double r818214 = x;
        double r818215 = r818213 - r818214;
        double r818216 = y;
        double r818217 = r818215 / r818216;
        double r818218 = 3.0;
        double r818219 = r818218 - r818214;
        double r818220 = r818219 / r818218;
        double r818221 = r818217 * r818220;
        return r818221;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.2

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

  3. Applied times-frac0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020035 
(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)))