Average Error: 5.7 → 0.1
Time: 2.4s
Precision: binary64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \frac{1 - \frac{x}{3}}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \frac{1 - \frac{x}{3}}{y}
double code(double x, double y) {
	return (((double) (((double) (1.0 - x)) * ((double) (3.0 - x)))) / ((double) (y * 3.0)));
}
↓
double code(double x, double y) {
	return ((double) (((double) (1.0 - x)) * (((double) (1.0 - (x / 3.0))) / y)));
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 5.7

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

  2. Simplified0.4

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

  4. Applied associate-/r*0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020196 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))