Average Error: 5.6 → 0.1
Time: 4.2s
Precision: binary64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{\frac{1 - x}{y}}{\frac{3}{3 - x}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{\frac{1 - x}{y}}{\frac{3}{3 - x}}
(FPCore (x y) :precision binary64 (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))
↓
(FPCore (x y) :precision binary64 (/ (/ (- 1.0 x) y) (/ 3.0 (- 3.0 x))))
double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}
↓
double code(double x, double y) {
	return ((1.0 - x) / y) / (3.0 / (3.0 - x));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.6
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.6

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

  3. Applied associate-/l*_binary640.3

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

  4. Simplified0.1

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

  6. Applied associate-/r/_binary640.2

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

  7. Applied associate-/r*_binary640.4

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

  8. Simplified0.3

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

  10. Applied associate-/l*_binary640.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2021176 
(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)))