Average Error: 5.6 → 0.1
Time: 3.4s
Precision: binary64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
↓
\[\frac{1 - x}{y \cdot \frac{3}{3 - x}} \]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y \cdot \frac{3}{3 - x}}

(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. Applied times-frac_binary640.1

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

  3. Applied clear-num_binary640.2

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

  4. Applied frac-times_binary640.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2021329 
(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)))