Average Error: 5.2 → 0.1
Time: 3.6s
Precision: binary64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
↓
\[\left(\frac{1}{y} - \frac{x}{y}\right) \cdot \frac{3 - x}{3} \]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(\frac{1}{y} - \frac{x}{y}\right) \cdot \frac{3 - x}{3}

(FPCore (x y) :precision binary64 (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))
↓
(FPCore (x y) :precision binary64 (* (- (/ 1.0 y) (/ x y)) (/ (- 3.0 x) 3.0)))
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 / y) - (x / y)) * ((3.0 - x) / 3.0);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.2
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. Applied times-frac_binary640.1

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

  3. Taylor expanded in x around 0 0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2022068 
(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)))