Average Error: 0.2 → 0.2
Time: 1.7s
Precision: binary64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
↓
\[y \cdot -0.41379310344827586 + 3 \cdot \left(y \cdot x\right) \]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
y \cdot -0.41379310344827586 + 3 \cdot \left(y \cdot x\right)

(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))
↓
(FPCore (x y)
 :precision binary64
 (+ (* y -0.41379310344827586) (* 3.0 (* y x))))
double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}
↓
double code(double x, double y) {
	return (y * -0.41379310344827586) + (3.0 * (y * 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

Original0.2
Target0.2
Herbie0.2
\[y \cdot \left(x \cdot 3 - 0.41379310344827586\right) \]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

  2. Simplified0.2

    \[\leadsto \color{blue}{\left(\left(x - 0.13793103448275862\right) \cdot 3\right) \cdot y} \]

  3. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right) - 0.41379310344827586 \cdot y} \]

  4. Simplified0.2

    \[\leadsto \color{blue}{y \cdot \left(-0.41379310344827586 + 3 \cdot x\right)} \]
  5. Using strategy rm

  6. Applied distribute-rgt-in_binary640.2

    \[\leadsto \color{blue}{-0.41379310344827586 \cdot y + \left(3 \cdot x\right) \cdot y} \]

  7. Simplified0.2

    \[\leadsto \color{blue}{y \cdot -0.41379310344827586} + \left(3 \cdot x\right) \cdot y \]

  8. Simplified0.2

    \[\leadsto y \cdot -0.41379310344827586 + \color{blue}{3 \cdot \left(x \cdot y\right)} \]

  9. Final simplification0.2

    \[\leadsto y \cdot -0.41379310344827586 + 3 \cdot \left(y \cdot x\right) \]

Reproduce

herbie shell --seed 2021198 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))