Average Error: 0.2 → 0.2
Time: 2.0s
Precision: binary64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[y \cdot \left(x \cdot 3 - 0.41379310344827586\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
y \cdot \left(x \cdot 3 - 0.41379310344827586\right)
(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))
↓
(FPCore (x y) :precision binary64 (* y (- (* x 3.0) 0.41379310344827586)))
double code(double x, double y) {
	return ((double) (((double) (((double) (x - (16.0 / 116.0))) * 3.0)) * y));
}
↓
double code(double x, double y) {
	return ((double) (y * ((double) (((double) (x * 3.0)) - 0.41379310344827586))));
}

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 Error: 0.2 bits

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

  2. Taylor expanded around 0 Error: 0.2 bits

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

  3. SimplifiedError: 0.2 bits

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

  4. Final simplificationError: 0.2 bits

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

Reproduce

herbie shell --seed 2020203 
(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))