Average Error: 16.3 → 0.0
Time: 1.9s
Precision: binary64
\[x + \left(1 - x\right) \cdot \left(1 - y\right)\]
↓
\[1 + y \cdot \left(x - 1\right)\]
x + \left(1 - x\right) \cdot \left(1 - y\right)
↓
1 + y \cdot \left(x - 1\right)
(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))
↓
(FPCore (x y) :precision binary64 (+ 1.0 (* y (- x 1.0))))
double code(double x, double y) {
	return ((double) (x + ((double) (((double) (1.0 - x)) * ((double) (1.0 - y))))));
}
↓
double code(double x, double y) {
	return ((double) (1.0 + ((double) (y * ((double) (x - 1.0))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.3
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program Error: 16.3 bits

    \[x + \left(1 - x\right) \cdot \left(1 - y\right)\]

  2. Taylor expanded around 0 Error: 0.0 bits

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

  3. SimplifiedError: 0.0 bits

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

  4. Final simplificationError: 0.0 bits

    \[\leadsto 1 + y \cdot \left(x - 1\right)\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- (* y x) (- y 1.0))

  (+ x (* (- 1.0 x) (- 1.0 y))))