Average Error: 16.9 → 0.0
Time: 2.0s
Precision: binary64
\[x + \left(1 - x\right) \cdot \left(1 - y\right)\]
↓
\[\left(1 + x \cdot y\right) - y\]
x + \left(1 - x\right) \cdot \left(1 - y\right)
↓
\left(1 + x \cdot y\right) - y
(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))
↓
(FPCore (x y) :precision binary64 (- (+ 1.0 (* x y)) y))
double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}
↓
double code(double x, double y) {
	return (1.0 + (x * y)) - y;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.9
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program 16.9

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

  2. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2021043 
(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))))