Average Error: 16.7 → 0.0

Time: 6.3s

Precision: binary64

Cost: 448

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

↓

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

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

↓

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

(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))

↓

(FPCore (x y) :precision binary64 (+ (- 1.0 y) (* y x)))

double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}

↓

double code(double x, double y) {
	return (1.0 - y) + (y * x);
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	16.7
Target	0.0
Herbie	0.0

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

Alternatives

Alternative 1
Error	26.0
Cost	60736

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

Alternative 2
Error	25.8
Cost	14656

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

Alternative 3
Error	21.3
Cost	3008

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

Alternative 4
Error	50.7
Cost	2112

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

Alternative 5
Error	57.0
Cost	1600

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

Alternative 6
Error	30.9
Cost	1472

\[\frac{1 + \left(\left(y \cdot y\right) \cdot \left(3 - y\right) - y \cdot 3\right)}{\left(1 + y \cdot y\right) - y \cdot 2}\]

Alternative 7
Error	16.7
Cost	576

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

Alternative 8
Error	27.0
Cost	320

\[y \cdot x - y\]

Alternative 9
Error	44.4
Cost	192

\[y \cdot x\]

Alternative 10
Error	18.9
Cost	192

\[1 - y\]

Alternative 11
Error	36.2
Cost	64

\[1\]

Alternative 12
Error	62.3
Cost	64

\[0\]

Alternative 13
Error	62.4
Cost	64

\[-1\]

Error

Derivation

Initial program 16.7
\[x + \left(1 - x\right) \cdot \left(1 - y\right)\]
Simplified0.0
\[\leadsto \color{blue}{\left(1 - y\right) + x \cdot y}\]
Simplified0.0
\[\leadsto \color{blue}{\left(1 - y\right) + y \cdot x}\]
Final simplification0.0
\[\leadsto \left(1 - y\right) + y \cdot x\]

Reproduce

herbie shell --seed 2021042 
(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))))