Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3

Average Error: 16.4 → 0.0

Time: 2.6s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((1.0d0 - x) * (1.0d0 - y))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 + (y * x)) - y
end function

Java

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

↓

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

Python

def code(x, y):
	return x + ((1.0 - x) * (1.0 - y))

↓

def code(x, y):
	return (1.0 + (y * x)) - y

Julia

function code(x, y)
	return Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y)))
end

↓

function code(x, y)
	return Float64(Float64(1.0 + Float64(y * x)) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((1.0 - x) * (1.0 - y));
end

↓

function tmp = code(x, y)
	tmp = (1.0 + (y * x)) - y;
end

Wolfram

code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]

Target

Original	16.4
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 16.4

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

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, 1\right) - y} \]

3. Taylor expanded in x around 0 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	10.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+115}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.7193464721373824 \cdot 10^{+37}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 2
Error	10.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+115}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.7193464721373824 \cdot 10^{+37}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3
Error	19.8
Cost	392

\[\begin{array}{l} \mathbf{if}\;y \leq -1.8490581912368364 \cdot 10^{-18}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 2.3583391504686918 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 4
Error	18.7
Cost	192

\[1 - y \]

Alternative 5
Error	37.0
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022228 
(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))))