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

Average Accuracy: 74.4% → 100.0%

Time: 2.9s

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	74.4%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 74.4%

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

2. Taylor expanded in x around -inf 100.0%

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

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	69.4%
Cost	788

\[\begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+135}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+113}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-51}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 2
Accuracy	84.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-51} \lor \neg \left(y \leq 1.3 \cdot 10^{-21}\right):\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 3
Accuracy	84.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-52}:\\ \;\;\;\;y \cdot x - y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-19}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 4
Accuracy	69.9%
Cost	392

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 5
Accuracy	77.9%
Cost	324

\[\begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 6
Accuracy	43.6%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023140 
(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))))