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

Average Error: 15.9 → 0.0

Time: 2.0s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (y * (x + (-1.0d0))) + 1.0d0
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 (y * (x + -1.0)) + 1.0;
}

Python

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

↓

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

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(y * Float64(x + -1.0)) + 1.0)
end

MATLAB

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

↓

function tmp = code(x, y)
	tmp = (y * (x + -1.0)) + 1.0;
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[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]

Target

Original	15.9
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 15.9

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

2. Simplified 0.0

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

   [Start] 15.9	\[ x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   rational_best_oopsla_all_46_json_45_simplify-87 [=>] 15.9	\[ x + \color{blue}{\left(-\left(1 - x\right)\right) \cdot \left(y - 1\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-13 [=>] 15.9	\[ x + \color{blue}{\left(y \cdot \left(-\left(1 - x\right)\right) - \left(-\left(1 - x\right)\right) \cdot 1\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 15.9	\[ x + \left(y \cdot \left(-\left(1 - x\right)\right) - \color{blue}{\left(-\left(1 - x\right)\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-97 [=>] 15.9	\[ x + \left(y \cdot \left(-\left(1 - x\right)\right) - \color{blue}{\left(0 - \left(1 - x\right)\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-36 [=>] 15.9	\[ x + \left(y \cdot \left(-\left(1 - x\right)\right) - \color{blue}{\left(x - \left(1 - 0\right)\right)}\right) \]
   metadata-eval [=>] 15.9	\[ x + \left(y \cdot \left(-\left(1 - x\right)\right) - \left(x - \color{blue}{1}\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-45 [=>] 15.9	\[ x + \left(y \cdot \left(-\left(1 - x\right)\right) - \color{blue}{\left(x + -1\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-109 [=>] 0.0	\[ \color{blue}{y \cdot \left(-\left(1 - x\right)\right) - -1} \]
   rational_best_oopsla_all_46_json_45_simplify-1 [=>] 0.0	\[ \color{blue}{y \cdot \left(-\left(1 - x\right)\right) + 1} \]
   rational_best_oopsla_all_46_json_45_simplify-97 [=>] 0.0	\[ y \cdot \color{blue}{\left(0 - \left(1 - x\right)\right)} + 1 \]
   rational_best_oopsla_all_46_json_45_simplify-36 [=>] 0.0	\[ y \cdot \color{blue}{\left(x - \left(1 - 0\right)\right)} + 1 \]
   metadata-eval [=>] 0.0	\[ y \cdot \left(x - \color{blue}{1}\right) + 1 \]
   rational_best_oopsla_all_46_json_45_simplify-45 [=>] 0.0	\[ y \cdot \color{blue}{\left(x + -1\right)} + 1 \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	9.9
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(x - 1\right)\\ \mathbf{if}\;y \leq -360000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-43}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	27.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-43}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3
Error	9.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+48}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+90}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4
Error	36.5
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023090 
(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))))