Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3

Average Error: 5.6 → 0.1

Time: 8.5s

Precision: binary64

Cost: 704

Math

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

↓

\[\frac{x + -3}{3} \cdot \frac{x + -1}{y} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))

↓

(FPCore (x y) :precision binary64 (* (/ (+ x -3.0) 3.0) (/ (+ x -1.0) y)))

C

double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}

↓

double code(double x, double y) {
	return ((x + -3.0) / 3.0) * ((x + -1.0) / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) * (3.0d0 - x)) / (y * 3.0d0)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + (-3.0d0)) / 3.0d0) * ((x + (-1.0d0)) / y)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}

↓

public static double code(double x, double y) {
	return ((x + -3.0) / 3.0) * ((x + -1.0) / y);
}

Python

def code(x, y):
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0)

↓

def code(x, y):
	return ((x + -3.0) / 3.0) * ((x + -1.0) / y)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) * Float64(3.0 - x)) / Float64(y * 3.0))
end

↓

function code(x, y)
	return Float64(Float64(Float64(x + -3.0) / 3.0) * Float64(Float64(x + -1.0) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) * (3.0 - x)) / (y * 3.0);
end

↓

function tmp = code(x, y)
	tmp = ((x + -3.0) / 3.0) * ((x + -1.0) / y);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(N[(x + -3.0), $MachinePrecision] / 3.0), $MachinePrecision] * N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Target

Original	5.6
Target	0.1
Herbie	0.1

\[\frac{1 - x}{y} \cdot \frac{3 - x}{3} \]

Derivation

1. Initial program 5.6

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

2. Simplified 0.1

   \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}} \]
   Proof

   [Start] 5.6	\[ \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   times-frac [=>] 0.1	\[ \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}} \]

3. Final simplification 0.1

   \[\leadsto \frac{x + -3}{3} \cdot \frac{x + -1}{y} \]

Alternatives

Alternative 1
Error	1.4
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\left(1 - x\right) \cdot \frac{\frac{x}{-3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

Alternative 2
Error	1.4
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;\frac{3 - x}{-3 \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

Alternative 3
Error	1.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\frac{3 - x}{\frac{y}{\frac{x}{-3}}}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{3 - x}{-3 \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 4
Error	1.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\frac{3 - x}{\frac{y}{\frac{x}{-3}}}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x + -3}{3}\\ \end{array} \]

Alternative 5
Error	1.9
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \]

Alternative 6
Error	1.9
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \end{array} \]

Alternative 7
Error	1.9
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} - \frac{x}{y}\\ \end{array} \]

Alternative 8
Error	1.5
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -4.6 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

Alternative 9
Error	1.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\left(1 - x\right) \cdot \left(-0.3333333333333333 \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternative 10
Error	0.4
Cost	704

\[\left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

Alternative 11
Error	0.2
Cost	704

\[\left(x + -1\right) \cdot \frac{0.3333333333333333 \cdot \left(x + -3\right)}{y} \]

Alternative 12
Error	21.0
Cost	192

\[\frac{1}{y} \]

Reproduce

herbie shell --seed 2022354 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))