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

Average Error: 5.5 → 0.2

Time: 10.7s

Precision: binary64

Cost: 1216

Math

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

↓

\[\begin{array}{l} t_0 := 3 \cdot \frac{y}{3 - x}\\ \frac{1}{t_0} - \frac{x}{t_0} \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 3.0 (/ y (- 3.0 x))))) (- (/ 1.0 t_0) (/ x t_0))))

C

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

↓

double code(double x, double y) {
	double t_0 = 3.0 * (y / (3.0 - x));
	return (1.0 / t_0) - (x / t_0);
}

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
    real(8) :: t_0
    t_0 = 3.0d0 * (y / (3.0d0 - x))
    code = (1.0d0 / t_0) - (x / t_0)
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) {
	double t_0 = 3.0 * (y / (3.0 - x));
	return (1.0 / t_0) - (x / t_0);
}

Python

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

↓

def code(x, y):
	t_0 = 3.0 * (y / (3.0 - x))
	return (1.0 / t_0) - (x / t_0)

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)
	t_0 = Float64(3.0 * Float64(y / Float64(3.0 - x)))
	return Float64(Float64(1.0 / t_0) - Float64(x / t_0))
end

MATLAB

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

↓

function tmp = code(x, y)
	t_0 = 3.0 * (y / (3.0 - x));
	tmp = (1.0 / t_0) - (x / t_0);
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_] := Block[{t$95$0 = N[(3.0 * N[(y / N[(3.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(1.0 / t$95$0), $MachinePrecision] - N[(x / t$95$0), $MachinePrecision]), $MachinePrecision]]

Target

Original	5.5
Target	0.1
Herbie	0.2

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

Derivation

1. Initial program 5.5

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

2. Applied egg-rr 0.2

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

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.3
Cost	968

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+68}:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 10^{+76}:\\ \;\;\;\;\frac{\frac{\left(3 - x\right) \cdot \left(1 - x\right)}{y}}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \end{array} \]

Alternative 2
Error	1.5
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -14594907.282178322:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 0.22570405195942841:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \]

Alternative 3
Error	1.2
Cost	840

\[\begin{array}{l} t_0 := 0.3333333333333333 \cdot \frac{x + -4}{\frac{y}{x}}\\ \mathbf{if}\;x \leq -14594907.282178322:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.22570405195942841:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	2.0
Cost	712

\[\begin{array}{l} t_0 := \frac{x \cdot \frac{x}{y}}{3}\\ \mathbf{if}\;x \leq -14594907.282178322:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.857745496851575:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	2.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -14594907.282178322:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 1.857745496851575:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{3 \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 6
Error	2.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -14594907.282178322:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 1.857745496851575:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{3}{x}}\\ \end{array} \]

Alternative 7
Error	2.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -14594907.282178322:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 1.857745496851575:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{3 \cdot y}\\ \end{array} \]

Alternative 8
Error	1.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -14594907.282178322:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 1.857745496851575:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{3 \cdot y}\\ \end{array} \]

Alternative 9
Error	0.5
Cost	704

\[\frac{1 - x}{\frac{y}{3 - x}} \cdot 0.3333333333333333 \]

Alternative 10
Error	0.4
Cost	704

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

Alternative 11
Error	21.1
Cost	192

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

Reproduce

herbie shell --seed 2022290 
(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)))