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

Average Error: 5.7 → 0.2

Time: 11.8s

Precision: binary64

Cost: 7168

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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
    code = ((3.0d0 / (1.0d0 - x)) * (y / (3.0d0 - x))) ** (-1.0d0)
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 Math.pow(((3.0 / (1.0 - x)) * (y / (3.0 - x))), -1.0);
}

Python

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

↓

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

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

MATLAB

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

↓

function tmp = code(x, y)
	tmp = ((3.0 / (1.0 - x)) * (y / (3.0 - x))) ^ -1.0;
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_] := N[Power[N[(N[(3.0 / N[(1.0 - x), $MachinePrecision]), $MachinePrecision] * N[(y / N[(3.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]

Target

Original	5.7
Target	0.1
Herbie	0.2

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

Derivation

1. Initial program 5.7

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

2. Applied egg-rr 0.2

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

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.2
Cost	1216

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

Alternative 2
Error	1.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -107374263682434540:\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 0.07130029820204853:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)\\ \end{array} \]

Alternative 3
Error	1.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -107374263682434540:\\ \;\;\;\;\frac{0.3333333333333333 - \frac{x}{3}}{\frac{-y}{x}}\\ \mathbf{elif}\;x \leq 0.07130029820204853:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)\\ \end{array} \]

Alternative 4
Error	2.0
Cost	712

\[\begin{array}{l} t_0 := \frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{if}\;x \leq -107374263682434540:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.07130029820204853:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	2.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -107374263682434540:\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 0.07130029820204853:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{3 \cdot y}\\ \end{array} \]

Alternative 6
Error	0.4
Cost	704

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

Alternative 7
Error	21.4
Cost	192

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

Reproduce

herbie shell --seed 2022318 
(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)))