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

Average Error: 5.7 → 0.2

Time: 27.4s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (((1.0d0 - x) / y) * (x + (-3.0d0))) / (-3.0d0)
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 (((1.0 - x) / y) * (x + -3.0)) / -3.0;
}

Python

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

↓

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

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(Float64(Float64(1.0 - x) / y) * Float64(x + -3.0)) / -3.0)
end

MATLAB

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

↓

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

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

Alternatives

Alternative 1
Error	1.4
Cost	904

\[\begin{array}{l} t_0 := \frac{\left(-\frac{x}{y}\right) \cdot \left(x + -3\right)}{-3}\\ \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1}{y} + -1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	1.4
Cost	840

\[\begin{array}{l} t_0 := \left(0.3333333333333333 \cdot x\right) \cdot \frac{x + -3}{y}\\ \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + -1.3333333333333333 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	1.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\frac{1 - x}{-3} \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + -1.3333333333333333 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(0.3333333333333333 \cdot x\right) \cdot \frac{x + -3}{y}\\ \end{array} \]

Alternative 4
Error	1.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\frac{1 - x}{-3} \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1}{y} + -1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(0.3333333333333333 \cdot x\right) \cdot \frac{x + -3}{y}\\ \end{array} \]

Alternative 5
Error	2.0
Cost	712

\[\begin{array}{l} t_0 := \left(0.3333333333333333 \cdot x\right) \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -1.72:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.1:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	1.5
Cost	712

\[\begin{array}{l} t_0 := \left(0.3333333333333333 \cdot x\right) \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -4.7:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + -1.3333333333333333 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	0.4
Cost	704

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

Alternative 8
Error	21.4
Cost	192

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

Reproduce

herbie shell --seed 2023010 
(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)))