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

Average Error: 5.3 → 0.2

Time: 7.7s

Precision: binary64

Cost: 832

Math

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

↓

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

FPCore

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

↓

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

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

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

Python

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

↓

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

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(1.0 - x) * Float64(1.0 / Float64(3.0 * Float64(y / Float64(3.0 - x)))))
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) * (1.0 / (3.0 * (y / (3.0 - x))));
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[(1.0 - x), $MachinePrecision] * N[(1.0 / N[(3.0 * N[(y / N[(3.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	5.3
Target	0.1
Herbie	0.2

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

Derivation

1. Initial program 5.3

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

2. Applied egg-rr 0.2

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

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	1.2
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -26.39673911123875:\\ \;\;\;\;\frac{\frac{x}{y} \cdot \left(x + -4\right)}{3}\\ \mathbf{elif}\;x \leq 0.0032627013708721782:\\ \;\;\;\;\frac{3 + x \cdot -4}{3 \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{3 \cdot y}\\ \end{array} \]

Alternative 2
Error	2.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -26.39673911123875:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 0.0032627013708721782:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \]

Alternative 3
Error	0.4
Cost	704

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

Alternative 4
Error	20.8
Cost	192

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

Reproduce

herbie shell --seed 2022289 
(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)))