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

Average Error: 6.0 → 6.1

Time: 8.2s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (* 0.3333333333333333 (/ (* (- 3.0 x) (- 1.0 x)) 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 0.3333333333333333 * (((3.0 - x) * (1.0 - x)) / 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 = 0.3333333333333333d0 * (((3.0d0 - x) * (1.0d0 - x)) / 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 0.3333333333333333 * (((3.0 - x) * (1.0 - x)) / y);
}

Python

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

↓

def code(x, y):
	return 0.3333333333333333 * (((3.0 - x) * (1.0 - x)) / 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(0.3333333333333333 * Float64(Float64(Float64(3.0 - x) * Float64(1.0 - x)) / 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 = 0.3333333333333333 * (((3.0 - x) * (1.0 - x)) / 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[(0.3333333333333333 * N[(N[(N[(3.0 - x), $MachinePrecision] * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Target

Original	6.0
Target	0.1
Herbie	6.1

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

Derivation

1. Initial program 6.0

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

2. Taylor expanded in y around 0 6.1

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

3. Final simplification 6.1

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

Alternatives

Alternative 1
Error	21.2
Cost	448

\[\frac{1 + -1.3333333333333333 \cdot x}{y} \]

Alternative 2
Error	21.5
Cost	192

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

Reproduce

herbie shell --seed 2023090 
(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)))