Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

Average Error: 0.0 → 0.0

Time: 1.8s

Precision: binary64

Cost: 6976

Math

\[\sqrt{1 - x \cdot x} \]

↓

\[\left(1 + \sqrt{1 - x \cdot x}\right) + -1 \]

FPCore

(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))

↓

(FPCore (x) :precision binary64 (+ (+ 1.0 (sqrt (- 1.0 (* x x)))) -1.0))

C

double code(double x) {
	return sqrt((1.0 - (x * x)));
}

↓

double code(double x) {
	return (1.0 + sqrt((1.0 - (x * x)))) + -1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt((1.0d0 - (x * x)))
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 + sqrt((1.0d0 - (x * x)))) + (-1.0d0)
end function

Java

public static double code(double x) {
	return Math.sqrt((1.0 - (x * x)));
}

↓

public static double code(double x) {
	return (1.0 + Math.sqrt((1.0 - (x * x)))) + -1.0;
}

Python

def code(x):
	return math.sqrt((1.0 - (x * x)))

↓

def code(x):
	return (1.0 + math.sqrt((1.0 - (x * x)))) + -1.0

Julia

function code(x)
	return sqrt(Float64(1.0 - Float64(x * x)))
end

↓

function code(x)
	return Float64(Float64(1.0 + sqrt(Float64(1.0 - Float64(x * x)))) + -1.0)
end

MATLAB

function tmp = code(x)
	tmp = sqrt((1.0 - (x * x)));
end

↓

function tmp = code(x)
	tmp = (1.0 + sqrt((1.0 - (x * x)))) + -1.0;
end

Wolfram

code[x_] := N[Sqrt[N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

↓

code[x_] := N[(N[(1.0 + N[Sqrt[N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\sqrt{1 - x \cdot x} \]

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

   \[\leadsto \left(1 + \sqrt{1 - x \cdot x}\right) + -1 \]

Alternatives

Alternative 1
Error	0.0
Cost	6720

\[\sqrt{1 - x \cdot x} \]

Alternative 2
Error	0.6
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022306 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))