Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1

Average Error: 0.0 → 0.0

Time: 2.5s

Precision: binary64

Cost: 960

Math

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

↓

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

FPCore

(FPCore (x) :precision binary64 (/ x (- 1.0 x)))

↓

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

C

double code(double x) {
	return x / (1.0 - x);
}

↓

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

Fortran

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

↓

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

Java

public static double code(double x) {
	return x / (1.0 - x);
}

↓

public static double code(double x) {
	return (x / ((1.0 / x) - x)) + (x / (1.0 - (x * x)));
}

Python

def code(x):
	return x / (1.0 - x)

↓

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

Julia

function code(x)
	return Float64(x / Float64(1.0 - x))
end

↓

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

MATLAB

function tmp = code(x)
	tmp = x / (1.0 - x);
end

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 15.5

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

3. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\frac{x}{\frac{1}{x} - x} + \frac{x}{1 - x \cdot x}} \]

4. Final simplification 0.0

   \[\leadsto \frac{x}{\frac{1}{x} - x} + \frac{x}{1 - x \cdot x} \]

Alternatives

Alternative 1
Error	1.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -3808397.5679019354:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 0.0008334005333199306:\\ \;\;\;\;x + x \cdot x\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Error	1.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -3808397.5679019354:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 0.0008334005333199306:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Error	0.0
Cost	320

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

Alternative 4
Error	31.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022308 
(FPCore (x)
  :name "Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1"
  :precision binary64
  (/ x (- 1.0 x)))