Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1

Average Accuracy: 100.0% → 100.0%

Time: 1.9s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	98.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Accuracy	98.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x + x \cdot x\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Accuracy	98.0%
Cost	328

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

Alternative 4
Accuracy	50.9%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023137 
(FPCore (x)
  :name "Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1"
  :precision binary64
  (/ x (- 1.0 x)))