Asymptote B

Average Error: 0.0 → 0.0

Time: 3.2s

Precision: binary64

Cost: 1216

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1 + x}{x}\\ \frac{t_0 + \left(x + -1\right)}{t_0 \cdot \left(x + -1\right)} \end{array} \]

FPCore

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

↓

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ (+ 1.0 x) x))) (/ (+ t_0 (+ x -1.0)) (* t_0 (+ x -1.0)))))

C

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

↓

double code(double x) {
	double t_0 = (1.0 + x) / x;
	return (t_0 + (x + -1.0)) / (t_0 * (x + -1.0));
}

Fortran

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

↓

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = (1.0d0 + x) / x
    code = (t_0 + (x + (-1.0d0))) / (t_0 * (x + (-1.0d0)))
end function

Java

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

↓

public static double code(double x) {
	double t_0 = (1.0 + x) / x;
	return (t_0 + (x + -1.0)) / (t_0 * (x + -1.0));
}

Python

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

↓

def code(x):
	t_0 = (1.0 + x) / x
	return (t_0 + (x + -1.0)) / (t_0 * (x + -1.0))

Julia

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

↓

function code(x)
	t_0 = Float64(Float64(1.0 + x) / x)
	return Float64(Float64(t_0 + Float64(x + -1.0)) / Float64(t_0 * Float64(x + -1.0)))
end

MATLAB

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

↓

function tmp = code(x)
	t_0 = (1.0 + x) / x;
	tmp = (t_0 + (x + -1.0)) / (t_0 * (x + -1.0));
end

Wolfram

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

↓

code[x_] := Block[{t$95$0 = N[(N[(1.0 + x), $MachinePrecision] / x), $MachinePrecision]}, N[(N[(t$95$0 + N[(x + -1.0), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.7
Cost	840

\[\begin{array}{l} t_0 := 1 + \frac{2}{x \cdot x}\\ \mathbf{if}\;x \leq -112.44324702630625:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.00037218625360065295:\\ \;\;\;\;\frac{x}{1 + x} + \left(-1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.7
Cost	712

\[\begin{array}{l} t_0 := 1 + \frac{2}{x \cdot x}\\ \mathbf{if}\;x \leq -112.44324702630625:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.00037218625360065295:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.7
Cost	712

\[\begin{array}{l} t_0 := 1 + \frac{2}{x \cdot x}\\ \mathbf{if}\;x \leq -112.44324702630625:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.00037218625360065295:\\ \;\;\;\;x + \frac{1}{x + -1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.0
Cost	704

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

Alternative 5
Error	31.6
Cost	192

\[x + -1 \]

Alternative 6
Error	31.8
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022317 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))