Asymptote B

Average Error: 0.0 → 0.0

Time: 2.3s

Precision: binary64

Cost: 13504

Math

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

↓

\[\frac{1}{x + -1} + \log \left(e^{\frac{x}{1 + x}}\right) \]

FPCore

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

↓

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

C

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

↓

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

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
    code = (1.0d0 / (x + (-1.0d0))) + log(exp((x / (1.0d0 + x))))
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) {
	return (1.0 / (x + -1.0)) + Math.log(Math.exp((x / (1.0 + x))));
}

Python

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

↓

def code(x):
	return (1.0 / (x + -1.0)) + math.log(math.exp((x / (1.0 + x))))

Julia

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

↓

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

MATLAB

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

↓

function tmp = code(x)
	tmp = (1.0 / (x + -1.0)) + log(exp((x / (1.0 + x))));
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_] := N[(N[(1.0 / N[(x + -1.0), $MachinePrecision]), $MachinePrecision] + N[Log[N[Exp[N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

   \[\leadsto \frac{1}{x + -1} + \log \left(e^{\frac{x}{1 + x}}\right) \]

Alternatives

Alternative 1
Error	1.3
Cost	712

\[\begin{array}{l} t_0 := 1 + \frac{2}{x \cdot x}\\ \mathbf{if}\;x \leq -1359751.0928823305:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.8705524238096927 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{1}{x + -1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.0
Cost	704

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

Alternative 3
Error	31.2
Cost	448

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

Alternative 4
Error	31.7
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022312 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))