Asymptote B

Average Error: 0.0 → 0.0

Time: 4.8s

Precision: binary64

Math

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

↓

\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + 1} + \frac{1}{x + -1}\right)\right) \]

FPCore

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

↓

(FPCore (x)
 :precision binary64
 (log1p (expm1 (+ (/ x (+ x 1.0)) (/ 1.0 (+ x -1.0))))))

C

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

↓

double code(double x) {
	return log1p(expm1(((x / (x + 1.0)) + (1.0 / (x + -1.0)))));
}

Java

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

↓

public static double code(double x) {
	return Math.log1p(Math.expm1(((x / (x + 1.0)) + (1.0 / (x + -1.0)))));
}

Python

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

↓

def code(x):
	return math.log1p(math.expm1(((x / (x + 1.0)) + (1.0 / (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)
	return log1p(expm1(Float64(Float64(x / Float64(x + 1.0)) + Float64(1.0 / Float64(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_] := N[Log[1 + N[(Exp[N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + 1} + \frac{1}{x + -1}\right)\right)} \]

3. Final simplification 0.0

   \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + 1} + \frac{1}{x + -1}\right)\right) \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))