Prelude:atanh from fay-base-0.20.0.1

Average Error: 0.0 → 0.0

Time: 2.2s

Precision: binary64

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

def code(x):
	return math.pow(((1.0 - x) / (1.0 + x)), -1.0)

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2022210 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1.0) (- 1.0 x)))