neg log

Average Error: 0.0 → 0.0

Time: 2.1s

Precision: binary64

Cost: 13248

Math

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

↓

\[\log \left(\sqrt{-1 + \frac{1}{x}}\right) \cdot -2 \]

FPCore

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

↓

(FPCore (x) :precision binary64 (* (log (sqrt (+ -1.0 (/ 1.0 x)))) -2.0))

C

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

↓

double code(double x) {
	return log(sqrt((-1.0 + (1.0 / x)))) * -2.0;
}

Fortran

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

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = log(sqrt(((-1.0d0) + (1.0d0 / x)))) * (-2.0d0)
end function

Java

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

↓

public static double code(double x) {
	return Math.log(Math.sqrt((-1.0 + (1.0 / x)))) * -2.0;
}

Python

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

↓

def code(x):
	return math.log(math.sqrt((-1.0 + (1.0 / x)))) * -2.0

Julia

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

↓

function code(x)
	return Float64(log(sqrt(Float64(-1.0 + Float64(1.0 / x)))) * -2.0)
end

MATLAB

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

↓

function tmp = code(x)
	tmp = log(sqrt((-1.0 + (1.0 / x)))) * -2.0;
end

Wolfram

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

↓

code[x_] := N[(N[Log[N[Sqrt[N[(-1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * -2.0), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 32.1

   \[\leadsto -\log \color{blue}{\left(\frac{{x}^{-2} + -1}{\frac{1}{x} - -1}\right)} \]

3. Applied egg-rr 0.0

   \[\leadsto -\color{blue}{2 \cdot \log \left(\sqrt{-1 + \frac{1}{x}}\right)} \]

4. Final simplification 0.0

   \[\leadsto \log \left(\sqrt{-1 + \frac{1}{x}}\right) \cdot -2 \]

Alternatives

Alternative 1
Error	0.0
Cost	6784

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

Alternative 2
Error	0.6
Cost	6592

\[x + \log x \]

Alternative 3
Error	1.2
Cost	6464

\[\log x \]

Alternative 4
Error	62.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022328 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1.0 x) 1.0))))