neg log

Average Error: 0.0 → 0.0

Time: 3.4s

Precision: binary64

Cost: 7040

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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((((x * (1.0d0 - x)) / x) / x))
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((((x * (1.0 - x)) / x) / x));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

3. Applied egg-rr 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	6784

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

Alternative 2
Error	1.1
Cost	6656

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

Alternative 3
Error	64.0
Cost	6528

\[-\log -1 \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1.0 x) 1.0))))