neg log

Average Error: 0.0 → 0.0

Time: 1.6s

Precision: binary64

Cost: 6912

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Java

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

↓

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

Python

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

↓

def code(x):
	return -math.log1p((-1.0 + ((1.0 / x) + -1.0)))

Julia

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

↓

function code(x)
	return Float64(-log1p(Float64(-1.0 + Float64(Float64(1.0 / x) + -1.0))))
end

Wolfram

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

↓

code[x_] := (-N[Log[1 + N[(-1.0 + N[(N[(1.0 / x), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	6784

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

Alternative 2
Error	0.5
Cost	6592

\[x + \log x \]

Alternative 3
Error	1.1
Cost	6464

\[\log x \]

Alternative 4
Error	62.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022318 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1.0 x) 1.0))))