?

Average Accuracy: 100.0% → 100.0%

Time: 2.4s

Precision: binary64

Cost: 19392

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

↓

\[-\log \left(\mathsf{expm1}\left(-\log x\right)\right) \]

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

↓

(FPCore (x) :precision binary64 (- (log (expm1 (- (log x))))))

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

↓

double code(double x) {
	return -log(expm1(-log(x)));
}

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

↓

public static double code(double x) {
	return -Math.log(Math.expm1(-Math.log(x)));
}

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

↓

def code(x):
	return -math.log(math.expm1(-math.log(x)))

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

↓

function code(x)
	return Float64(-log(expm1(Float64(-log(x)))))
end

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

↓

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

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

↓

-\log \left(\mathsf{expm1}\left(-\log x\right)\right)

Try it out?

In
Out

Enter valid numbers for all inputs

Initial program 100.0%
\[-\log \left(\frac{1}{x} - 1\right) \]
Applied egg-rr100.0%
\[\leadsto -\log \color{blue}{\left(\mathsf{expm1}\left(-\log x\right)\right)} \]
Final simplification100.0%
\[\leadsto -\log \left(\mathsf{expm1}\left(-\log x\right)\right) \]

Alternative 1
Accuracy	100.0%
Cost	6784

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

Alternative 2
Accuracy	99.1%
Cost	6592

\[x + \log x \]

Alternative 3
Accuracy	0.0%
Cost	6528

\[-\log -1 \]

Alternative 4
Accuracy	98.2%
Cost	6464

\[\log x \]

herbie shell --seed 2023129 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1.0 x) 1.0))))