Average Error: 0.0 → 0.0
Time: 6.7s
Precision: 64
Internal Precision: 128
\[-\log \left(\frac{1}{x} - 1\right)\]
\[-\log \left(\frac{1}{x} - 1\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[-\log \left(\frac{1}{x} - 1\right)\]
  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 6.5s)Debug log

sample199.0ms

Algorithm
intervals

simplify12.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

11.0ms
(- (log (- (/ 1 x) 1)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 2 expressions with local error:

0.0b
(log (- (/ 1 x) 1))
0.0b
(- (/ 1 x) 1)

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
2 → 36
Calls

2 calls. Slowest were:

8.0ms
(- (/ 1 x) 1)
7.0ms
(log (- (/ 1 x) 1))

series55.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

44.0ms
(log (- (/ 1 x) 1))
10.0ms
(- (/ 1 x) 1)

simplify651.0ms

Counts
17 → 42
Calls

17 calls. Slowest were:

219.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))
139.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
137.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))

prune361.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 2 expressions with local error:

5.6b
(expm1 (- (log x)))
0.0b
(log (expm1 (- (log x))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

2.0ms
(log (expm1 (- (log x))))
1.0ms
(expm1 (- (log x)))

series648.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

331.0ms
(log (expm1 (- (log x))))
316.0ms
(expm1 (- (log x)))

simplify596.0ms

Counts
11 → 31
Calls

11 calls. Slowest were:

310.0ms
(log (- (exp (- (log (/ -1 x)) (log -1))) 1))
263.0ms
(- (exp (- (log (/ -1 x)) (log -1))) 1)
4.0ms
(log (- (/ 1 x) 1))

prune335.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes171.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample3.3s

Algorithm
intervals