Average Error: 0.0 → 0.0
Time: 11.7s
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 2018360 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 5.9s)Debug log

start229.0ms

Algorithm
intervals

setup22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
2 → 36
Calls

2 calls. Slowest were:

4.0ms
(log (- (/ 1 x) 1))
3.0ms
(- (/ 1 x) 1)

series57.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

29.0ms
(- (/ 1 x) 1)
27.0ms
(log (- (/ 1 x) 1))

simplify514.0ms

Counts
17 → 42
Calls

17 calls. Slowest were:

208.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))
109.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
65.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))

prune351.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- (/ 1 x) 1))
0.5b
(cbrt (- (/ 1 x) 1))
0.5b
(cbrt (- (/ 1 x) 1))
0.5b
(* (cbrt (- (/ 1 x) 1)) (cbrt (- (/ 1 x) 1)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Counts
4 → 88
Calls

4 calls. Slowest were:

19.0ms
(* (cbrt (- (/ 1 x) 1)) (cbrt (- (/ 1 x) 1)))
4.0ms
(cbrt (- (/ 1 x) 1))
3.0ms
(cbrt (- (/ 1 x) 1))

series227.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

68.0ms
(cbrt (- (/ 1 x) 1))
66.0ms
(cbrt (- (/ 1 x) 1))
48.0ms
(* (cbrt (- (/ 1 x) 1)) (cbrt (- (/ 1 x) 1)))
45.0ms
(cbrt (- (/ 1 x) 1))

simplify3.0s

Counts
64 → 100
Calls

64 calls. Slowest were:

306.0ms
(- (cbrt -1) (+ (* 1/3 (/ (cbrt -1) x)) (* 1/9 (/ (cbrt -1) (pow x 2)))))
280.0ms
(- (cbrt -1) (+ (* 1/3 (/ (cbrt -1) x)) (* 1/9 (/ (cbrt -1) (pow x 2)))))
254.0ms
(- (cbrt -1) (+ (* 1/3 (/ (cbrt -1) x)) (* 1/9 (/ (cbrt -1) (pow x 2)))))

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes149.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms