Average Error: 0.0 → 0.0
Time: 9.5s
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 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 9.2s)Debug log

sample311.0ms

Algorithm
intervals

simplify56.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

55.0ms
(- (log (- (/ 1 x) 1)))

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
2 → 27
Calls

2 calls. Slowest were:

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

series88.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

77.0ms
(log (- (/ 1 x) 1))
10.0ms
(- (/ 1 x) 1)

simplify354.0ms

Counts
14 → 33
Calls

14 calls. Slowest were:

82.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))
68.0ms
(log (- (pow (/ 1 x) 3) (pow 1 3)))
56.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))

prune202.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (- (/ 1 x) 1))
0.2b
(sqrt (- (/ 1 x) 1))
0.0b
(log (sqrt (- (/ 1 x) 1)))
0.0b
(log (sqrt (- (/ 1 x) 1)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
4 → 68
Calls

4 calls. Slowest were:

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

series140.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

54.0ms
(log (sqrt (- (/ 1 x) 1)))
49.0ms
(log (sqrt (- (/ 1 x) 1)))
19.0ms
(sqrt (- (/ 1 x) 1))
17.0ms
(sqrt (- (/ 1 x) 1))

simplify2.1s

Counts
46 → 80
Calls

46 calls. Slowest were:

261.0ms
(- (+ (log (sqrt -1)) (* 1/2 (/ 1 (* x (pow (sqrt -1) 2))))) (* 1/4 (/ 1 (* (pow x 2) (pow (sqrt -1) 4)))))
250.0ms
(- (+ (log (sqrt -1)) (* 1/2 (/ 1 (* x (pow (sqrt -1) 2))))) (* 1/4 (/ 1 (* (pow x 2) (pow (sqrt -1) 4)))))
243.0ms
(- (+ (log (sqrt -1)) (* 1/2 (/ 1 (* x (pow (sqrt -1) 2))))) (* 1/4 (/ 1 (* (pow x 2) (pow (sqrt -1) 4)))))

prune822.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (log x))
0.0b
(- (* (* x x) -1/2) (+ x (log x)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 23
Calls

2 calls. Slowest were:

5.0ms
(- (* (* x x) -1/2) (+ x (log x)))
1.0ms
(+ x (log x))

series234.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

216.0ms
(+ x (log x))
18.0ms
(- (* (* x x) -1/2) (+ x (log x)))

simplify957.0ms

Counts
8 → 29
Calls

8 calls. Slowest were:

486.0ms
(- (log (/ -1 x)) (+ x (+ (* 1/2 (pow x 2)) (log -1))))
252.0ms
(- (log (/ 1 x)) (+ (* 1/2 (pow x 2)) x))
94.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))

prune252.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes147.0ms

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