Average Error: 0.1 → 0.1
Time: 11.4s
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 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2019008 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 11.1s)Debug log

sample219.0ms

Algorithm
intervals

simplify22.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

21.0ms
(- (log (- (/ 1 x) 1)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

6.0ms
(log (- (/ 1 x) 1))

series38.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

38.0ms
(log (- (/ 1 x) 1))

simplify417.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

102.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
100.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))
84.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))

prune180.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
3 → 32
Calls

3 calls. Slowest were:

9.0ms
(- (* (* x x) -1/2) (+ x (log x)))
4.0ms
(* (* x x) -1/2)
2.0ms
(+ x (log x))

series229.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

193.0ms
(+ x (log x))
20.0ms
(- (* (* x x) -1/2) (+ x (log x)))
16.0ms
(* (* x x) -1/2)

simplify1.2s

Counts
11 → 41
Calls

11 calls. Slowest were:

559.0ms
(- (log (/ 1 x)) (+ (* 1/2 (pow x 2)) x))
443.0ms
(- (log (/ -1 x)) (+ x (+ (* 1/2 (pow x 2)) (log -1))))
82.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))

prune307.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

30.8b
(log (- (* (/ 1 x) (/ 1 x)) 1))
0.3b
(* (/ 1 x) (/ 1 x))
0.0b
(- (log (- (* (/ 1 x) (/ 1 x)) 1)) (log (+ (/ 1 x) 1)))
0.0b
(log (+ (/ 1 x) 1))

rewrite29.0ms

Algorithm
rewrite-expression-head
Counts
4 → 85
Calls

4 calls. Slowest were:

12.0ms
(- (log (- (* (/ 1 x) (/ 1 x)) 1)) (log (+ (/ 1 x) 1)))
7.0ms
(log (+ (/ 1 x) 1))
4.0ms
(log (- (* (/ 1 x) (/ 1 x)) 1))

series142.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

61.0ms
(log (- (* (/ 1 x) (/ 1 x)) 1))
42.0ms
(- (log (- (* (/ 1 x) (/ 1 x)) 1)) (log (+ (/ 1 x) 1)))
27.0ms
(log (+ (/ 1 x) 1))
12.0ms
(* (/ 1 x) (/ 1 x))

simplify3.8s

Counts
60 → 97
Calls

60 calls. Slowest were:

452.0ms
(log (- (pow (* (/ 1 x) (/ 1 x)) 3) (pow 1 3)))
355.0ms
(log (- (pow (* (/ 1 x) (/ 1 x)) 3) (pow 1 3)))
190.0ms
(log (- (* (* (/ 1 x) (/ 1 x)) (* (/ 1 x) (/ 1 x))) (* 1 1)))

prune860.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes206.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample3.3s

Algorithm
intervals