Details

Time bar (total: 17.4s)

sample77.0ms

Algorithm
intervals
Results
42.0ms69×body1280valid
14.0ms51×body640valid
5.0ms34×body320valid
3.0ms88×body80valid
2.0ms95×body80nan
1.0ms14×body160valid

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04112
15112
done5112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize10.0ms

Local error

Found 1 expressions with local error:

3.7b
(log (+ 1.0 x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
4×log-prod *-un-lft-identity
2×add-sqr-sqrt pow1 log-div add-exp-log add-cube-cbrt
1×flip3-+ add-cbrt-cube rem-log-exp log-pow flip-+ distribute-lft-out add-log-exp
Counts
1 → 15
Calls
1 calls:
7.0ms
(log (+ 1.0 x))

series63.0ms

Counts
1 → 3
Calls
1 calls:
63.0ms
(log (+ 1.0 x))

simplify1.1s

Counts
18 → 18
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0585494
11234230
23694028
312634028
done50013877

prune106.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* 1.0 x) (+ (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) -1/2)))
0.0b
(* (* (/ x 1.0) (/ x 1.0)) -1/2)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
9×prod-exp cbrt-unprod
7×pow1
6×add-log-exp
4×add-sqr-sqrt cbrt-undiv div-exp associate-*l/
3×sum-log *-un-lft-identity associate-*r* pow-prod-down add-cube-cbrt
1×frac-times +-commutative associate-+r+ flip3-+ associate-*l* associate-*r/ *-commutative flip-+ unswap-sqr
Counts
2 → 41
Calls
2 calls:
16.0ms
(+ (* 1.0 x) (+ (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) -1/2)))
36.0ms
(* (* (/ x 1.0) (/ x 1.0)) -1/2)

series100.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(+ (* 1.0 x) (+ (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) -1/2)))
41.0ms
(* (* (/ x 1.0) (/ x 1.0)) -1/2)

simplify1.6s

Counts
47 → 47
Iterations

Useful iterations: done (1.6s)

IterNodesCost
09614116
131311458
2189410978
done500010768

prune154.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (log (- (* 1.0 1.0) (* x x))) (log (- 1.0 x)))
2.5b
(log (- (* 1.0 1.0) (* x x)))
3.7b
(log (- 1.0 x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
18×log-prod
15×*-un-lft-identity
13×add-sqr-sqrt
9×pow1
8×log-div
7×add-cube-cbrt
6×log-pow distribute-lft-out--
5×flip3-- add-exp-log flip-- associate--r+ difference-of-squares
4×associate--l+
3×add-cbrt-cube add-log-exp
2×associate--l- rem-log-exp associate--r-
1×sub-neg diff-log
Counts
3 → 61
Calls
3 calls:
14.0ms
(- (log (- (* 1.0 1.0) (* x x))) (log (- 1.0 x)))
7.0ms
(log (- (* 1.0 1.0) (* x x)))
4.0ms
(log (- 1.0 x))

series446.0ms

Counts
3 → 9
Calls
3 calls:
161.0ms
(- (log (- (* 1.0 1.0) (* x x))) (log (- 1.0 x)))
213.0ms
(log (- (* 1.0 1.0) (* x x)))
71.0ms
(log (- 1.0 x))

simplify1.3s

Counts
70 → 70
Iterations

Useful iterations: done (1.3s)

IterNodesCost
015028735
136323328
2144922520
done500122322

prune300.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 x) (+ (* (* (/ x 1.0) (* (/ x 1.0) (/ x 1.0))) 1/3) (* 1/2 (* (/ x 1.0) (/ x 1.0)))))
0.1b
(* (/ x 1.0) (* (/ x 1.0) (/ x 1.0)))
0.2b
(* (* (/ x 1.0) (* (/ x 1.0) (/ x 1.0))) 1/3)
7.6b
(- (+ (* 1.0 x) (+ (* (* (/ x 1.0) (* (/ x 1.0) (/ x 1.0))) 1/3) (* 1/2 (* (/ x 1.0) (/ x 1.0))))) (* 1.0 (* x x)))

rewrite4.4s

Algorithm
rewrite-expression-head
Rules
98×add-cbrt-cube add-exp-log
47×prod-exp cbrt-unprod
27×pow1
26×cbrt-undiv div-exp
18×add-log-exp
15×add-sqr-sqrt
14×associate-*l*
13×associate-*l/
12×*-un-lft-identity add-cube-cbrt
10×frac-times times-frac associate-*r/
9×pow-prod-down
6×sum-log
5×pow-prod-up
4×associate-*r*
3×diff-log
2×*-commutative unswap-sqr
1×pow2 +-commutative associate-+r+ sub-neg flip3-+ pow-plus flip3-- cube-unmult associate--l+ pow-sqr flip-+ div-inv flip--
Counts
4 → 130
Calls
4 calls:
410.0ms
(+ (* 1.0 x) (+ (* (* (/ x 1.0) (* (/ x 1.0) (/ x 1.0))) 1/3) (* 1/2 (* (/ x 1.0) (/ x 1.0)))))
65.0ms
(* (/ x 1.0) (* (/ x 1.0) (/ x 1.0)))
151.0ms
(* (* (/ x 1.0) (* (/ x 1.0) (/ x 1.0))) 1/3)
3.8s
(- (+ (* 1.0 x) (+ (* (* (/ x 1.0) (* (/ x 1.0) (/ x 1.0))) 1/3) (* 1/2 (* (/ x 1.0) (/ x 1.0))))) (* 1.0 (* x x)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(+ (* 1.0 x) (+ (* (* (/ x 1.0) (* (/ x 1.0) (/ x 1.0))) 1/3) (* 1/2 (* (/ x 1.0) (/ x 1.0)))))
71.0ms
(* (/ x 1.0) (* (/ x 1.0) (/ x 1.0)))
79.0ms
(* (* (/ x 1.0) (* (/ x 1.0) (/ x 1.0))) 1/3)
65.0ms
(- (+ (* 1.0 x) (+ (* (* (/ x 1.0) (* (/ x 1.0) (/ x 1.0))) 1/3) (* 1/2 (* (/ x 1.0) (/ x 1.0))))) (* 1.0 (* x x)))

simplify3.6s

Counts
142 → 142
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
021146900
167637977
2416634187
done500034187

prune546.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes135.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 21.3b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
016525
122525
done22525

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.9s2308×body1280valid
532.0ms1644×body640valid
179.0ms806×body320valid
95.0ms2729×body80nan
92.0ms2821×body80valid
38.0ms421×body160valid