Details

Time bar (total: 11.7s)

sample46.0ms

Algorithm
intervals
Results
25.0ms98×body1280valid
7.0ms123×body80valid
4.0ms20×body640valid
2.0ms10×body320valid
1.0ms5×body160valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
310
210
19
06

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1))
2.0b
(- (atan (+ N 1)) (atan N))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
1.0ms
(atan (+ N 1))
5.0ms
(- (atan (+ N 1)) (atan N))

series15.0ms

Counts
2 → 6
Calls
2 calls:
2.0ms
(atan (+ N 1))
14.0ms
(- (atan (+ N 1)) (atan N))

simplify2.6s

Counts
30 → 30
Iterations
IterNodes
65474
51652
4618
3287
2149
175
041

prune117.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1) N)
0.4b
(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
3×associate-*r*
2×associate-*l/ insert-posit16 add-log-exp
1×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out unswap-sqr
Counts
2 → 30
Calls
2 calls:
30.0ms
(* (+ N 1) N)
1.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series64.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(* (+ N 1) N)
4.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.0s

Counts
36 → 36
Iterations
IterNodes
43175
3832
2305
1119
055

prune160.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt N) (cbrt N))
0.6b
(cbrt N)
0.6b
(cbrt N)
0.6b
(cbrt N)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 77
Calls
4 calls:
8.0ms
(* (cbrt N) (cbrt N))
1.0ms
(cbrt N)
1.0ms
(cbrt N)
1.0ms
(cbrt N)

series1.1s

Counts
4 → 12
Calls
4 calls:
320.0ms
(* (cbrt N) (cbrt N))
249.0ms
(cbrt N)
259.0ms
(cbrt N)
232.0ms
(cbrt N)

simplify1.2s

Counts
89 → 89
Iterations
IterNodes
42748
3814
2309
1132
063

prune396.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
0.4b
(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))
0.6b
(cbrt N)
32.6b
(cbrt (* N N))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log
7×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube associate-*r*
4×associate-*l/ insert-posit16 add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×pow1/3
1×flip3-+ associate-*l* *-commutative flip-+
Counts
4 → 54
Calls
4 calls:
42.0ms
(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
0.0ms
(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))
1.0ms
(cbrt N)
3.0ms
(cbrt (* N N))

series660.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
7.0ms
(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))
276.0ms
(cbrt N)
315.0ms
(cbrt (* N N))

simplify768.0ms

Counts
66 → 66
Iterations
IterNodes
32149
2650
1243
0103

prune300.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes60.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
29
19
06

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.4s2890×body1280valid
300.0ms3991×body80valid
160.0ms644×body640valid
57.0ms298×body320valid
25.0ms177×body160valid