Details

Time bar (total: 10.6s)

sample41.0ms

Algorithm
intervals
Results
22.0ms92×body1280valid
6.0ms127×body80valid
4.0ms19×body640valid
2.0ms13×body320valid
1.0ms5×body160valid

simplify19.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize12.0ms

Local error

Found 2 expressions with local error:

1.6b
(- (atan (+ N 1)) (atan N))
0.0b
(atan (+ N 1))

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:
Slowest
5.0ms
(- (atan (+ N 1)) (atan N))
1.0ms
(atan (+ N 1))

series14.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
12.0ms
(- (atan (+ N 1)) (atan N))
2.0ms
(atan (+ N 1))

simplify1.8s

Counts
30 → 30

prune230.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity
5×pow1 add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
4×associate-*l*
3×associate-*r* insert-posit16
2×flip3-+ associate-*l/ flip-+
1×+-commutative sum-log pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
3 → 42
Calls
3 calls:
Slowest
20.0ms
(* (+ N 1) N)
11.0ms
(+ 1 (* (+ N 1) N))
0.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series61.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
42.0ms
(* (+ N 1) N)
15.0ms
(+ 1 (* (+ N 1) N))
4.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.3s

Counts
51 → 51

prune297.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

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:
Slowest
8.0ms
(* (cbrt N) (cbrt N))
1.0ms
(cbrt N)
1.0ms
(cbrt N)
1.0ms
(cbrt N)

series813.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
223.0ms
(* (cbrt N) (cbrt N))
200.0ms
(cbrt N)
196.0ms
(cbrt N)
194.0ms
(cbrt N)

simplify946.0ms

Counts
89 → 89

prune627.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

31.5b
(cbrt (* N N))
0.6b
(cbrt N)
0.4b
(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))
0.2b
(* (* (+ N 1) (cbrt (* N N))) (cbrt N))

rewrite50.0ms

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:
Slowest
45.0ms
(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
3.0ms
(cbrt (* N N))
1.0ms
(cbrt N)
0.0ms
(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))

series472.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
205.0ms
(cbrt (* N N))
199.0ms
(cbrt N)
56.0ms
(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
12.0ms
(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))

simplify604.0ms

Counts
66 → 66

prune487.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.3b

regimes77.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s2849×body1280valid
204.0ms4070×body80valid
158.0ms638×body640valid
45.0ms300×body320valid
15.0ms143×body160valid