Details

Time bar (total: 14.3s)

sample60.0ms

Algorithm
intervals
Results
29.0ms98×body1280valid
8.0ms117×body80valid
6.0ms24×body640valid
3.0ms14×body320valid
0.0ms3×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize17.0ms

Local error

Found 1 expressions with local error:

1.3b
(- (atan (+ N 1.0)) (atan N))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
9×prod-diff
8×add-cube-cbrt
3×fma-neg add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log diff-atan add-exp-log log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 29
Calls
1 calls:
10.0ms
(- (atan (+ N 1.0)) (atan N))

series20.0ms

Counts
1 → 3
Calls
1 calls:
20.0ms
(- (atan (+ N 1.0)) (atan N))

simplify7.6s

Counts
32 → 32
Iterations
IterNodes
done5000
34363
2503
1136
062

prune113.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.0b
(atan2 (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)))
3.4b
(- (+ N 1.0) N)

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
17×add-sqr-sqrt
13×add-cube-cbrt
12×prod-diff
8×add-log-exp
6×distribute-lft-out
5×pow1 add-cbrt-cube add-exp-log
4×fma-neg associate-*l*
3×expm1-log1p-u associate-*r* log1p-expm1-u
2×diff-log associate-*l/ distribute-lft-out--
1×sum-log sub-neg flip3-+ flip3-- pow-prod-down prod-exp associate--l+ *-commutative cbrt-unprod flip-+ flip-- difference-of-squares unswap-sqr
Counts
3 → 67
Calls
3 calls:
31.0ms
(* (+ N 1.0) N)
0.0ms
(atan2 (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)))
46.0ms
(- (+ N 1.0) N)

series68.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(* (+ N 1.0) N)
7.0ms
(atan2 (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)))
2.0ms
(- (+ N 1.0) N)

simplify1.7s

Counts
76 → 76
Iterations
IterNodes
done5001
21237
1252
0106

prune258.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize8.0ms

Local error

Found 1 expressions with local error:

0.6b
(atan2 1.0 (fma N (+ 1.0 N) 1))

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt log1p-expm1-u add-log-exp
Counts
1 → 9
Calls
1 calls:
0.0ms
(atan2 1.0 (fma N (+ 1.0 N) 1))

series3.0ms

Counts
1 → 3
Calls
1 calls:
2.0ms
(atan2 1.0 (fma N (+ 1.0 N) 1))

simplify1.6s

Counts
12 → 12
Iterations
IterNodes
done5001
81017
7376
6195
5125
487
362
238
125
018

prune50.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(atan2 1.0 (fma N (+ 1.0 N) 1))
0.6b
(atan2 1.0 (fma N (+ 1.0 N) 1))
14.9b
(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
14.9b
(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 48
Calls
4 calls:
0.0ms
(atan2 1.0 (fma N (+ 1.0 N) 1))
0.0ms
(atan2 1.0 (fma N (+ 1.0 N) 1))
1.0ms
(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
5.0ms
(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

series31.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 1.0 (fma N (+ 1.0 N) 1))
2.0ms
(atan2 1.0 (fma N (+ 1.0 N) 1))
13.0ms
(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
14.0ms
(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

simplify1.3s

Counts
60 → 60
Iterations
IterNodes
done5001
62055
5504
4228
3159
289
146
033

prune200.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

regimes43.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done9
19
06

end0.0ms

sample1.1s

Algorithm
intervals
Results
612.0ms2881×body1280valid
180.0ms4036×body80valid
88.0ms625×body640valid
54.0ms302×body320valid
12.0ms156×body160valid