Details

Time bar (total: 13.6s)

sample57.0ms

Algorithm
intervals
Results
24.0ms77×body1280valid
9.0ms142×body80valid
6.0ms23×body640valid
2.0ms8×body320valid
1.0ms6×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize18.0ms

Local error

Found 1 expressions with local error:

1.4b
(- (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))

series23.0ms

Counts
1 → 3
Calls
1 calls:
23.0ms
(- (atan (+ N 1.0)) (atan N))

simplify6.2s

Counts
32 → 32
Iterations
IterNodes
done5000
34363
2503
1136
062

prune85.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 1 expressions with local error:

0.2b
(atan2 (- 1.0 0) (fma N (+ 1.0 N) 1))

rewrite1.0ms

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 0) (fma N (+ 1.0 N) 1))

series6.0ms

Counts
1 → 3
Calls
1 calls:
6.0ms
(atan2 (- 1.0 0) (fma N (+ 1.0 N) 1))

simplify3.2s

Counts
12 → 12
Iterations
IterNodes
done5000
94998
81072
7474
6301
5215
4142
3101
252
130
020

prune45.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 1.0 (fma N (+ N 1.0) 1))
0.7b
(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
12.5b
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.5b
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 90
Calls
4 calls:
0.0ms
(atan2 1.0 (fma N (+ N 1.0) 1))
10.0ms
(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
1.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series34.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 1.0 (fma N (+ N 1.0) 1))
3.0ms
(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
16.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify637.0ms

Counts
102 → 102
Iterations
IterNodes
done5001
2600
1122
063

prune296.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (sqrt (sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))) (sqrt (sqrt (atan2 1.0 (fma (+ N 1.0) N 1))))))
12.5b
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.5b
(sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))
12.5b
(sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1
14×add-sqr-sqrt
13×sqrt-prod
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
7×pow-prod-down
6×sqrt-pow1 pow1/2 associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square prod-exp cbrt-unprod
2×sqrt-unprod unswap-sqr
1×associate-*r* *-commutative
Counts
4 → 73
Calls
4 calls:
38.0ms
(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (sqrt (sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))) (sqrt (sqrt (atan2 1.0 (fma (+ N 1.0) N 1))))))
1.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms
(sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))
1.0ms
(sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))

series79.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (sqrt (sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))) (sqrt (sqrt (atan2 1.0 (fma (+ N 1.0) N 1))))))
15.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0ms
(sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))
13.0ms
(sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))

simplify997.0ms

Counts
85 → 85
Iterations
IterNodes
done5000
31034
2349
1137
071

prune287.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

regimes53.0ms

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
done11
211
110
08

end0.0ms

sample1.4s

Algorithm
intervals
Results
640.0ms2900×body1280valid
370.0ms638×body640valid
173.0ms3994×body80valid
38.0ms323×body320valid
11.0ms145×body160valid