Details

Time bar (total: 1.9s)

sample28.0ms

Algorithm
intervals
Results
14.0ms99×body1280valid
4.0ms124×body80valid
2.0ms16×body640valid
1.0ms9×body320valid
1.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
1.6b
(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 38
Calls
2 calls:
0.0ms
(atan (+ N 1.0))
3.0ms
(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
10.0ms
(- (atan (+ N 1.0)) (atan N))

simplify49.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0129365
1345264
21480254
35001198

prune72.0ms

Filtered
44 candidates to 27 candidates (61.4%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

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

series2.0ms

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

simplify97.0ms

Algorithm
egg-herbie
Counts
12 → 12
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02157
13250
25550
37050
48950
514350
656750
7177950
8500150

prune25.0ms

Filtered
12 candidates to 9 candidates (75.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 1.0 (fma N (+ N 1.0) 1))
0.5b
(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
17.3b
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
17.3b
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
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 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 90
Calls
4 calls:
0.0ms
(atan2 1.0 (fma N (+ N 1.0) 1))
7.0ms
(* (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)))

series30.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(atan2 1.0 (fma N (+ N 1.0) 1))
2.0ms
(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
11.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify107.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0100554
1375496
22244476
35001461

prune167.0ms

Filtered
102 candidates to 55 candidates (53.9%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
17.3b
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
17.3b
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
17.3b
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-pow1
51×pow1
36×pow1/2
34×pow-prod-up
16×add-sqr-sqrt
14×sqrt-prod
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
8×pow-sqr
7×pow-prod-down
6×pow-plus associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square prod-exp cbrt-unprod
2×sqrt-unprod swap-sqr unswap-sqr
1×associate-*l* *-commutative
Counts
4 → 99
Calls
4 calls:
37.0ms
(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (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)))
1.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series37.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
11.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
11.0ms
(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify188.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0197608
1590481
23838465
35001465

prune184.0ms

Filtered
111 candidates to 54 candidates (48.6%)
Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes23.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
093
193

end0.0ms

sample755.0ms

Algorithm
intervals
Results
401.0ms2829×body1280valid
130.0ms4035×body80valid
77.0ms649×body640valid
28.0ms315×body320valid
11.0ms172×body160valid