Details

Time bar (total: 11.8s)

sample43.0ms

Algorithm
intervals
Results
24.0ms79×body1280valid
6.0ms135×body80valid
3.0ms22×body640valid
2.0ms14×body320valid
1.0ms6×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done12
212
111
06

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1))
1.8b
(- (atan (+ N 1)) (atan N))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
1.0ms
(atan (+ N 1))
8.0ms
(- (atan (+ N 1)) (atan N))

series15.0ms

Counts
2 → 6
Calls
2 calls:
2.0ms
(atan (+ N 1))
13.0ms
(- (atan (+ N 1)) (atan N))

simplify2.2s

Counts
46 → 46
Iterations
IterNodes
done5005
42140
3773
2288
1140
067

prune160.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma N (+ N 1) 1)
0.2b
(atan2 1 (fma N (+ N 1) 1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×fma-udef
Counts
2 → 21
Calls
2 calls:
1.0ms
(fma N (+ N 1) 1)
1.0ms
(atan2 1 (fma N (+ N 1) 1))

series36.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(fma N (+ N 1) 1)
4.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify1.5s

Counts
27 → 27
Iterations
IterNodes
done5001
41118
3254
284
149
030

prune119.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 1 expressions with local error:

0.2b
(atan2 1 (+ (fma N N 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 insert-posit16 log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(atan2 1 (+ (fma N N N) 1))

series4.0ms

Counts
1 → 3
Calls
1 calls:
4.0ms
(atan2 1 (+ (fma N N N) 1))

simplify2.7s

Counts
13 → 13
Iterations
IterNodes
done5001
91275
8521
7275
6164
584
457
341
229
121
015

prune50.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 1 (+ (fma N N N) 1))
0.6b
(* (sqrt (atan2 1 (+ (fma N N N) 1))) (sqrt (atan2 1 (+ (fma N N N) 1))))
12.5b
(sqrt (atan2 1 (+ (fma N N N) 1)))
12.5b
(sqrt (atan2 1 (+ (fma N N N) 1)))

rewrite31.0ms

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 insert-posit16 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 → 94
Calls
4 calls:
0.0ms
(atan2 1 (+ (fma N N N) 1))
23.0ms
(* (sqrt (atan2 1 (+ (fma N N N) 1))) (sqrt (atan2 1 (+ (fma N N N) 1))))
3.0ms
(sqrt (atan2 1 (+ (fma N N N) 1)))
3.0ms
(sqrt (atan2 1 (+ (fma N N N) 1)))

series38.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 1 (+ (fma N N N) 1))
4.0ms
(* (sqrt (atan2 1 (+ (fma N N N) 1))) (sqrt (atan2 1 (+ (fma N N N) 1))))
17.0ms
(sqrt (atan2 1 (+ (fma N N N) 1)))
14.0ms
(sqrt (atan2 1 (+ (fma N N N) 1)))

simplify3.1s

Counts
106 → 106
Iterations
IterNodes
done5000
44110
3658
2247
1118
065

prune241.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes77.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done8
18
05

end0.0ms

sample1.4s

Algorithm
intervals
Results
880.0ms2805×body1280valid
270.0ms4054×body80valid
107.0ms652×body640valid
71.0ms336×body320valid
14.0ms153×body160valid