Details

sample34.0ms

Algorithm

intervals

Results

16.0ms	100×	body	1280	valid
5.0ms	124×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.3b	(- (atan (+ N 1.0)) (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` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
7.0ms	(- (atan (+ N 1.0)) (atan N))

series15.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
13.0ms	(- (atan (+ N 1.0)) (atan N))

simplify6.5s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
3	4357
2	506
1	139
0	66

prune144.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b	(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))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify3.4s

Counts

12 → 12

Iterations

Iter	Nodes
done	5000
9	4998
8	1072
7	474
6	301
5	215
4	142
3	101
2	52
1	30
0	20

prune68.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.6b	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
16.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 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` `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))
24.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
2.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
2.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series33.0ms

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))))
14.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
14.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify800.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	600
1	122
0	63

prune391.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.2b	(pow (sqrt (sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))) 3)
16.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.9b	(sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `unpow-prod-down` `cube-prod`
6×	`sqrt-pow1`
5×	`pow-pow` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 81

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
7.0ms	(pow (sqrt (sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))) 3)
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
2.0ms	(sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
200.0ms	(pow (sqrt (sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))) 3)
24.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
25.0ms	(sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))

simplify972.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	946
1	257
0	96

prune331.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes96.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
2	11
1	10
0	8

end0.0ms

sample1.3s

Algorithm

intervals

Results

864.0ms	2854×	body	1280	valid
149.0ms	4046×	body	80	valid
86.0ms	617×	body	640	valid
70.0ms	326×	body	320	valid
12.0ms	157×	body	160	valid