Details

sample95.0ms

Algorithm

intervals

Results

45.0ms	66×	body	2560	valid
13.0ms	54×	body	640	valid
11.0ms	28×	body	1280	valid
6.0ms	34×	body	320	valid
5.0ms	59×	body	80	valid
2.0ms	15×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize13.0ms

Local error

Found 2 expressions with local error:

2.6b	(- 1.0 (cos x))
18.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
56.0ms	(/ (- 1.0 (cos x)) (* x x))

series122.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- 1.0 (cos x))
73.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	116	808
1	301	681
2	1709	566
done	5001	553

prune202.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma 1/720 (pow x 4) 1/2)
12.2b	(fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 1/720 (pow x 4) 1/2)
0.0ms	(fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))

series161.0ms

Counts

2 → 6

Calls

2 calls:

108.0ms	(fma 1/720 (pow x 4) 1/2)
52.0ms	(fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))

simplify1.1s

Counts

26 → 26

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	35	298
1	58	292
2	201	255
3	1166	255
done	5001	255

prune105.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))))
0.0b	(expm1 (fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2)))
0.3b	(fma 1/720 (pow x 4) 1/2)
12.2b	(fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`fma-udef`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 42

Calls

4 calls:

0.0ms	(log1p (expm1 (fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))))
0.0ms	(expm1 (fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2)))
0.0ms	(fma 1/720 (pow x 4) 1/2)
0.0ms	(fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))

series428.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(log1p (expm1 (fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))))
79.0ms	(expm1 (fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2)))
122.0ms	(fma 1/720 (pow x 4) 1/2)
57.0ms	(fma -1/24 (* x x) (fma 1/720 (pow x 4) 1/2))

simplify3.0s

Counts

54 → 54

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	67	733
1	126	695
2	416	610
3	2486	605
done	5001	604

prune262.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

12.2b	(fma -1/24 (* x x) (* (* (cbrt (fma 1/720 (pow x 4) 1/2)) (cbrt (fma 1/720 (pow x 4) 1/2))) (cbrt (fma 1/720 (pow x 4) 1/2))))
16.3b	(cbrt (fma 1/720 (pow x 4) 1/2))
16.3b	(cbrt (fma 1/720 (pow x 4) 1/2))
16.3b	(cbrt (fma 1/720 (pow x 4) 1/2))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(fma -1/24 (* x x) (* (* (cbrt (fma 1/720 (pow x 4) 1/2)) (cbrt (fma 1/720 (pow x 4) 1/2))) (cbrt (fma 1/720 (pow x 4) 1/2))))
1.0ms	(cbrt (fma 1/720 (pow x 4) 1/2))
1.0ms	(cbrt (fma 1/720 (pow x 4) 1/2))
1.0ms	(cbrt (fma 1/720 (pow x 4) 1/2))

series2.7s

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma -1/24 (* x x) (* (* (cbrt (fma 1/720 (pow x 4) 1/2)) (cbrt (fma 1/720 (pow x 4) 1/2))) (cbrt (fma 1/720 (pow x 4) 1/2))))
826.0ms	(cbrt (fma 1/720 (pow x 4) 1/2))
821.0ms	(cbrt (fma 1/720 (pow x 4) 1/2))
955.0ms	(cbrt (fma 1/720 (pow x 4) 1/2))

simplify2.6s

Counts

61 → 61

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	81	1196
1	164	1166
2	500	925
3	3500	826
done	5001	787

prune318.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes149.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.6b

bsearch151.0ms

Steps

Iters	Range		Point
11	0.022891638200552334	5.118117448855024e+31	0.033975437319783745
10	-911936.9907706906	-4.3470241882695893e-07	-0.03103024640337793

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	22	37
1	25	30
done	25	30

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1658×	body	2560	valid
661.0ms	1259×	body	1280	valid
469.0ms	1430×	body	640	valid
270.0ms	943×	body	320	valid
211.0ms	2222×	body	80	valid
122.0ms	488×	body	160	valid