Details

sample293.0ms

Algorithm

intervals

Results

145.0ms	66×	body	2560	valid
60.0ms	60×	body	640	valid
59.0ms	75×	body	1280	valid
9.0ms	34×	body	320	valid
4.0ms	15×	body	160	valid
1.0ms	6×	body	80	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize15.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.6b	(- 1.0 (cos x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 68

Calls

2 calls:

24.0ms	(/ (- 1.0 (cos x)) (sin x))
14.0ms	(- 1.0 (cos x))

series111.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(/ (- 1.0 (cos x)) (sin x))
38.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

74 → 74

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	134	964
1	309	834
2	1215	733
done	5001	692

prune308.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/240 (pow x 5) (* 1/2 x))

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` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 1/240 (pow x 5) (* 1/2 x))

series186.0ms

Counts

1 → 3

Calls

1 calls:

186.0ms

(fma 1/240 (pow x 5) (* 1/2 x))

simplify4.5s

Counts

13 → 13

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	18	140
1	30	137
2	86	121
3	346	121
4	1710	121
done	5001	121

prune118.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.6b	(- 1.0 (cos x))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`log-prod`
25×	`exp-sum`
24×	`times-frac`
9×	`prod-diff`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `flip--` `log1p-expm1-u`
3×	`fma-neg` `associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 118

Calls

4 calls:

41.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
14.0ms	(exp (log (- 1.0 (cos x))))
14.0ms	(log (- 1.0 (cos x)))
16.0ms	(- 1.0 (cos x))

series187.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
32.0ms	(exp (log (- 1.0 (cos x))))
89.0ms	(log (- 1.0 (cos x)))
22.0ms	(- 1.0 (cos x))

simplify978.0ms

Counts

130 → 130

Iterations

Useful iterations: done (973.0ms)

Iter	Nodes	Cost
0	200	1750
1	374	1389
2	1294	1247
done	5001	1206

prune441.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(log (- 1.0 (cos x)))
0.3b	(pow E (log (- 1.0 (cos x))))
2.6b	(- 1.0 (cos x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
36×	`times-frac`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
9×	`prod-diff`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `log1p-expm1-u` `pow-sub`
3×	`fma-neg` `associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 144

Calls

4 calls:

27.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
7.0ms	(log (- 1.0 (cos x)))
14.0ms	(pow E (log (- 1.0 (cos x))))
15.0ms	(- 1.0 (cos x))

series810.0ms

Counts

4 → 12

Calls

4 calls:

371.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
88.0ms	(log (- 1.0 (cos x)))
318.0ms	(pow E (log (- 1.0 (cos x))))
33.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

156 → 156

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	246	2382
1	533	2135
2	2173	1776
done	5001	1730

prune563.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 0.1b

regimes271.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.4b

bsearch151.0ms

Steps

Iters	Range		Point
11	0.022891638200552334	5.118117448855024e+31	0.02331429387269753
10	-911936.9907706906	-4.3470241882695893e-07	-0.018543641276894153

simplify11.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	25	41
1	31	32
2	33	32
done	33	32

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.8s	1654×	body	2560	valid
2.6s	2742×	body	1280	valid
1.1s	1844×	body	640	valid
393.0ms	940×	body	320	valid
134.0ms	489×	body	160	valid
77.0ms	327×	body	80	valid
20.0ms	4×	body	5120	valid