Details

sample126.0ms

Algorithm

intervals

Results

60.0ms	45×	body	2560	valid
20.0ms	42×	body	1280	valid
14.0ms	47×	body	640	valid
8.0ms	34×	body	320	valid
6.0ms	68×	body	80	valid
5.0ms	20×	body	160	valid

simplify31.0ms

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: 31.2b

localize16.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1.0 (cos x))
13.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite46.0ms

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:

16.0ms	(- 1.0 (cos x))
24.0ms	(/ (- 1.0 (cos x)) (* x x))

series121.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(- 1.0 (cos x))
87.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.3s

Counts

64 → 64

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	116	808
1	269	678
2	747	566
3	2669	526
done	5001	517

prune229.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(/ (/ (- 1.0 (cos x)) x) x)
2.4b	(- 1.0 (cos x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 165

Calls

3 calls:

20.0ms	(/ (- 1.0 (cos x)) x)
37.0ms	(/ (/ (- 1.0 (cos x)) x) x)
15.0ms	(- 1.0 (cos x))

series167.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ (- 1.0 (cos x)) x)
72.0ms	(/ (/ (- 1.0 (cos x)) x) x)
25.0ms	(- 1.0 (cos x))

simplify3.7s

Counts

174 → 174

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	259	2577
1	583	2358
2	1473	2183
3	4779	2121
done	5000	2121

prune503.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (cbrt (pow (- 1.0 (cos x)) 3)) x) x)
0.3b	(cbrt (pow (- 1.0 (cos x)) 3))
0.4b	(pow (- 1.0 (cos x)) 3)
2.4b	(- 1.0 (cos x))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

411×	`times-frac`
265×	`add-sqr-sqrt` `*-un-lft-identity`
208×	`cbrt-prod`
207×	`add-cube-cbrt`
70×	`unpow-prod-down` `cube-prod`
61×	`associate-/l*`
29×	`distribute-lft-out--` `difference-of-squares`
14×	`cube-mult` `unpow3` `sqr-pow`
10×	`add-exp-log`
9×	`prod-diff` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `flip3--` `fma-neg` `div-exp` `associate-/r*` `flip--`
2×	`cbrt-div`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `pow-exp` `clear-num` `rem-cbrt-cube` `associate-/l/` `rem-cube-cbrt`

Counts

4 → 352

Calls

4 calls:

68.0ms	(/ (/ (cbrt (pow (- 1.0 (cos x)) 3)) x) x)
10.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
19.0ms	(pow (- 1.0 (cos x)) 3)
13.0ms	(- 1.0 (cos x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (/ (cbrt (pow (- 1.0 (cos x)) 3)) x) x)
34.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
73.0ms	(pow (- 1.0 (cos x)) 3)
33.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

364 → 364

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	486	7451
1	901	5733
2	2210	5261
done	5000	5143

prune820.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (pow (pow (- 1.0 (cos x)) 3) 1/3) x) x)
0.4b	(pow (- 1.0 (cos x)) 3)
0.4b	(pow (pow (- 1.0 (cos x)) 3) 1/3)
2.4b	(- 1.0 (cos x))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

432×	`times-frac`
278×	`unpow-prod-down`
273×	`add-sqr-sqrt` `*-un-lft-identity`
215×	`add-cube-cbrt`
70×	`cube-prod`
64×	`associate-/l*`
29×	`distribute-lft-out--` `difference-of-squares`
27×	`sqr-pow`
22×	`add-exp-log`
14×	`cube-mult` `unpow3`
12×	`add-cbrt-cube`
11×	`div-exp`
9×	`prod-diff` `pow-exp`
6×	`pow-unpow` `add-log-exp`
5×	`pow1` `cbrt-undiv` `pow-to-exp` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-/r*`
2×	`cube-div` `flip3--` `pow-pow` `unpow1/3` `flip--`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `associate-/l/` `rem-cube-cbrt`

Counts

4 → 375

Calls

4 calls:

121.0ms	(/ (/ (pow (pow (- 1.0 (cos x)) 3) 1/3) x) x)
23.0ms	(pow (- 1.0 (cos x)) 3)
31.0ms	(pow (pow (- 1.0 (cos x)) 3) 1/3)
7.0ms	(- 1.0 (cos x))

series384.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (/ (pow (pow (- 1.0 (cos x)) 3) 1/3) x) x)
69.0ms	(pow (- 1.0 (cos x)) 3)
230.0ms	(pow (pow (- 1.0 (cos x)) 3) 1/3)
21.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

387 → 387

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	557	8452
1	1119	6357
2	3081	5570
done	5000	5469

prune748.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes127.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch109.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	0.02733685303105121
9	-1501.2167507114543	-0.006495210018506858	-0.03155884382850993

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	40
1	30	40
done	30	40

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.4s	1538×	body	2560	valid
516.0ms	1280×	body	1280	valid
386.0ms	1481×	body	640	valid
344.0ms	2287×	body	80	valid
231.0ms	957×	body	320	valid
53.0ms	457×	body	160	valid