Details

sample273.0ms

Algorithm

intervals

Results

105.0ms	46×	body	2560	valid
69.0ms	92×	body	1280	valid
47.0ms	29×	body	320	valid
32.0ms	63×	body	640	valid
2.0ms	11×	body	160	valid
2.0ms	15×	body	80	valid

simplify16.0ms

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: 25.8b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.1b	(- 1.0 (cos x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(- 1.0 (cos x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify2.8s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	106	665
1	235	645
2	531	609
3	1194	609
4	3136	608
done	5000	608

prune239.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.1b	(- 1.0 (cos x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`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 → 98

Calls

4 calls:

21.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
11.0ms	(exp (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series268.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
34.0ms	(exp (log (- 1.0 (cos x))))
125.0ms	(log (- 1.0 (cos x)))
34.0ms	(- 1.0 (cos x))

simplify3.4s

Counts

110 → 110

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	168	1421
1	285	1183
2	624	1107
3	1442	1107
4	3676	1088
done	5000	1088

prune321.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(pow E (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.1b	(- 1.0 (cos x))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `pow-sub`
3×	`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 → 124

Calls

4 calls:

30.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
14.0ms	(pow E (log (- 1.0 (cos x))))
10.0ms	(log (- 1.0 (cos x)))
13.0ms	(- 1.0 (cos x))

series715.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
275.0ms	(pow E (log (- 1.0 (cos x))))
95.0ms	(log (- 1.0 (cos x)))
31.0ms	(- 1.0 (cos x))

simplify2.4s

Counts

136 → 136

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	214	2049
1	407	1916
2	999	1631
3	3374	1625
done	5001	1625

prune486.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow E (log (- 1.0 (cos x)))) (/ 1 (sin x)))
0.3b	(pow E (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.1b	(- 1.0 (cos x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
34×	`add-exp-log`
30×	`*-un-lft-identity`
18×	`add-cube-cbrt` `log-prod`
17×	`times-frac`
16×	`prod-exp`
13×	`unpow-prod-up` `associate-r`
12×	`associate-l` `unswap-sqr`
10×	`pow-exp`
9×	`unpow-prod-down` `add-cbrt-cube`
8×	`log-div` `div-exp`
7×	`pow1`
6×	`pow-sub` `add-log-exp`
5×	`pow-to-exp` `e-exp-1` `flip3--` `flip--` `sqr-pow`
4×	`rec-exp` `pow-unpow` `1-exp` `distribute-lft-out--` `difference-of-squares`
2×	`frac-times` `associate-*l/` `log-pow` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `diff-log` `associate-r/` `rem-log-exp` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 125

Calls

4 calls:

41.0ms	(* (pow E (log (- 1.0 (cos x)))) (/ 1 (sin x)))
11.0ms	(pow E (log (- 1.0 (cos x))))
9.0ms	(log (- 1.0 (cos x)))
14.0ms	(- 1.0 (cos x))

series833.0ms

Counts

4 → 12

Calls

4 calls:

364.0ms	(* (pow E (log (- 1.0 (cos x)))) (/ 1 (sin x)))
333.0ms	(pow E (log (- 1.0 (cos x))))
112.0ms	(log (- 1.0 (cos x)))
24.0ms	(- 1.0 (cos x))

simplify4.0s

Counts

137 → 137

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	217	1975
1	506	1742
2	1241	1418
3	4196	1412
done	5002	1412

prune513.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

regimes224.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 29.9b

bsearch117.0ms

Steps

Iters	Range		Point
9	0.0033303272193615503	311302.39110615524	0.022196995022368538
9	-7.35943201301068	-4.403108084983288e-07	-0.022316068015986585

simplify13.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	60
1	53	60
done	53	60

end0.0ms

sample8.2s

Algorithm

intervals

Results

3.3s	1590×	body	2560	valid
2.8s	2797×	body	1280	valid
998.0ms	1830×	body	640	valid
490.0ms	477×	body	160	valid
305.0ms	961×	body	320	valid
36.0ms	341×	body	80	valid
22.0ms	4×	body	5120	valid