Details

sample142.0ms

Algorithm

intervals

Results

77.0ms	54×	body	2560	valid
35.0ms	84×	body	1280	valid
15.0ms	69×	body	640	valid
4.0ms	29×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	7×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite16.0ms

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:

10.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify1.4s

Counts

74 → 74

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	134	964
1	291	831
2	741	731
3	2756	719
done	5000	718

prune190.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.2b	(- 1.0 (cos x))

rewrite29.0ms

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:

14.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series148.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
18.0ms	(exp (log (- 1.0 (cos x))))
75.0ms	(log (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

130 → 130

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	200	1750
1	352	1386
2	829	1259
3	2744	1210
done	5000	1209

prune283.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.7b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.2b	(- 1.0 (cos x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
15.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
13.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series134.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
46.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
35.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

144 → 144

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	195	1743
1	367	1509
2	857	1372
3	3011	1333
done	5001	1332

prune361.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (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)))
1.2b	(- 1.0 (cos x))

rewrite28.0ms

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:

12.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
4.0ms	(pow E (log (- 1.0 (cos x))))
4.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series498.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
192.0ms	(pow E (log (- 1.0 (cos x))))
69.0ms	(log (- 1.0 (cos x)))
22.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

156 → 156

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	246	2382
1	474	2142
2	1256	1773
3	4962	1726
done	5000	1726

prune365.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 0.1b

regimes215.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.1b

bsearch81.0ms

Steps

Iters	Range		Point
10	3.2824798326487284e-15	0.08347146558812443	0.023267676544555443
9	-5.7596417613087905	-6.7357437175194845e-09	-0.019541465084207187

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	31	40
2	33	40
done	33	40

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1566×	body	2560	valid
1.2s	2771×	body	1280	valid
449.0ms	1917×	body	640	valid
152.0ms	941×	body	320	valid
48.0ms	444×	body	160	valid
23.0ms	357×	body	80	valid
13.0ms	4×	body	5120	valid