Details

sample431.0ms

Algorithm

intervals

Results

217.0ms	48×	body	2560	valid
96.0ms	82×	body	1280	valid
34.0ms	54×	body	640	valid
21.0ms	42×	body	320	valid
5.0ms	11×	body	160	valid
3.0ms	19×	body	80	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (tan x))
0.9b	(- x (sin x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

61.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series244.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(/ (- x (sin x)) (- x (tan x)))
80.0ms	(- x (tan x))
51.0ms	(- x (sin x))

simplify998.0ms

Counts

89 → 89

Iterations

Useful iterations: done (995.0ms)

Iter	Nodes	Cost
0	157	1237
1	371	1200
2	1358	1149
done	5001	1147

prune323.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.2b	(/ (sin x) (cos x))
0.9b	(- x (/ (sin x) (cos x)))
0.9b	(- x (sin x))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
46×	`times-frac`
25×	`add-cube-cbrt`
22×	`difference-of-squares`
15×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `div-inv` `associate-/l/`
1×	`quot-tan` `div-sub`

Counts

4 → 115

Calls

4 calls:

71.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
20.0ms	(/ (sin x) (cos x))
24.0ms	(- x (/ (sin x) (cos x)))
7.0ms	(- x (sin x))

series296.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
39.0ms	(/ (sin x) (cos x))
83.0ms	(- x (/ (sin x) (cos x)))
42.0ms	(- x (sin x))

simplify1.3s

Counts

127 → 127

Iterations

Useful iterations: 2 (342.0ms)

Iter	Nodes	Cost
0	206	2024
1	479	1960
2	1886	1880
done	5000	1880

prune487.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (/ (sin x) (cos x)))
0.9b	(- x (sin x))
1.3b	(/ (- x (sin x)) (- x (* (* (cbrt (/ (sin x) (cos x))) (cbrt (/ (sin x) (cos x)))) (cbrt (/ (sin x) (cos x))))))
19.2b	(- x (* (* (cbrt (/ (sin x) (cos x))) (cbrt (/ (sin x) (cos x)))) (cbrt (/ (sin x) (cos x)))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

3.0ms	(cbrt (/ (sin x) (cos x)))
9.0ms	(- x (sin x))
36.0ms	(/ (- x (sin x)) (- x (* (* (cbrt (/ (sin x) (cos x))) (cbrt (/ (sin x) (cos x)))) (cbrt (/ (sin x) (cos x))))))
6.0ms	(- x (* (* (cbrt (/ (sin x) (cos x))) (cbrt (/ (sin x) (cos x)))) (cbrt (/ (sin x) (cos x)))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(cbrt (/ (sin x) (cos x)))
38.0ms	(- x (sin x))
109.0ms	(/ (- x (sin x)) (- x (* (* (cbrt (/ (sin x) (cos x))) (cbrt (/ (sin x) (cos x)))) (cbrt (/ (sin x) (cos x))))))
110.0ms	(- x (* (* (cbrt (/ (sin x) (cos x))) (cbrt (/ (sin x) (cos x)))) (cbrt (/ (sin x) (cos x)))))

simplify1.3s

Counts

100 → 100

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	206	2789
1	463	2733
2	1801	1424
done	5001	1422

prune340.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.8b	(- (/ x (- x (/ (sin x) (cos x)))) (/ (sin x) (- x (/ (sin x) (cos x)))))
0.9b	(- x (/ (sin x) (cos x)))
0.9b	(- x (/ (sin x) (cos x)))

rewrite321.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

11.0ms	(/ (sin x) (cos x))
248.0ms	(- (/ x (- x (/ (sin x) (cos x)))) (/ (sin x) (- x (/ (sin x) (cos x)))))
32.0ms	(- x (/ (sin x) (cos x)))
26.0ms	(- x (/ (sin x) (cos x)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (sin x) (cos x))
323.0ms	(- (/ x (- x (/ (sin x) (cos x)))) (/ (sin x) (- x (/ (sin x) (cos x)))))
66.0ms	(- x (/ (sin x) (cos x)))
73.0ms	(- x (/ (sin x) (cos x)))

simplify940.0ms

Counts

100 → 100

Iterations

Useful iterations: done (929.0ms)

Iter	Nodes	Cost
0	173	1738
1	371	1691
2	1324	1605
done	5000	1600

prune376.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.0b

bsearch116.0ms

Steps

Iters	Range		Point
9	5.2366538615162886e-09	1.4124627081995123	0.03372325990928043
7	-3.309911606533295	-0.03117879455470207	-0.033546375590763663

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	27	75
1	34	49
done	34	49

end0.0ms

sample14.1s

Algorithm

intervals

Results

7.5s	1621×	body	2560	valid
3.6s	2728×	body	1280	valid
1.6s	1861×	body	640	valid
865.0ms	943×	body	320	valid
139.0ms	473×	body	160	valid
63.0ms	374×	body	80	valid