Details

sample479.0ms

Algorithm

intervals

Results

122.0ms	53×	body	2560	valid
67.0ms	104×	body	1280	valid
19.0ms	55×	body	640	valid
8.0ms	27×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	7×	body	80	valid

simplify15.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.8b	(- x (sin x))
0.9b	(- x (tan x))

rewrite23.0ms

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:

11.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series179.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
38.0ms	(- x (sin x))
63.0ms	(- x (tan x))

simplify1.2s

Counts

89 → 89

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	952	1147
3	2623	1147
done	5000	1145

prune217.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.9b	(- x (tan x))
0.9b	(- x (tan x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

7.0ms	(/ (sin x) (- x (tan x)))
50.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series352.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (sin x) (- x (tan x)))
182.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
54.0ms	(- x (tan x))
54.0ms	(- x (tan x))

simplify1.5s

Counts

106 → 106

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	177	1565
1	377	1511
2	1015	1449
3	3615	1445
done	5001	1444

prune261.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
15.4b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
15.4b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
42×	`div-exp`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
14×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow-pow` `frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 136

Calls

4 calls:

1.0ms	(pow (sin x) 2)
1.0ms	(pow (sin x) 2)
6.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
8.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin x) 2)
18.0ms	(pow (sin x) 2)
59.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
75.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

simplify1.0s

Counts

148 → 148

Iterations

Useful iterations: 2 (196.0ms)

Iter	Nodes	Cost
0	161	1988
1	373	1788
2	1381	1628
done	5001	1628

prune372.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- x (sin x))
0.8b	(- x (sin x))
0.8b	(- x (sin x))
0.9b	(- x (tan x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

3.0ms	(- x (sin x))
3.0ms	(- x (sin x))
3.0ms	(- x (sin x))
2.0ms	(- x (tan x))

series156.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- x (sin x))
32.0ms	(- x (sin x))
32.0ms	(- x (sin x))
55.0ms	(- x (tan x))

simplify2.1s

Counts

68 → 68

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	76	559
1	153	543
2	344	510
3	657	510
4	1507	510
5	4292	510
done	5000	510

prune188.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes35.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.6b

bsearch120.0ms

Steps

Iters	Range		Point
10	1.4157702531433464e-05	3675686898.170574	2.434958728416592
10	-0.4379170495851395	-3.268197633477337e-18	-0.02695924982513673

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	75
1	50	75
done	50	75

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.7s	1656×	body	2560	valid
1.9s	2701×	body	1280	valid
644.0ms	1911×	body	640	valid
228.0ms	904×	body	320	valid
83.0ms	482×	body	160	valid
32.0ms	346×	body	80	valid