Details

sample636.0ms

Algorithm

intervals

Results

300.0ms	52×	body	2560	valid
157.0ms	91×	body	1280	valid
52.0ms	38×	body	320	valid
36.0ms	46×	body	640	valid
7.0ms	20×	body	160	valid
2.0ms	9×	body	80	valid

simplify26.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.8b	(- x (sin x))

rewrite88.0ms

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:

26.0ms	(/ (- x (sin x)) (- x (tan x)))
16.0ms	(- x (tan x))
41.0ms	(- x (sin x))

series241.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(/ (- x (sin x)) (- x (tan x)))
64.0ms	(- x (tan x))
89.0ms	(- x (sin x))

simplify1.7s

Counts

89 → 89

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	915	1147
3	2339	1147
done	5000	1133

prune314.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
14.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

27.0ms	(* 27/2800 (pow x 4))
22.0ms	(* 9/40 (pow x 2))
36.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series167.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* 27/2800 (pow x 4))
48.0ms	(* 9/40 (pow x 2))
74.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify2.4s

Counts

75 → 75

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	121	788
1	277	703
2	674	643
3	2581	637
done	5000	634

prune188.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
14.1b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

22.0ms	(* 27/2800 (pow x 4))
23.0ms	(* 9/40 (pow x 2))
12.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series288.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* 27/2800 (pow x 4))
47.0ms	(* 9/40 (pow x 2))
183.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify2.4s

Counts

73 → 73

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	113	715
1	254	624
2	574	570
3	2285	560
done	5000	555

prune204.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.7b	(- x (tan x))
1.8b	(- x (sin x))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
200×	`add-sqr-sqrt` `*-un-lft-identity`
92×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv`
2×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

4 → 228

Calls

4 calls:

24.0ms	(/ (- x (tan x)) (- x (sin x)))
31.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
5.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series418.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- x (tan x)) (- x (sin x)))
140.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
106.0ms	(- x (tan x))
52.0ms	(- x (sin x))

simplify3.2s

Counts

240 → 240

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	320	4580
1	731	4054
2	1748	3747
3	4613	3667
done	5000	3667

prune466.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.3b

bsearch109.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.029468351736831863
8	-11.923248480236845	-0.0008047768791668974	-0.02915706671350092

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	43
1	32	33
done	32	33

end0.0ms

sample13.4s

Algorithm

intervals

Results

5.6s	1596×	body	2560	valid
3.9s	2769×	body	1280	valid
2.4s	1873×	body	640	valid
872.0ms	958×	body	320	valid
204.0ms	470×	body	160	valid
54.0ms	334×	body	80	valid