Details

sample466.0ms

Algorithm

intervals

Results

112.0ms	50×	body	2560	valid
61.0ms	93×	body	1280	valid
19.0ms	57×	body	640	valid
6.0ms	24×	body	320	valid
3.0ms	20×	body	160	valid
1.0ms	12×	body	80	valid

simplify14.0ms

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: 31.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
3.1b	(- x (tan x))
3.1b	(- x (sin x))

rewrite35.0ms

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)))
2.0ms	(- x (tan x))
18.0ms	(- x (sin x))

series177.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify995.0ms

Counts

89 → 89

Iterations

Useful iterations: done (992.0ms)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	959	1147
3	2670	1147
done	5000	1145

prune214.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
15.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite21.0ms

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:

5.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
8.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series112.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 9/40 (pow x 2))
49.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify1.3s

Counts

75 → 75

Iterations

Useful iterations: 3 (419.0ms)

Iter	Nodes	Cost
0	121	788
1	279	703
2	796	643
3	2530	637
done	5000	637

prune148.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize10.0ms

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))))
3.1b	(- x (tan x))
3.1b	(- x (sin x))

rewrite47.0ms

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:

11.0ms	(/ (- x (tan x)) (- x (sin x)))
17.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
2.0ms	(- x (tan x))
3.0ms	(- x (sin x))

series244.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- x (tan x)) (- x (sin x)))
79.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
55.0ms	(- x (tan x))
31.0ms	(- x (sin x))

simplify712.0ms

Counts

240 → 240

Iterations

Useful iterations: done (705.0ms)

Iter	Nodes	Cost
0	320	4580
1	749	4054
2	1826	3747
done	5000	3735

prune359.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

3.1b	(- x (tan x))
3.1b	(- x (sin x))
3.1b	(- x (sin x))
3.1b	(- x (sin 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:

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

series151.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- x (tan x))
31.0ms	(- x (sin x))
35.0ms	(- x (sin x))
31.0ms	(- x (sin x))

simplify2.0s

Counts

68 → 68

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	76	559
1	153	543
2	344	510
3	660	510
4	1501	510
5	4262	510
done	5001	510

prune196.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.0b

bsearch85.0ms

Steps

Iters	Range		Point
9	6.379368274952145e-05	25.411711264148785	0.029125046562482146
10	-155084744.97222546	-0.0009113054925467739	-0.02756549793614824

simplify4.0ms

Iterations

Useful iterations: 1 (1.0ms)

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

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.7s	1658×	body	2560	valid
1.8s	2659×	body	1280	valid
658.0ms	1836×	body	640	valid
219.0ms	945×	body	320	valid
88.0ms	508×	body	160	valid
37.0ms	394×	body	80	valid