Details

sample610.0ms

Algorithm

intervals

Results

330.0ms	56×	body	2560	valid
114.0ms	78×	body	1280	valid
78.0ms	59×	body	640	valid
18.0ms	38×	body	320	valid
5.0ms	15×	body	160	valid
2.0ms	10×	body	80	valid

simplify27.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize78.0ms

Local error

Found 3 expressions with local error:

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

rewrite69.0ms

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×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 80

Calls

3 calls:

35.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
18.0ms	(- x (sin x))

series306.0ms

Counts

3 → 9

Calls

3 calls:

144.0ms	(/ (- x (sin x)) (- x (tan x)))
67.0ms	(- x (tan x))
94.0ms	(- x (sin x))

simplify607.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1382
1	372
0	157

prune451.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 9/40 (* (pow x 2) 27/2800))
0.1b	(* (pow x 2) (- 9/40 (* (pow x 2) 27/2800)))
0.2b	(* (pow x 2) 27/2800)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

8.0ms	(- 9/40 (* (pow x 2) 27/2800))
23.0ms	(* (pow x 2) (- 9/40 (* (pow x 2) 27/2800)))
10.0ms	(* (pow x 2) 27/2800)

series280.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(- 9/40 (* (pow x 2) 27/2800))
137.0ms	(* (pow x 2) (- 9/40 (* (pow x 2) 27/2800)))
54.0ms	(* (pow x 2) 27/2800)

simplify736.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1003
1	237
0	105

prune261.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.1b	(/ (sin x) (cos x))
1.8b	(- x (/ (sin x) (cos x)))
1.8b	(- x (sin x))

rewrite78.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `associate-/r/` `div-inv` `associate-/l/`
1×	`quot-tan` `div-sub`

Counts

4 → 115

Calls

4 calls:

40.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
15.0ms	(/ (sin x) (cos x))
13.0ms	(- x (/ (sin x) (cos x)))
5.0ms	(- x (sin x))

series281.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
28.0ms	(/ (sin x) (cos x))
96.0ms	(- x (/ (sin x) (cos x)))
47.0ms	(- x (sin x))

simplify920.0ms

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	1881
1	479
0	206

prune524.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
1.8b	(- 1 (/ (sin x) x))
14.9b	(/ (/ (pow (sin x) 2) (cos x)) x)
15.1b	(/ (pow (sin x) 2) (* x x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

190×	`times-frac`
107×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
99×	`add-cube-cbrt`
45×	`unpow-prod-down`
36×	`associate-/l*`
28×	`add-exp-log`
15×	`unpow2` `sqr-pow`
14×	`add-cbrt-cube`
13×	`div-exp`
6×	`div-inv` `add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`pow-to-exp` `associate-/r*` `pow-exp` `difference-of-squares`
3×	`pow-unpow` `prod-exp`
2×	`clear-num` `frac-2neg`
1×	`sub-neg` `pow-pow` `flip3--` `diff-log` `cbrt-unprod` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 202

Calls

4 calls:

3.0ms	(pow (sin x) 2)
17.0ms	(- 1 (/ (sin x) x))
23.0ms	(/ (/ (pow (sin x) 2) (cos x)) x)
19.0ms	(/ (pow (sin x) 2) (* x x))

series290.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin x) 2)
75.0ms	(- 1 (/ (sin x) x))
125.0ms	(/ (/ (pow (sin x) 2) (cos x)) x)
70.0ms	(/ (pow (sin x) 2) (* x x))

simplify547.0ms

Counts

214 → 214

Iterations

Iter	Nodes
done	5001
1	984
0	393

prune1.3s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes68.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.3b

bsearch209.0ms

Steps

Iters	Range		Point
10	5.09324609688744e-06	47495130.80298876	2.491803263157965
10	-1138.2876542095912	-1.6260248627107784e-07	-0.02976690073964273

simplify5.0ms

Iterations

Iter	Nodes
done	43
1	43
0	37

end0.0ms

sample13.9s

Algorithm

intervals

Results

6.3s	1586×	body	2560	valid
3.8s	2745×	body	1280	valid
1.5s	956×	body	320	valid
1.4s	1906×	body	640	valid
565.0ms	479×	body	160	valid
56.0ms	328×	body	80	valid