Details

sample532.0ms

Algorithm

intervals

Results

109.0ms	49×	body	2560	valid
91.0ms	92×	body	1280	valid
17.0ms	53×	body	640	valid
7.0ms	33×	body	320	valid
3.0ms	16×	body	160	valid
1.0ms	13×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5
done	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.1b	(- x (tan x))
2.1b	(- x (sin x))

rewrite40.0ms

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:

23.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series181.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- x (sin x)) (- x (tan x)))
54.0ms	(- x (tan x))
48.0ms	(- x (sin x))

simplify144.0ms

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685
done	5001	685

prune201.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.2b	(/ (sin x) (cos x))
2.1b	(- x (/ (sin x) (cos x)))
2.1b	(- x (sin x))

rewrite66.0ms

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:

34.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
8.0ms	(/ (sin x) (cos x))
13.0ms	(- x (/ (sin x) (cos x)))
6.0ms	(- x (sin x))

series184.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
23.0ms	(/ (sin x) (cos x))
50.0ms	(- x (/ (sin x) (cos x)))
35.0ms	(- x (sin x))

simplify45.0ms

Counts

127 → 127

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	458	1225
1	1565	1175
2	5001	1173
done	5001	1173

prune259.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (cos x))
0.2b	(* (sin x) (/ 1 (cos x)))
2.1b	(- x (* (sin x) (/ 1 (cos x))))
2.1b	(- x (sin x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`div-exp` `prod-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3--` `diff-log` `1-exp` `flip--` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

6.0ms	(/ 1 (cos x))
21.0ms	(* (sin x) (/ 1 (cos x)))
5.0ms	(- x (* (sin x) (/ 1 (cos x))))
6.0ms	(- x (sin x))

series118.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1 (cos x))
20.0ms	(* (sin x) (/ 1 (cos x)))
53.0ms	(- x (* (sin x) (/ 1 (cos x))))
32.0ms	(- x (sin x))

simplify42.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	346	567
1	1397	505
2	5001	475
done	5001	475

prune185.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
15.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite42.0ms

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:

11.0ms	(* 27/2800 (pow x 4))
11.0ms	(* 9/40 (pow x 2))
18.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series117.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* 27/2800 (pow x 4))
26.0ms	(* 9/40 (pow x 2))
50.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify41.0ms

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315
done	5001	315

prune135.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes24.0ms

Accuracy

100% (0.0b remaining)

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

bsearch70.0ms

Steps

Iters	Range		Point
9	0.00021078761332869983	22.544919195950573	0.03458526336808176
8	-1.6220908197114983	-0.002799490342594777	-0.029080846659882604

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	14
1	34	14
done	34	14

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1578×	body	2560	valid
1.9s	2771×	body	1280	valid
648.0ms	1866×	body	640	valid
215.0ms	948×	body	320	valid
73.0ms	462×	body	160	valid
42.0ms	375×	body	80	valid