Details

sample143.0ms

Algorithm

intervals

Results

76.0ms	57×	body	2560	valid
39.0ms	83×	body	1280	valid
16.0ms	73×	body	640	valid
4.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	7×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

58 → 58

Iterations

Useful iterations: 4 (800.0ms)

Iter	Nodes	Cost
0	106	665
1	235	645
2	525	609
3	1298	609
4	4026	608
done	5000	608

prune148.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/240 (pow x 5))
0.3b	(* 1/24 (pow x 3))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`associate-r`
12×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp` `add-cbrt-cube`
4×	`cube-prod` `sqr-pow`
2×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`
1×	`cube-mult` `unpow3`

Counts

2 → 56

Calls

2 calls:

5.0ms	(* 1/240 (pow x 5))
7.0ms	(* 1/24 (pow x 3))

series88.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(* 1/240 (pow x 5))
40.0ms	(* 1/24 (pow x 3))

simplify939.0ms

Counts

62 → 62

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	96	484
1	217	416
2	550	396
3	2155	396
done	5001	396

prune138.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin x) (- 1.0 (cos x)))
0.2b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
1.2b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 159

Calls

3 calls:

7.0ms	(/ (sin x) (- 1.0 (cos x)))
10.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

series275.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ (sin x) (- 1.0 (cos x)))
220.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
19.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

168 → 168

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	239	2702
1	514	2361
2	1091	2144
3	2779	2092
done	5000	2091

prune240.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (- 1.0 (cos x)) (sin x)) (+ 1.0 (cos x)))
0.3b	(+ 1.0 (cos x))
0.3b	(+ 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
19×	`associate-l`
16×	`times-frac`
14×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`flip3-+` `associate-r` `flip-+` `distribute-lft-out--` `difference-of-squares`
3×	`distribute-lft-out`
2×	`+-commutative` `frac-times` `associate-*r/` `prod-exp` `sum-log` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip--` `div-inv`

Counts

4 → 83

Calls

4 calls:

23.0ms	(* (/ (- 1.0 (cos x)) (sin x)) (+ 1.0 (cos x)))
3.0ms	(+ 1.0 (cos x))
3.0ms	(+ 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series126.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (/ (- 1.0 (cos x)) (sin x)) (+ 1.0 (cos x)))
10.0ms	(+ 1.0 (cos x))
10.0ms	(+ 1.0 (cos x))
21.0ms	(- 1.0 (cos x))

simplify571.0ms

Counts

95 → 95

Iterations

Useful iterations: 2 (140.0ms)

Iter	Nodes	Cost
0	138	1144
1	453	1122
2	1327	1024
done	5001	1024

prune200.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes113.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.6b

bsearch84.0ms

Steps

Iters	Range		Point
10	5.968040026638966e-05	117627206.70733242	0.0228384202901173
10	-64880754058.88788	-2.651420353119469e-05	-0.020365697215685236

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	61
1	44	61
done	44	61

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	1656×	body	2560	valid
1.2s	2763×	body	1280	valid
422.0ms	1843×	body	640	valid
138.0ms	921×	body	320	valid
48.0ms	448×	body	160	valid
23.0ms	365×	body	80	valid
16.0ms	4×	body	5120	valid