Details

sample81.0ms

Algorithm

intervals

Results

40.0ms	58×	body	2560	valid
11.0ms	34×	body	1280	valid
10.0ms	54×	body	640	valid
4.0ms	32×	body	320	valid
3.0ms	64×	body	80	valid
1.0ms	14×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
16.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

9.0ms	(- 1.0 (cos x))
26.0ms	(/ (- 1.0 (cos x)) (* x x))

series105.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- 1.0 (cos x))
77.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify689.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (208.0ms)

Iter	Nodes	Cost
0	88	507
1	232	489
2	1094	441
done	5001	441

prune149.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
11.0b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite102.0ms

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--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

12.0ms	(* 1/720 (pow x 4))
14.0ms	(* 1/24 (pow x 2))
74.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series143.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* 1/720 (pow x 4))
35.0ms	(* 1/24 (pow x 2))
68.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify715.0ms

Counts

75 → 75

Iterations

Useful iterations: done (713.0ms)

Iter	Nodes	Cost
0	121	780
1	286	701
2	1130	645
done	5000	635

prune198.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
11.0b	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

rewrite43.0ms

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` `associate-+r+` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

3 → 67

Calls

3 calls:

12.0ms	(* 1/720 (pow x 4))
12.0ms	(* 1/24 (pow x 2))
16.0ms	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

series154.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* 1/720 (pow x 4))
37.0ms	(* 1/24 (pow x 2))
66.0ms	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

simplify736.0ms

Counts

76 → 76

Iterations

Useful iterations: done (734.0ms)

Iter	Nodes	Cost
0	121	782
1	291	697
2	1063	641
done	5000	639

prune229.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.0b	(- 1.0 (cos x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

21.0ms	(/ (/ (- 1.0 (cos x)) x) x)
17.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series143.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ (/ (- 1.0 (cos x)) x) x)
51.0ms	(/ (- 1.0 (cos x)) x)
25.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

156 → 156

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	229	2262
1	549	2156
2	2484	2048
done	5000	2028

prune338.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes48.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.1b

bsearch70.0ms

Steps

Iters	Range		Point
8	0.0004268116563047139	15.006088268796836	0.0325473048632644
8	-0.031678663534995	-9.641814872486784e-07	-0.03100648570835607

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	41
1	34	32
done	34	32

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.3s	1546×	body	2560	valid
949.0ms	1267×	body	1280	valid
351.0ms	1498×	body	640	valid
207.0ms	932×	body	320	valid
166.0ms	2300×	body	80	valid
53.0ms	457×	body	160	valid