Details

sample57.0ms

Algorithm

intervals

Results

24.0ms	57×	body	2560	valid
13.0ms	41×	body	1280	valid
8.0ms	59×	body	640	valid
2.0ms	23×	body	320	valid
2.0ms	63×	body	80	valid
1.0ms	13×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	29	8
done	29	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1.0 (cos x))
17.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

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:

2.0ms	(- 1.0 (cos x))
9.0ms	(/ (- 1.0 (cos x)) (* x x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
45.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.1s

Counts

48 → 48

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	88	507
1	218	489
2	636	441
3	2189	441
done	5000	440

prune103.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
11.6b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite38.0ms

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:

5.0ms	(* 1/720 (pow x 4))
6.0ms	(* 1/24 (pow x 2))
23.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series105.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* 1/720 (pow x 4))
24.0ms	(* 1/24 (pow x 2))
42.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify1.4s

Counts

75 → 75

Iterations

Useful iterations: 3 (426.0ms)

Iter	Nodes	Cost
0	121	780
1	274	701
2	823	643
3	2860	629
done	5001	629

prune149.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
1.2b	(- 1.0 (cos x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 114

Calls

3 calls:

7.0ms	(/ (- 1.0 (cos x)) x)
21.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms	(- 1.0 (cos x))

series106.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- 1.0 (cos x)) x)
42.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
18.0ms	(- 1.0 (cos x))

simplify848.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (212.0ms)

Iter	Nodes	Cost
0	189	1536
1	519	1379
2	1542	1227
done	5000	1227

prune219.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ 1.0 (cos x)))
0.3b	(+ 1.0 (cos x))
0.3b	(pow (cos x) 3)
1.1b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

10.0ms	(* (cos x) (+ 1.0 (cos x)))
3.0ms	(+ 1.0 (cos x))
1.0ms	(pow (cos x) 3)
18.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series114.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (cos x) (+ 1.0 (cos x)))
10.0ms	(+ 1.0 (cos x))
31.0ms	(pow (cos x) 3)
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify615.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (168.0ms)

Iter	Nodes	Cost
0	145	1155
1	346	1045
2	1371	992
done	5000	992

prune238.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes39.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.5b

bsearch90.0ms

Steps

Iters	Range		Point
10	5.968040026638966e-05	117627206.70733242	0.02844105962587155
10	-64880754058.88788	-2.651420353119469e-05	-0.02660967226737158

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	91
1	62	91
done	62	91

end0.0ms

sample1.5s

Algorithm

intervals

Results

743.0ms	1660×	body	2560	valid
286.0ms	1248×	body	1280	valid
196.0ms	1448×	body	640	valid
95.0ms	918×	body	320	valid
72.0ms	2275×	body	80	valid
37.0ms	451×	body	160	valid