Details

sample50.0ms

Algorithm

intervals

Results

22.0ms	52×	body	2560	valid
8.0ms	41×	body	1280	valid
6.0ms	45×	body	640	valid
3.0ms	33×	body	320	valid
2.0ms	69×	body	80	valid
1.0ms	16×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1.0 (cos x))
14.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite28.0ms

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:

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

series66.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239
done	5002	239

prune112.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(/ (sqrt (- 1.0 (cos x))) x)
2.2b	(- 1.0 (cos x))
2.2b	(- 1.0 (cos x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
40×	`sqrt-prod`
38×	`add-cube-cbrt`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r*`
4×	`pow1` `flip3--` `sqrt-div` `flip--` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 126

Calls

4 calls:

17.0ms	(/ (sqrt (- 1.0 (cos x))) x)
19.0ms	(/ (sqrt (- 1.0 (cos x))) x)
6.0ms	(- 1.0 (cos x))
7.0ms	(- 1.0 (cos x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
88.0ms	(/ (sqrt (- 1.0 (cos x))) x)
19.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify97.0ms

Counts

138 → 138

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	242	1020
1	706	972
2	2968	960
3	5002	960
done	5002	960

prune309.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.9b	(/ (cos x) (* x x))
0.9b	(/ 1.0 (* x x))
16.9b	(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

13.0ms	(/ (cos x) (* x x))
8.0ms	(/ 1.0 (* x x))
35.0ms	(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

series134.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ (cos x) (* x x))
29.0ms	(/ 1.0 (* x x))
75.0ms	(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

simplify64.0ms

Counts

72 → 72

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	269	413
1	885	365
2	3007	362
3	5001	362
done	5001	362

prune143.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))
14.6b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (pow x 2)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`add-exp-log` `distribute-lft-out--`
10×	`add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
4×	`div-exp`
3×	`difference-cubes` `pow-unpow` `prod-exp`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `flip3-+` `associate-*l/` `pow-exp` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 141

Calls

4 calls:

8.0ms	(+ (cos x) 1.0)
4.0ms	(pow (cos x) 3)
24.0ms	(- (pow 1.0 3) (pow (cos x) 3))
85.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (pow x 2)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (cos x) 1.0)
28.0ms	(pow (cos x) 3)
53.0ms	(- (pow 1.0 3) (pow (cos x) 3))
156.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (pow x 2)))

simplify85.0ms

Counts

153 → 153

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	583	1686
1	2883	1574
2	5001	1530
done	5001	1530

prune349.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.3b

bsearch65.0ms

Steps

Iters	Range		Point
10	0.00012253353073063669	15794870057.515802	0.02887089759792522
9	-2.7342232818785663	-5.599255928070541e-06	-0.0289378252595692

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	15
1	30	15
done	30	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

720.0ms	1628×	body	2560	valid
286.0ms	1270×	body	1280	valid
213.0ms	1430×	body	640	valid
96.0ms	912×	body	320	valid
69.0ms	2261×	body	80	valid
35.0ms	499×	body	160	valid