Details

sample47.0ms

Algorithm

intervals

Results

20.0ms	45×	body	2560	valid
8.0ms	39×	body	1280	valid
6.0ms	42×	body	640	valid
3.0ms	89×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	16×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
12.8b	(/ (- 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:

4.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series64.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
46.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify59.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

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

prune106.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
28×	`cbrt-prod`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1`
10×	`swap-sqr` `add-log-exp`
9×	`flip3--` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

10.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series195.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
17.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
22.0ms	(- 1.0 (cos x))

simplify100.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	224	813
1	704	769
2	3166	698
3	5001	681

prune244.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series74.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- 1.0 (cos x))
17.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))

simplify105.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	88	304
1	226	284
2	608	284
3	2555	284
4	5001	284

prune219.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ (cos x) (* x x))
0.5b	(/ 1.0 (* x x))
14.3b	(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

rewrite19.0ms

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:

5.0ms	(/ (cos x) (* x x))
4.0ms	(/ 1.0 (* x x))
8.0ms	(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

series132.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ (cos x) (* x x))
24.0ms	(/ 1.0 (* x x))
75.0ms	(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (19.0ms)

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

prune126.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes94.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.5b

bsearch70.0ms

Steps

Iters	Range		Point
10	9.598072339636849e-08	814.2255113159289	0.03176890082881835
11	-402.67606408878214	-1.1015269942960052e-19	-0.033395966236815566

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	11
1	34	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

764.0ms	1666×	body	2560	valid
275.0ms	1211×	body	1280	valid
217.0ms	1506×	body	640	valid
98.0ms	926×	body	320	valid
79.0ms	2227×	body	80	valid
38.0ms	464×	body	160	valid