Details

sample126.0ms

Algorithm

intervals

Results

59.0ms	44×	body	2560	valid
38.0ms	90×	body	1280	valid
13.0ms	58×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	18×	body	160	valid
1.0ms	15×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 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:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series55.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify87.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune149.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	46	12	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	12	59

Merged error: 0.1b

Counts

59 → 12

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
110×	`*-un-lft-identity`
109×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
31×	`associate-/r*`
21×	`associate-/r/`
18×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
10×	`add-cbrt-cube` `associate-/l*`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `clear-num`
3×	`frac-2neg`
2×	`rec-exp` `1-exp` `remove-double-div`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 171

Calls

3 calls:

11.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms	(/ (sin x) (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series93.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
35.0ms	(/ (sin x) (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify65.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	518	1634
1	2445	1488
2	5001	1372

prune266.0ms

Filtered

180 candidates to 89 candidates (49.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	172	8	180
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	179	13	192

Merged error: 0.1b

Counts

192 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sqrt (- 1.0 (cos x))) (sin x)) (sqrt (- 1.0 (cos x))))
0.2b	(/ (sqrt (- 1.0 (cos x))) (sin x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
60×	`sqrt-prod`
52×	`times-frac`
47×	`add-cube-cbrt`
42×	`sqrt-div`
32×	`frac-times` `associate-/l*`
28×	`associate-l`
23×	`flip3--` `flip--`
16×	`associate-*l/`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `associate-/l/` `add-log-exp`
6×	`pow1` `unswap-sqr`
4×	`frac-2neg` `clear-num`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 182

Calls

4 calls:

23.0ms	(* (/ (sqrt (- 1.0 (cos x))) (sin x)) (sqrt (- 1.0 (cos x))))
7.0ms	(/ (sqrt (- 1.0 (cos x))) (sin x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series175.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (/ (sqrt (- 1.0 (cos x))) (sin x)) (sqrt (- 1.0 (cos x))))
96.0ms	(/ (sqrt (- 1.0 (cos x))) (sin x))
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify77.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	551	2115
1	2335	1951
2	5002	1921

prune460.0ms

Filtered

194 candidates to 125 candidates (64.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	188	6	194
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	192	15	207

Merged error: 0.1b

Counts

207 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
0.3b	(+ (cos x) 1.0)
0.3b	(pow (cos x) 3)
1.7b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

601×	`add-sqr-sqrt`
597×	`*-un-lft-identity`
448×	`times-frac`
319×	`associate-l`
288×	`difference-of-squares`
219×	`unpow-prod-down` `cube-prod`
145×	`sqr-pow`
117×	`distribute-lft-out`
111×	`add-cube-cbrt`
90×	`distribute-lft-out--`
87×	`associate-r`
75×	`pow-unpow`
72×	`difference-cubes`
29×	`*-commutative` `unswap-sqr`
28×	`associate-/l*`
16×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `rem-cube-cbrt`

Counts

4 → 583

Calls

4 calls:

52.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
4.0ms	(+ (cos x) 1.0)
3.0ms	(pow (cos x) 3)
17.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series268.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
10.0ms	(+ (cos x) 1.0)
28.0ms	(pow (cos x) 3)
57.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify137.0ms

Algorithm

egg-herbie

Counts

595 → 595

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1474	11944
1	5002	11572

prune870.0ms

Filtered

595 candidates to 219 candidates (36.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	587	8	595
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	594	16	610

Merged error: 0.1b

Counts

610 → 16

regimes84.0ms

Accuracy

98.9% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.7b

bsearch93.0ms

Steps

Iters	Range		Point
8	2.0262054515877825e-05	0.3235305135594418	0.022624277856211048
10	-85019.06990604498	-4.503960361653909e-11	-0.02058278953964613

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	25
1	47	25

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.2s	1640×	body	2560	valid
1.2s	2700×	body	1280	valid
455.0ms	1880×	body	640	valid
141.0ms	908×	body	320	valid
55.0ms	501×	body	160	valid
30.0ms	365×	body	80	valid
24.0ms	6×	body	5120	valid