Details

sample54.0ms

Algorithm

intervals

Results

21.0ms	44×	body	2560	valid
11.0ms	49×	body	1280	valid
7.0ms	49×	body	640	valid
4.0ms	32×	body	320	valid
2.0ms	64×	body	80	valid
1.0ms	18×	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

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: 31.6b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
13.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
75×	`times-frac`
48×	`add-cube-cbrt`
18×	`swap-sqr` `associate-r` `associate-l`
17×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`*-commutative` `unswap-sqr`
5×	`associate-/l*`
4×	`add-log-exp`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`

Counts

2 → 126

Calls

2 calls:

4.0ms	(- 1.0 (cos x))
12.0ms	(/ (- 1.0 (cos x)) (* x x))

series69.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- 1.0 (cos x))
45.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify54.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	489	1050
1	1964	1000
2	5002	981

prune223.0ms

Filtered

132 candidates to 73 candidates (55.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	9	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	9	133

Merged error: 0.0b

Counts

133 → 9

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.9b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 159

Calls

3 calls:

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

series109.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (/ (- 1.0 (cos x)) x) x)
47.0ms	(/ (- 1.0 (cos x)) x)
19.0ms	(- 1.0 (cos x))

simplify57.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	548	1317
1	1948	1244
2	5003	1233

prune289.0ms

Filtered

168 candidates to 112 candidates (66.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	167	10	177

Merged error: 0.0b

Counts

177 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
6.9b	(/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

150×	`add-sqr-sqrt`
128×	`times-frac`
121×	`cbrt-prod`
114×	`*-un-lft-identity`
74×	`add-cube-cbrt`
54×	`associate-l`
27×	`associate-r`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`unswap-sqr`
16×	`associate-/r*`
15×	`add-cbrt-cube`
10×	`add-log-exp`
9×	`add-exp-log` `*-commutative`
8×	`associate-/l*`
6×	`cbrt-undiv`
4×	`pow1` `flip3--` `flip--` `cbrt-unprod`
3×	`sub-neg` `diff-log`
2×	`cbrt-div` `div-exp` `associate-/l/`
1×	`frac-2neg` `prod-exp` `clear-num` `div-inv`

Counts

4 → 214

Calls

4 calls:

4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
13.0ms	(/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x))

series377.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
323.0ms	(/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x))

simplify69.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	622	2467
1	2203	2349
2	5001	2294

prune511.0ms

Filtered

226 candidates to 139 candidates (61.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	227	9	236

Merged error: 0.0b

Counts

236 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

6.9b	(/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x))
7.4b	(cbrt (/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x)))
7.4b	(cbrt (/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x)))
7.4b	(cbrt (/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

880×	`cbrt-prod`
567×	`add-sqr-sqrt`
512×	`times-frac`
423×	`*-un-lft-identity`
287×	`add-cube-cbrt`
216×	`associate-l`
108×	`associate-r`
95×	`cbrt-div`
72×	`unswap-sqr`
68×	`distribute-lft-out--` `difference-of-squares`
64×	`associate-/r*`
36×	`*-commutative`
32×	`associate-/l*`
15×	`add-cbrt-cube`
9×	`add-exp-log`
8×	`associate-/l/`
6×	`cbrt-undiv`
4×	`pow1` `flip3--` `frac-2neg` `clear-num` `flip--` `cbrt-unprod` `div-inv` `add-log-exp`
3×	`pow1/3`
2×	`div-exp`
1×	`prod-exp`

Counts

4 → 679

Calls

4 calls:

17.0ms	(/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x))
18.0ms	(cbrt (/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x)))
18.0ms	(cbrt (/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x)))
19.0ms	(cbrt (/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x)))

series969.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x))
256.0ms	(cbrt (/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x)))
263.0ms	(cbrt (/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x)))
259.0ms	(cbrt (/ (cbrt (- 1.0 (cos x))) (* (cbrt x) x)))

simplify134.0ms

Algorithm

egg-herbie

Counts

691 → 691

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	846	10075
1	2533	9792
2	5002	9542

prune2.1s

Filtered

691 candidates to 418 candidates (60.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	690	1	691
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	690	10	700

Merged error: 0b

Counts

700 → 10

regimes56.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.2b

bsearch65.0ms

Steps

Iters	Range		Point
8	2.0262054515877825e-05	0.3235305135594418	0.030296156057222207
10	-85019.06990604498	-4.503960361653909e-11	-0.03159820685045102

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	10
1	29	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

792.0ms	1648×	body	2560	valid
299.0ms	1252×	body	1280	valid
229.0ms	1469×	body	640	valid
107.0ms	907×	body	320	valid
77.0ms	2220×	body	80	valid
37.0ms	504×	body	160	valid