Details

sample135.0ms

Algorithm

intervals

Results

67.0ms	50×	body	2560	valid
42.0ms	95×	body	1280	valid
12.0ms	54×	body	640	valid
5.0ms	33×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	13×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite11.0ms

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))

series58.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify80.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

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

prune134.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	47	11	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	11	59

Merged error: 0.1b

Counts

59 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.7b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.1b	(- 1.0 (cos x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
9.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series129.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
44.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify89.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune253.0ms

Filtered

124 candidates to 88 candidates (71.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	122	13	135

Merged error: 0.1b

Counts

135 → 13

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.1b	(/ (sin x) (- 1.0 (cos x)))
2.1b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 159

Calls

3 calls:

9.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms	(/ (sin x) (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series88.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
34.0ms	(/ (sin x) (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify62.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	510	1595
1	2396	1452
2	5002	1339

prune219.0ms

Filtered

168 candidates to 87 candidates (51.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	167	14	181

Merged error: 0.1b

Counts

181 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (* (sin x) (/ 1 (- 1.0 (cos x)))))
0.1b	(/ 1 (- 1.0 (cos x)))
0.1b	(* (sin x) (/ 1 (- 1.0 (cos x))))
2.1b	(- 1.0 (cos x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r`
20×	`div-exp` `add-cbrt-cube`
16×	`prod-exp`
10×	`pow1` `rec-exp` `1-exp`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `associate-/r` `associate-/r/` `associate-/l` `add-log-exp`
4×	`cbrt-unprod`
3×	`flip3--` `pow-flip` `associate-l` `flip--` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `un-div-inv` `inv-pow`
1×	`sub-neg` `diff-log` `*-commutative`

Counts

4 → 139

Calls

4 calls:

13.0ms	(/ 1 (* (sin x) (/ 1 (- 1.0 (cos x)))))
6.0ms	(/ 1 (- 1.0 (cos x)))
11.0ms	(* (sin x) (/ 1 (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series118.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (* (sin x) (/ 1 (- 1.0 (cos x)))))
32.0ms	(/ 1 (- 1.0 (cos x)))
34.0ms	(* (sin x) (/ 1 (- 1.0 (cos x))))
18.0ms	(- 1.0 (cos x))

simplify53.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	461	962
1	2011	807
2	5001	756

prune173.0ms

Filtered

151 candidates to 78 candidates (51.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	11	12
Picked	0	1	1
Done	1	0	1
Total	152	13	165

Merged error: 0.1b

Counts

165 → 13

regimes131.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.3b

bsearch70.0ms

Steps

Iters	Range		Point
9	0.0002199982819353488	137964.03928948785	0.02010055841724964
9	-0.41295360884021565	-1.1902930357079885e-07	-0.02453727723232867

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	19
1	38	19

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.2s	1634×	body	2560	valid
1.2s	2734×	body	1280	valid
458.0ms	1853×	body	640	valid
146.0ms	930×	body	320	valid
59.0ms	476×	body	160	valid
30.0ms	368×	body	80	valid
16.0ms	5×	body	5120	valid