Details

sample139.0ms

Algorithm

intervals

Results

74.0ms	56×	body	2560	valid
36.0ms	82×	body	1280	valid
12.0ms	52×	body	640	valid
5.0ms	33×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	13×	body	80	valid

simplify5.0ms

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 (100.0%)

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: 30.2b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.7b	(- 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))
3.0ms	(- 1.0 (cos x))

series16.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

simplify77.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2640	373
3	5002	373

prune122.0ms

Filtered

58 candidates to 42 candidates (27.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	44	14	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	14	59

Merged error: 0.2b

Counts

59 → 14

localize14.0ms

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)
0.4b	(pow (cos x) 3)
1.5b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite45.0ms

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×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
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` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

22.0ms	(/ (- (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)
2.0ms	(pow (cos x) 3)
10.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series44.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
2.0ms	(+ (cos x) 1.0)
5.0ms	(pow (cos x) 3)
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify83.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	566	1663
1	2538	1547
2	5001	1503

prune247.0ms

Filtered

151 candidates to 84 candidates (44.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	146	5	151
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	149	16	165

Merged error: 0.1b

Counts

165 → 16

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.7b	(- 1.0 (cos x))

rewrite26.0ms

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

series31.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
13.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

simplify86.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (20.0ms)

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

prune192.0ms

Filtered

124 candidates to 88 candidates (29.0%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	123	17	140

Merged error: 0.1b

Counts

140 → 17

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
1.5b	(- (pow 1.0 3) (pow (cos x) 3))
1.7b	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
32×	`difference-of-squares`
31×	`*-un-lft-identity`
27×	`unpow-prod-down` `cube-prod`
26×	`log-pow`
25×	`exp-prod`
17×	`sqr-pow`
10×	`distribute-lft-out--`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log` `log-prod` `add-cbrt-cube`
3×	`pow-unpow`
2×	`difference-cubes` `sub-neg` `exp-sum`
1×	`+-commutative` `cube-mult` `pow-to-exp` `log-div` `flip3--` `pow-pow` `flip3-+` `exp-diff` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 109

Calls

4 calls:

4.0ms	(+ (cos x) 1.0)
2.0ms	(pow (cos x) 3)
10.0ms	(- (pow 1.0 3) (pow (cos x) 3))
15.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ (cos x) 1.0)
5.0ms	(pow (cos x) 3)
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))
7.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify46.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	348	673
1	1242	636
2	5001	608

prune177.0ms

Filtered

121 candidates to 69 candidates (43.0%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	0	15	15
Picked	1	0	1
Done	0	1	1
Total	120	18	138

Merged error: 0.1b

Counts

138 → 18

regimes250.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.6b

bsearch41.0ms

Steps

Iters	Range		Point
10	1.8861453929162526e-07	127140.91663662092	0.024841528028594986
10	-81569296.22560106	-6.097158829196934e-11	-0.020927617013354313

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	33
1	46	33

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1582×	body	2560	valid
1.2s	2802×	body	1280	valid
442.0ms	1872×	body	640	valid
153.0ms	895×	body	320	valid
66.0ms	491×	body	160	valid
23.0ms	355×	body	80	valid
10.0ms	3×	body	5120	valid

Details

sample139.0ms

simplify5.0ms

prune2.0ms

localize7.0ms

rewrite11.0ms

series16.0ms

simplify77.0ms

prune122.0ms

localize14.0ms

rewrite45.0ms

series44.0ms

simplify83.0ms

prune247.0ms

localize10.0ms

rewrite26.0ms

series31.0ms

simplify86.0ms

prune192.0ms

localize18.0ms

rewrite36.0ms

series21.0ms

simplify46.0ms

prune177.0ms

regimes250.0ms

bsearch41.0ms

simplify1.0ms

end0.0ms

sample4.2s

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