Details

sample109.0ms

Algorithm

intervals

Results

40.0ms	101×	body	1280	valid
36.0ms	26×	body	2560	valid
14.0ms	63×	body	640	valid
5.0ms	35×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	11×	body	80	valid

simplify7.0ms

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

prune3.0ms

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: 16.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (- 1.0 (cos x)) (sin x))
0.7b	(- 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))

series12.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

simplify81.0ms

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

prune127.0ms

Filtered

58 candidates to 42 candidates (27.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	43	15	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	15	59

Merged error: 0.3b

Counts

59 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.5b	(- (pow 1.0 3) (pow (cos x) 3))
0.5b	(pow (cos x) 3)
0.7b	(+ (cos x) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

21.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))
3.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)

series38.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))
5.0ms	(pow (cos x) 3)
2.0ms	(+ (cos x) 1.0)

simplify96.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	617	2953
1	2699	2889
2	5002	2810

prune353.0ms

Filtered

201 candidates to 105 candidates (47.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	192	9	201
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	197	19	216

Merged error: 0.3b

Counts

216 → 19

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (pow 1.0 3) (pow (cos x) 3))
0.5b	(pow (cos x) 3)
0.6b	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))
0.7b	(+ (cos x) 1.0)

rewrite35.0ms

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:

11.0ms	(- (pow 1.0 3) (pow (cos x) 3))
2.0ms	(pow (cos x) 3)
14.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))
4.0ms	(+ (cos x) 1.0)

series23.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (pow 1.0 3) (pow (cos x) 3))
5.0ms	(pow (cos x) 3)
7.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))
2.0ms	(+ (cos x) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	348	673
1	1238	636
2	5001	608

prune247.0ms

Filtered

121 candidates to 69 candidates (43.0%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	2	16	18
Picked	0	1	1
Done	0	0	0
Total	119	21	140

Merged error: 0.2b

Counts

140 → 21

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
0.5b	(- (pow 1.0 3) (pow (cos x) 3))
0.5b	(pow (cos x) 3)
0.7b	(+ (cos x) 1.0)

rewrite46.0ms

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:

23.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))
2.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)

series45.0ms

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

simplify85.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	566	1663
1	2535	1547
2	5002	1503

prune193.0ms

Filtered

151 candidates to 85 candidates (43.7%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	3	16	19
Picked	1	0	1
Done	0	1	1
Total	153	19	172

Merged error: 0.2b

Counts

172 → 19

regimes123.0ms

Accuracy

96.4% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 15.3b

bsearch78.0ms

Steps

Iters	Range		Point
11	9.244429547692074e-24	0.06968268467981475	0.022872755459207934
15	-163.36048396326007	3.867226923396042e-305	-0.021593100134724912

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	40
1	52	40

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	2911×	body	1280	valid
996.0ms	769×	body	2560	valid
506.0ms	2188×	body	640	valid
178.0ms	1078×	body	320	valid
69.0ms	573×	body	160	valid
32.0ms	480×	body	80	valid
3.0ms	1×	body	5120	valid

Details

sample109.0ms

simplify7.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series12.0ms

simplify81.0ms

prune127.0ms

localize16.0ms

rewrite49.0ms

series38.0ms

simplify96.0ms

prune353.0ms

localize20.0ms

rewrite35.0ms

series23.0ms

simplify49.0ms

prune247.0ms

localize16.0ms

rewrite46.0ms

series45.0ms

simplify85.0ms

prune193.0ms

regimes123.0ms

bsearch78.0ms

simplify2.0ms

end0.0ms

sample3.2s

Profiling