Details

analyze224.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample67.0ms

Algorithm

intervals

Results

34.0ms	58×	body	2560	valid
10.0ms	40×	body	1280	valid
9.0ms	55×	body	640	valid
3.0ms	28×	body	320	valid
2.0ms	61×	body	80	valid
1.0ms	14×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	8
1	16	8

prune2.0ms

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: 34.9b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
15.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 41

Calls

2 calls:

4.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
6.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify30.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5871	438

prune85.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	39	8	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	8	48

Merged error: 0.1b

Counts

48 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 4) 1/720)
0.1b	(* x (* x 1/24))
0.4b	(* x 1/24)
11.2b	(+ (* (pow x 4) 1/720) (- 1/2 (* x (* x 1/24))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`*-commutative`
2×	`sum-log` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `pow-exp` `flip-+`

Counts

4 → 75

Calls

4 calls:

5.0ms	(* (pow x 4) 1/720)
4.0ms	(* x (* x 1/24))
3.0ms	(* x 1/24)
6.0ms	(+ (* (pow x 4) 1/720) (- 1/2 (* x (* x 1/24))))

series13.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (pow x 4) 1/720)
3.0ms	(* x (* x 1/24))
2.0ms	(* x 1/24)
5.0ms	(+ (* (pow x 4) 1/720) (- 1/2 (* x (* x 1/24))))

simplify30.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5078	653

prune109.0ms

Filtered

54 candidates to 87 candidates (-61.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	87	8	95

Merged error: 0.1b

Counts

95 → 8

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)
1.5b	(- 1.0 (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 146

Calls

3 calls:

8.0ms	(/ (/ (- 1.0 (cos x)) x) x)
5.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series14.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ (/ (- 1.0 (cos x)) x) x)
5.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5245	1987

prune157.0ms

Filtered

102 candidates to 155 candidates (-52.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	153	10	163

Merged error: 0.1b

Counts

163 → 10

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
0.1b	(/ x (- 1.0 (cos x)))
0.1b	(/ 1 (/ x (- 1.0 (cos x))))
1.5b	(- 1.0 (cos x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

774×	`times-frac`
443×	`add-sqr-sqrt` `*-un-lft-identity`
337×	`add-cube-cbrt`
74×	`associate-/l*`
53×	`distribute-lft-out--` `difference-of-squares`
39×	`associate-/r/`
36×	`add-exp-log`
29×	`associate-/r*`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
18×	`flip3--` `flip--`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`rec-exp` `1-exp`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `associate-/l/` `inv-pow`

Counts

4 → 454

Calls

4 calls:

19.0ms	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
5.0ms	(/ x (- 1.0 (cos x)))
8.0ms	(/ 1 (/ x (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

series22.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
7.0ms	(/ x (- 1.0 (cos x)))
5.0ms	(/ 1 (/ x (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

simplify142.0ms

Algorithm

egg-herbie

Counts

466 → 466

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4962	7469
1	4962	7469

prune446.0ms

Filtered

254 candidates to 466 candidates (-83.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	465	1	466
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	466	10	476

Merged error: 0.1b

Counts

476 → 10

regimes146.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.8b

bsearch51.0ms

Steps

Iters	Range		Point
9	0.0005384656241850175	57.48121287645445	0.03290940923071691
10	-0.8796650844704564	-7.336273207056607e-13	-0.02996085913414137

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	32
1	32	32

end0.0ms

analyze220.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample1.8s

Algorithm

intervals

Results

817.0ms	1608×	body	2560	valid
342.0ms	1258×	body	1280	valid
242.0ms	1479×	body	640	valid
109.0ms	936×	body	320	valid
87.0ms	2240×	body	80	valid
43.0ms	479×	body	160	valid

Details

analyze224.0ms

sample67.0ms

simplify2.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series9.0ms

simplify30.0ms

prune85.0ms

localize8.0ms

rewrite20.0ms

series13.0ms

simplify30.0ms

prune109.0ms

localize6.0ms

rewrite26.0ms

series14.0ms

simplify49.0ms

prune157.0ms

localize7.0ms

rewrite70.0ms

series22.0ms

simplify142.0ms

prune446.0ms

regimes146.0ms

bsearch51.0ms

simplify1.0ms

end0.0ms

analyze220.0ms

sample1.8s

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