Details

analyze521.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample138.0ms

Algorithm

intervals

Results

64.0ms	47×	body	2560	valid
45.0ms	97×	body	1280	valid
14.0ms	56×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	12×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	229	7
1	229	7

prune3.0ms

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: 27.4b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.2b	(- 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 → 51

Calls

2 calls:

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

series10.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

simplify41.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5058	605

prune114.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	45	12	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	12	58

Merged error: 0.2b

Counts

58 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x)))
0.4b	(+ 1.0 (cos x))
0.4b	(pow (cos x) 3)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite41.0ms

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 → 138

Calls

4 calls:

19.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x)))
3.0ms	(+ 1.0 (cos x))
2.0ms	(pow (cos x) 3)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series46.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x)))
2.0ms	(+ 1.0 (cos x))
5.0ms	(pow (cos x) 3)
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5700	2661

prune240.0ms

Filtered

84 candidates to 150 candidates (-78.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	148	14	162

Merged error: 0.2b

Counts

162 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ 1.0 (cos x))
0.4b	(pow (cos x) 3)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))
2.1b	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

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` `add-cbrt-cube`
4×	`log-prod`
3×	`pow-unpow`
2×	`difference-cubes` `sub-neg`
1×	`+-commutative` `cube-mult` `pow-to-exp` `log-div` `flip3--` `pow-pow` `flip3-+` `exp-diff` `diff-log` `unpow3` `rem-log-exp` `exp-sum` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 107

Calls

4 calls:

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

series20.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ 1.0 (cos x))
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))))

simplify35.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5121	1112

prune232.0ms

Filtered

70 candidates to 119 candidates (-70.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	118	15	133

Merged error: 0.2b

Counts

133 → 15

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
2.3b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 76

Calls

3 calls:

3.0ms	(/ 1.0 (sin x))
4.0ms	(/ (cos x) (sin x))
15.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series24.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/ 1.0 (sin x))
5.0ms	(/ (cos x) (sin x))
14.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4880	864
1	4880	864

prune85.0ms

Filtered

67 candidates to 85 candidates (-26.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	88	12	100

Merged error: 0.1b

Counts

100 → 12

regimes87.0ms

Accuracy

98.5% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 31.0b

bsearch38.0ms

Steps

Iters	Range		Point
8	0.0025069256093046386	1.9558254983902248	0.01952280889875721
9	-0.7051333342028844	-4.56453109903329e-07	-0.024164467200655196

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	95
1	83	95

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.4s	1668×	body	2560	valid
1.4s	2737×	body	1280	valid
496.0ms	1870×	body	640	valid
165.0ms	901×	body	320	valid
64.0ms	459×	body	160	valid
28.0ms	362×	body	80	valid
12.0ms	3×	body	5120	valid

Details

analyze521.0ms

sample138.0ms

simplify10.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series10.0ms

simplify41.0ms

prune114.0ms

localize15.0ms

rewrite41.0ms

series46.0ms

simplify41.0ms

prune240.0ms

localize20.0ms

rewrite35.0ms

series20.0ms

simplify35.0ms

prune232.0ms

localize8.0ms

rewrite24.0ms

series24.0ms

simplify78.0ms

prune85.0ms

regimes87.0ms

bsearch38.0ms

simplify2.0ms

end0.0ms

sample4.7s

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