Details

analyze775.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

sample201.0ms

Algorithm

intervals

Results

153.0ms	163×	body	80	valid
9.0ms	28×	body	1280	valid
9.0ms	35×	body	640	valid
4.0ms	13×	body	1280	nan
3.0ms	13×	body	640	nan
3.0ms	42×	body	80	nan
3.0ms	14×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	8×	body	320	nan
1.0ms	6×	body	160	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5225	27

prune11.0ms

Filtered

1 candidates to 1 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: 45.0b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
14.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 79

Calls

4 calls:

17.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
16.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
13.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
57.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
188.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify43.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5044	2021

prune201.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	89	4	93

Merged error: 3.7b

Counts

93 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
1.0b	(+ (* t t) (/ l (/ x l)))
5.2b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
30.8b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `add-log-exp`
7×	`pow1` `sqrt-prod`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`associate-r`
2×	`+-commutative` `associate-+r+` `sum-log` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
11.0ms	(+ (* t t) (/ l (/ x l)))
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
12.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
9.0ms	(+ (* t t) (/ l (/ x l)))
15.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
24.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify27.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5246	1361

prune156.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	74	7	81

Merged error: 3.7b

Counts

81 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
1.0b	(+ (* t t) (* l (/ l x)))
5.2b	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
30.8b	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-*r/`
8×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
7×	`pow1` `sqrt-prod`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`associate-r`
2×	`+-commutative` `associate-+r+` `sum-log` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
4.0ms	(+ (* t t) (* l (/ l x)))
8.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
9.0ms	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sqrt 2.0) t)
9.0ms	(+ (* t t) (* l (/ l x)))
15.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
24.0ms	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5002	1369

prune135.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	77	7	84

Merged error: 3.7b

Counts

84 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
1.0b	(+ (* t t) (/ l (/ x l)))
5.2b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
30.8b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-sqr-sqrt` `associate-l` `add-cbrt-cube`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 67

Calls

4 calls:

8.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
11.0ms	(+ (* t t) (/ l (/ x l)))
12.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
10.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
9.0ms	(+ (* t t) (/ l (/ x l)))
15.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
24.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify26.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5001	1386

prune156.0ms

Filtered

61 candidates to 79 candidates (-29.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	77	9	86

Merged error: 3.7b

Counts

86 → 9

regimes395.0ms

Accuracy

74.9% (6.0b remaining)

Error of 10.1b against oracle of 4.2b and baseline of 27.9b

bsearch488.0ms

Steps

Iters	Range		Point
9	2.1146073311356353e+130	5.362051102104383e+135	2.0450614983521334e+132
8	2.225756032728017e-176	1.214787737411498e-173	2.2538051772827984e-176
9	7.530146293466049e-248	8.726008755037594e-243	8.649079172249573e-243
10	-1.1730997492055264e-175	-2.3651903036199614e-185	-1.1631519311837101e-175
1	-7.421600693922005e-120	-6.767036463194733e-120	-6.930677520876551e-120
9	-9.003662074961365e+126	-1.0998778362763488e+121	-1.8244705587929496e+124

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	156	183
1	156	183

end0.0ms

sample1.9s

Algorithm

intervals

Results

363.0ms	5101×	body	80	valid
275.0ms	841×	body	1280	valid
270.0ms	1042×	body	640	valid
182.0ms	565×	body	1280	nan
155.0ms	596×	body	640	nan
127.0ms	650×	body	320	valid
99.0ms	1425×	body	80	nan
69.0ms	364×	body	320	nan
52.0ms	366×	body	160	valid
25.0ms	188×	body	160	nan

Details

analyze775.0ms

sample201.0ms

simplify34.0ms

prune11.0ms

localize16.0ms

rewrite53.0ms

series339.0ms

simplify43.0ms

prune201.0ms

localize17.0ms

rewrite38.0ms

series52.0ms

simplify27.0ms

prune156.0ms

localize18.0ms

rewrite27.0ms

series55.0ms

simplify38.0ms

prune135.0ms

localize19.0ms

rewrite43.0ms

series52.0ms

simplify26.0ms

prune156.0ms

regimes395.0ms

bsearch488.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling