Details

analyze766.0ms

Algorithm: search

sample62.0ms

Algorithm

intervals

Results

13.0ms	179×	body	80	valid
8.0ms	23×	body	1280	valid
7.0ms	27×	body	640	valid
6.0ms	18×	body	1280	nan
4.0ms	17×	body	640	nan
3.0ms	16×	body	320	valid
3.0ms	40×	body	80	nan
2.0ms	12×	body	320	nan
2.0ms	11×	body	160	valid
1.0ms	7×	body	160	nan

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	14
1	93	14
2	193	14
3	414	14
4	718	14
5	1192	14
6	2816	14
7	5001	14

prune6.0ms

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: 39.4b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
0.5b	(* (sqrt 2.0) t)
11.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`associate-l`
21×	`times-frac`
19×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
7×	`sqrt-prod`
6×	`associate-r` `add-log-exp`
5×	`distribute-lft-out`
4×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `sqrt-div` `associate-r/` `pow-prod-down` `associate--l+` `associate-/r/` `-commutative` `flip-+`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `associate-*l/` `div-inv`

Counts

4 → 102

Calls

4 calls:

14.0ms	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
5.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
12.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
4.0ms	(* (sqrt 2.0) t)
56.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
333.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify89.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	700	1206
1	3840	1127
2	5001	1126

prune259.0ms

Filtered

81 candidates to 114 candidates (-40.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Merged error: 5.3b

Counts

115 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (pow l 2) x)
4.7b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
9.2b	(/ (pow t 2) x)
27.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

5.0ms	(/ (pow l 2) x)
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (pow l 2) x)
15.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
3.0ms	(/ (pow t 2) x)
28.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	526	1067
1	2113	984
2	5001	978

prune338.0ms

Filtered

97 candidates to 142 candidates (-46.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	139	10	149

Merged error: 3.9b

Counts

149 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (pow t 2) (* l (/ l x)))
4.7b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.2b	(/ (pow t 2) x)
27.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-r/` `associate-/l` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 92

Calls

4 calls:

4.0ms	(+ (pow t 2) (* l (/ l x)))
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
5.0ms	(/ (pow t 2) x)
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (pow t 2) (* l (/ l x)))
15.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
3.0ms	(/ (pow t 2) x)
25.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	456	925
1	1936	858
2	5003	855

prune241.0ms

Filtered

75 candidates to 104 candidates (-38.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	103	11	114

Merged error: 3.9b

Counts

114 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
4.7b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
9.2b	(/ (pow t 2) x)
27.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-r/` `associate-/l` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 92

Calls

4 calls:

4.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
18.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
3.0ms	(/ (pow t 2) x)
29.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	463	1308
1	1965	1213
2	5001	1210

prune191.0ms

Filtered

75 candidates to 104 candidates (-38.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	104	11	115

Merged error: 3.9b

Counts

115 → 11

regimes590.0ms

Accuracy

75.1% (6.1b remaining)

Error of 9.8b against oracle of 3.8b and baseline of 28.1b

bsearch1.0s

Steps

Iters	Range		Point
9	3.2273724874149295e-52	2.636325875301829e-43	2.584586791235412e-43
9	-2.530314617473807e+74	-3.1755666509625157e+69	-2.0903492561486186e+74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	57
1	60	57

end0.0ms

analyze770.0ms

Algorithm: search

sample1.9s

Algorithm

intervals

Results

364.0ms	5084×	body	80	valid
292.0ms	851×	body	1280	valid
287.0ms	1075×	body	640	valid
184.0ms	552×	body	1280	nan
155.0ms	594×	body	640	nan
128.0ms	639×	body	320	valid
103.0ms	1465×	body	80	nan
69.0ms	350×	body	320	nan
49.0ms	351×	body	160	valid
23.0ms	173×	body	160	nan

Details

analyze766.0ms

sample62.0ms

simplify79.0ms

prune6.0ms

localize16.0ms

rewrite46.0ms

series423.0ms

simplify89.0ms

prune259.0ms

localize17.0ms

rewrite30.0ms

series49.0ms

simplify62.0ms

prune338.0ms

localize17.0ms

rewrite30.0ms

series51.0ms

simplify58.0ms

prune241.0ms

localize21.0ms

rewrite28.0ms

series63.0ms

simplify61.0ms

prune191.0ms

regimes590.0ms

bsearch1.0s

simplify2.0ms

end0.0ms

analyze770.0ms

sample1.9s

Profiling