Details

sample86.0ms

Algorithm

intervals

Results

20.0ms	38×	body	640	valid
16.0ms	308×	body	80	nan
8.0ms	155×	body	80	valid
7.0ms	23×	body	1280	valid
4.0ms	16×	body	1280	nan
3.0ms	21×	body	320	valid
2.0ms	12×	body	640	nan
2.0ms	19×	body	160	valid
2.0ms	11×	body	320	nan
0.0ms	5×	body	160	nan

simplify94.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Filtered

1 candidates to 0 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: 45.3b

Counts

2 → 1

localize18.0ms

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))))
0.5b	(* (sqrt 2.0) t)
15.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sqrt-div` `associate--l+`
3×	`flip3--` `flip--`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-/r/` `-commutative` `associate-/l`
1×	`sub-neg` `frac-2neg` `pow1/2` `clear-num` `div-inv`

Counts

4 → 19

Calls

4 calls:

16.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
3.0ms	(* (sqrt 2.0) t)
14.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
14.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

419.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
43.0ms	(* (sqrt 2.0) t)
213.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify136.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	273	392
1	991	384
2	4595	366
3	5001	366

prune113.0ms

Filtered

31 candidates to 24 candidates (77.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	4	32

Merged error: 6.9b

Counts

32 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

5.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.4b	(/ (pow l 2) x)
9.5b	(/ (pow t 2) x)
30.4b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/`
24×	`frac-add`
14×	`flip3-+` `sqrt-div` `flip-+`
12×	`associate-/l*`
10×	`clear-num`
6×	`frac-2neg` `unpow2` `sqr-pow`
4×	`associate-+r+` `un-div-inv`
3×	`+-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `div-inv`
1×	`pow1/2`

Counts

4 → 44

Calls

4 calls:

10.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
3.0ms	(/ (pow l 2) x)
3.0ms	(/ (pow t 2) x)
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series260.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
159.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	450	1071
1	1879	1037
2	5001	1037

prune201.0ms

Filtered

56 candidates to 39 candidates (69.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	53	7	60

Merged error: 4.4b

Counts

60 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
5.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
9.5b	(/ (pow t 2) x)
30.4b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/`
24×	`frac-add`
15×	`flip3-+` `flip-+`
14×	`sqrt-div`
10×	`associate-/l*`
9×	`clear-num`
5×	`frac-2neg` `unpow2` `sqr-pow`
4×	`+-commutative` `associate-+r+` `un-div-inv`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`pow1/2` `div-inv`

Counts

4 → 42

Calls

4 calls:

5.0ms	(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
11.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
3.0ms	(/ (pow t 2) x)
10.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
67.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
18.0ms	(/ (pow t 2) x)
162.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	457	1215
1	1746	1200
2	5002	1200

prune216.0ms

Filtered

54 candidates to 37 candidates (68.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	53	8	61

Merged error: 4.3b

Counts

61 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
5.0b	(+ (+ (/ (* l 2.0) (/ x l)) (* 4.0 (/ (pow t 2) x))) (* (pow t 2) 2.0))
9.5b	(/ (pow t 2) x)
30.4b	(sqrt (+ (+ (/ (* l 2.0) (/ x l)) (* 4.0 (/ (pow t 2) x))) (* (pow t 2) 2.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

2×	`+-commutative` `associate-+l+` `flip3-+` `sqrt-div` `flip-+` `associate-/l*`
1×	`frac-2neg` `pow1/2` `clear-num` `*-commutative` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 14

Calls

4 calls:

2.0ms	(* (sqrt 2.0) t)
15.0ms	(+ (+ (/ (* l 2.0) (/ x l)) (* 4.0 (/ (pow t 2) x))) (* (pow t 2) 2.0))
3.0ms	(/ (pow t 2) x)
13.0ms	(sqrt (+ (+ (/ (* l 2.0) (/ x l)) (* 4.0 (/ (pow t 2) x))) (* (pow t 2) 2.0)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sqrt 2.0) t)
63.0ms	(+ (+ (/ (* l 2.0) (/ x l)) (* 4.0 (/ (pow t 2) x))) (* (pow t 2) 2.0))
23.0ms	(/ (pow t 2) x)
350.0ms	(sqrt (+ (+ (/ (* l 2.0) (/ x l)) (* 4.0 (/ (pow t 2) x))) (* (pow t 2) 2.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	168	230
1	554	224
2	2650	214
3	5001	210

prune67.0ms

Filtered

26 candidates to 17 candidates (65.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	26	8	34

Merged error: 4.3b

Counts

34 → 8

regimes395.0ms

Accuracy

75% (6.0b remaining)

Error of 9.8b against oracle of 3.9b and baseline of 27.6b

bsearch598.0ms

Steps

Iters	Range		Point
8	3.403568998745067e+87	4.905813436801621e+90	4.488332034392144e+90
8	1.7245540549261378e-174	7.545122391836811e-171	4.899761605523815e-171
10	3.871683063339351e-223	9.005404400815374e-213	6.311404485509687e-213
4	-6.914198310900146e-265	-3.618629021631408e-265	-6.769228911391228e-265
8	-9.505671634543452e-166	-2.1070939213285662e-168	-9.359052842342105e-167
6	-31565395626.252914	-3186624082.971198	-31115301794.108517

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	121
1	90	121

end0.0ms

sample2.1s

Algorithm

intervals

Results

512.0ms	10323×	body	80	nan
260.0ms	5047×	body	80	valid
229.0ms	903×	body	1280	valid
207.0ms	1044×	body	640	valid
152.0ms	598×	body	1280	nan
122.0ms	604×	body	640	nan
95.0ms	635×	body	320	valid
48.0ms	335×	body	320	nan
37.0ms	371×	body	160	valid
18.0ms	188×	body	160	nan