Details

sample94.0ms

Algorithm

intervals

Results

32.0ms	353×	body	80	nan
9.0ms	33×	body	1280	valid
8.0ms	157×	body	80	valid
6.0ms	31×	body	640	valid
5.0ms	20×	body	1280	nan
3.0ms	23×	body	320	valid
3.0ms	17×	body	640	nan
2.0ms	12×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	12×	body	160	nan

simplify86.0ms

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: 46.7b

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))))
0.4b	(* (sqrt 2.0) t)
11.5b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.6b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite55.0ms

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:

22.0ms	(/ (* (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)))

series1.9s

Counts

4 → 12

Calls

4 calls:

429.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
45.0ms	(* (sqrt 2.0) t)
217.0ms	(- (* (/ (+ 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)))

simplify121.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (26.0ms)

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: 6.6b

Counts

32 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
4.1b	(/ (pow l 2) x)
11.3b	(/ (pow t 2) x)
31.0b	(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)))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
163.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	450	1043
1	1695	1037
2	5001	1037

prune208.0ms

Filtered

56 candidates to 39 candidates (69.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	53	7	60

Merged error: 5.1b

Counts

60 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
11.3b	(/ (pow t 2) x)
31.0b	(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)
11.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
68.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
18.0ms	(/ (pow t 2) x)
163.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 1 (11.0ms)

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

prune210.0ms

Filtered

54 candidates to 37 candidates (68.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	54	7	61

Merged error: 5.1b

Counts

61 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow l 2) (/ 1 x)))))
4.2b	(* (pow l 2) (/ 1 x))
11.3b	(/ (pow t 2) x)
31.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow l 2) (/ 1 x))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

11.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow l 2) (/ 1 x)))))
5.0ms	(* (pow l 2) (/ 1 x))
3.0ms	(/ (pow t 2) x)
11.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow l 2) (/ 1 x))))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow l 2) (/ 1 x)))))
24.0ms	(* (pow l 2) (/ 1 x))
19.0ms	(/ (pow t 2) x)
165.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow l 2) (/ 1 x))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	471	1186
1	1826	1173
2	5002	1173

prune199.0ms

Filtered

60 candidates to 40 candidates (66.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	60	7	67

Merged error: 5.1b

Counts

67 → 7

regimes308.0ms

Accuracy

78.6% (5.1b remaining)

Error of 9.3b against oracle of 4.2b and baseline of 28.1b

bsearch223.0ms

Steps

Iters	Range		Point
11	3.2321547942223635e+94	4.0220332976538206e+117	4.7260634120673066e+114
7	-3.36057631032774e+99	-5.613938849311412e+97	-1.1373404966465423e+99

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	51
1	64	51
2	64	51

end0.0ms

sample2.1s

Algorithm

intervals

Results

505.0ms	10233×	body	80	nan
263.0ms	5089×	body	80	valid
224.0ms	897×	body	1280	valid
197.0ms	996×	body	640	valid
150.0ms	593×	body	1280	nan
121.0ms	625×	body	640	nan
95.0ms	648×	body	320	valid
53.0ms	370×	body	320	nan
36.0ms	370×	body	160	valid
17.0ms	174×	body	160	nan