Details

sample72.0ms

Algorithm

intervals

Results

15.0ms	306×	body	80	nan
8.0ms	159×	body	80	valid
6.0ms	24×	body	1280	valid
5.0ms	26×	body	640	valid
4.0ms	16×	body	1280	nan
4.0ms	27×	body	320	valid
3.0ms	17×	body	640	nan
2.0ms	20×	body	160	valid
1.0ms	8×	body	320	nan
1.0ms	11×	body	160	nan

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	27
1	39	27
2	86	27
3	179	27
4	353	27
5	583	27
6	936	27
7	1824	27
8	3618	27
done	5001	27

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize17.0ms

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)
12.4b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite73.0ms

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 → 80

Calls

4 calls:

25.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
28.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

427.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
40.0ms	(* (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)))

simplify659.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	168	2472
1	425	2287
2	1914	2075
done	5000	2075

prune297.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.0b

localize17.0ms

Local error

Found 4 expressions with local error:

3.4b	(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
5.9b	(/ (pow l 2) x)
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

rewrite54.0ms

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-+l+` `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:

13.0ms	(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
7.0ms	(/ (pow l 2) x)
4.0ms	(/ (pow t 2) x)
25.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

series374.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
18.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
268.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

simplify757.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (176.0ms)

Iter	Nodes	Cost
0	254	2312
1	538	2086
2	2124	1875
done	5000	1875

prune470.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
3.4b	(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
31.0ms	(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
4.0ms	(/ (pow t 2) x)
60.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sqrt 2.0) t)
69.0ms	(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
19.0ms	(/ (pow t 2) x)
276.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

simplify780.0ms

Counts

115 → 115

Iterations

Useful iterations: 2 (168.0ms)

Iter	Nodes	Cost
0	216	2198
1	496	1882
2	2016	1608
done	5001	1608

prune402.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
3.4b	(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

rewrite126.0ms

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-+l+` `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:

27.0ms	(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
31.0ms	(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
4.0ms	(/ (pow t 2) x)
60.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
70.0ms	(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
19.0ms	(/ (pow t 2) x)
273.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

simplify686.0ms

Counts

104 → 104

Iterations

Useful iterations: done (683.0ms)

Iter	Nodes	Cost
0	202	2323
1	470	1966
2	1800	1646
done	5000	1640

prune407.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

regimes448.0ms

Accuracy

76.3% (5.5b remaining)

Error of 9.3b against oracle of 3.8b and baseline of 27.0b

bsearch478.0ms

Steps

Iters	Range		Point
8	2.856659494861968e+113	8.814288912248196e+117	2.527401613686204e+114
6	-1.183890802660123e-282	-2.1055594324771466e-283	-3.3196210034371617e-283
10	-2.4994760714008124e-200	-2.1048616109453496e-212	-4.738432652811407e-208
8	-3.6441438461771793e+143	-1.8976906426182426e+140	-4.097588426365747e+140

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	212
1	74	212
done	74	212

end0.0ms

sample2.0s

Algorithm

intervals

Results

478.0ms	10109×	body	80	nan
261.0ms	5145×	body	80	valid
200.0ms	801×	body	1280	valid
200.0ms	1012×	body	640	valid
139.0ms	591×	body	1280	nan
111.0ms	587×	body	640	nan
93.0ms	654×	body	320	valid
46.0ms	337×	body	320	nan
37.0ms	388×	body	160	valid
19.0ms	215×	body	160	nan