Details

sample85.0ms

Algorithm

intervals

Results

16.0ms	315×	body	80	nan
14.0ms	20×	body	1280	nan
9.0ms	168×	body	80	valid
7.0ms	36×	body	640	valid
6.0ms	23×	body	1280	valid
4.0ms	22×	body	640	nan
2.0ms	14×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	9×	body	320	nan
1.0ms	6×	body	160	nan

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	27
1	39	27
2	86	27
3	177	27
4	344	27
5	550	27
6	899	27
7	1592	27
8	3229	27
done	5001	27

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize19.0ms

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)
15.0b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite72.0ms

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:

30.0ms	(/ (* (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)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

440.0ms	(/ (* (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)))

simplify605.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (148.0ms)

Iter	Nodes	Cost
0	168	2472
1	416	2283
2	1675	2085
done	5001	2085

prune305.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 6.1b

localize19.0ms

Local error

Found 4 expressions with local error:

5.6b	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
6.9b	(/ (pow t 2) x)
6.9b	(/ (pow l 2) x)
27.7b	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite60.0ms

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`
9×	`add-log-exp`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
3×	`sum-log` `sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `sqrt-div` `pow-exp` `clear-num` `flip-+` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `associate-+r+` `sqrt-pow1` `pow1/2`

Counts

4 → 126

Calls

4 calls:

16.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
4.0ms	(/ (pow l 2) x)
32.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
19.0ms	(/ (pow t 2) x)
24.0ms	(/ (pow l 2) x)
276.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

simplify597.0ms

Counts

138 → 138

Iterations

Useful iterations: 2 (189.0ms)

Iter	Nodes	Cost
0	229	2129
1	453	1871
2	1722	1692
done	5000	1692

prune505.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
5.6b	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))
6.9b	(/ (pow t 2) x)
27.7b	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))))

rewrite91.0ms

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`
9×	`add-log-exp`
8×	`add-cbrt-cube` `associate-/l*`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`unpow2` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*` `sum-log`
2×	`flip3-+` `sqrt-div` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `associate-+r+` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 99

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
28.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
50.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sqrt 2.0) t)
68.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))
19.0ms	(/ (pow t 2) x)
273.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))))

simplify630.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (178.0ms)

Iter	Nodes	Cost
0	191	1755
1	406	1533
2	1612	1407
done	5000	1407

prune358.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
5.6b	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (* 4.0 (/ (pow t 2) x))))
6.9b	(/ (pow t 2) x)
27.7b	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (* 4.0 (/ (pow t 2) x)))))

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

1.0ms	(cbrt x)
121.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
240.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (* 4.0 (/ (pow t 2) x)))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
85.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
290.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (* 4.0 (/ (pow t 2) x)))))

simplify535.0ms

Counts

100 → 100

Iterations

Useful iterations: done (531.0ms)

Iter	Nodes	Cost
0	184	1966
1	392	1730
2	1434	1485
done	5000	1413

prune380.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.2b

regimes405.0ms

Accuracy

75.6% (5.9b remaining)

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

bsearch507.0ms

Steps

Iters	Range		Point
9	8249416806277068.0	6.908956904862703e+24	6.769189022626266e+24
9	-5.149414502062706e-287	-6.479421214823862e-296	-5.07338813022938e-287
9	-1.9154334448410318e-177	-2.122947083583308e-184	-1.1776830540197237e-181
8	-7.474441928331378e+61	-1.7381937350890755e+58	-8.171560713962325e+60

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	168
1	64	168
done	64	168

end0.0ms

sample2.1s

Algorithm

intervals

Results

496.0ms	10142×	body	80	nan
263.0ms	5082×	body	80	valid
219.0ms	879×	body	1280	valid
198.0ms	994×	body	640	valid
145.0ms	587×	body	1280	nan
114.0ms	590×	body	640	nan
97.0ms	649×	body	320	valid
47.0ms	316×	body	320	nan
38.0ms	396×	body	160	valid
21.0ms	217×	body	160	nan