Details

sample295.0ms

Algorithm

intervals

Results

92.0ms	299×	body	80	nan
24.0ms	168×	body	80	valid
11.0ms	24×	body	1280	valid
11.0ms	26×	body	640	valid
8.0ms	15×	body	1280	nan
8.0ms	19×	body	640	nan
8.0ms	20×	body	320	valid
7.0ms	18×	body	320	nan
4.0ms	18×	body	160	valid
1.0ms	8×	body	160	nan

simplify6.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	18	27
1	39	27
2	93	27
3	189	27
4	397	27
5	661	27
6	1122	27
7	2624	27
8	4131	27
done	5000	27

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize33.0ms

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)
13.6b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.4b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite230.0ms

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:

86.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
18.0ms	(* (sqrt 2.0) t)
64.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
55.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.7s

Counts

4 → 12

Calls

4 calls:

626.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
55.0ms	(* (sqrt 2.0) t)
329.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.5s

Counts

92 → 92

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	168	2472
1	414	2283
2	1552	2077
done	5000	2025

prune493.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize26.0ms

Local error

Found 4 expressions with local error:

5.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
6.7b	(/ (pow t 2) x)
6.7b	(/ (pow l 2) x)
29.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite92.0ms

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:

24.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
9.0ms	(/ (pow t 2) x)
17.0ms	(/ (pow l 2) x)
38.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series385.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
20.0ms	(/ (pow t 2) x)
27.0ms	(/ (pow l 2) x)
236.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify1.4s

Counts

142 → 142

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	254	2317
1	535	2084
2	1727	1868
done	5000	1862

prune764.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* t t) (* l (/ l x)))
5.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x)))))
6.7b	(/ (pow t 2) x)
29.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite92.0ms

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:

8.0ms	(+ (* t t) (* l (/ l x)))
26.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x)))))
18.0ms	(/ (pow t 2) x)
37.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* t t) (* l (/ l x)))
81.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x)))))
33.0ms	(/ (pow t 2) x)
233.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))

simplify1.3s

Counts

104 → 104

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	199	1996
1	465	1806
2	1657	1633
done	5000	1623

prune651.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize59.0ms

Local error

Found 4 expressions with local error:

6.7b	(/ (pow t 2) x)
6.7b	(/ (pow t 2) x)
29.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))
29.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

19.0ms	(/ (pow t 2) x)
17.0ms	(/ (pow t 2) x)
32.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))
21.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (pow t 2) x)
34.0ms	(/ (pow t 2) x)
235.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))
273.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))

simplify1.2s

Counts

144 → 144

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	169	2408
1	391	2144
2	1351	1942
done	5000	1930

prune960.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

regimes568.0ms

Accuracy

75.5% (5.9b remaining)

Error of 9.7b against oracle of 3.8b and baseline of 27.9b

bsearch1.2s

Steps

Iters	Range		Point
8	7.407251155982859e+145	4.879894848387411e+149	6.335165898555757e+148
6	-1.4231360660802614e-302	-2.7726430826687857e-303	-1.4020051272573528e-302
8	-2.3731648380204055e-262	-6.820981679032075e-265	-8.549619549454068e-265
5	-1.5004718450719783e+25	-4.978593612221029e+24	-8.54333635658851e+24

simplify34.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	50	220
1	60	220
done	60	220

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.9s	10248×	body	80	nan
991.0ms	1001×	body	640	valid
902.0ms	5159×	body	80	valid
700.0ms	851×	body	1280	valid
440.0ms	576×	body	1280	nan
258.0ms	591×	body	640	nan
235.0ms	635×	body	320	valid
100.0ms	334×	body	320	nan
79.0ms	354×	body	160	valid
36.0ms	180×	body	160	nan