Details

sample418.0ms

Algorithm

intervals

Results

115.0ms	301×	body	80	nan
43.0ms	170×	body	80	valid
35.0ms	30×	body	1280	valid
25.0ms	27×	body	640	valid
22.0ms	20×	body	1280	nan
13.0ms	19×	body	320	valid
12.0ms	14×	body	640	nan
8.0ms	11×	body	320	nan
5.0ms	10×	body	160	valid
1.0ms	3×	body	160	nan

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
7	3164
6	1632
5	695
4	400
3	180
2	91
1	40
0	18

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
12.7b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
23.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`sqrt-div` `insert-posit16`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

88.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
15.0ms	(* (sqrt 2) t)
49.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
33.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

507.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
58.0ms	(* (sqrt 2) t)
273.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.4s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify7.6s

Counts

96 → 96

Iterations

Iter	Nodes
3	7219
2	1568
1	440
0	170

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.1b

localize66.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ l (/ x l)) (* t t))
4.8b	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
10.4b	(* (/ 4 x) (* t t))
30.2b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
13×	`associate-l`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1` `times-frac`
8×	`add-log-exp`
6×	`prod-exp` `cbrt-unprod`
5×	`flip3-+` `associate-*l/` `flip-+`
4×	`sqrt-div` `frac-add` `associate-*r/` `insert-posit16`
3×	`pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+r+` `sum-log` `div-exp` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `div-inv`

Counts

4 → 82

Calls

4 calls:

27.0ms	(+ (/ l (/ x l)) (* t t))
33.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
29.0ms	(* (/ 4 x) (* t t))
32.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

series723.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (/ l (/ x l)) (* t t))
130.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
53.0ms	(* (/ 4 x) (* t t))
467.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

simplify675.0ms

Counts

94 → 94

Iterations

Iter	Nodes
2	2070
1	527
0	176

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.0b

localize46.0ms

Local error

Found 4 expressions with local error:

10.4b	(* (/ 4 x) (* t t))
10.4b	(* (/ 4 x) (* t t))
30.2b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
30.2b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
26×	`associate-l`
20×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
16×	`pow1`
12×	`prod-exp` `cbrt-unprod`
8×	`sqrt-div`
6×	`pow-prod-down` `associate-*l/` `sqrt-prod`
4×	`cbrt-undiv` `flip3-+` `div-exp` `frac-add` `associate-*r/` `flip-+` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `div-inv`

Counts

4 → 108

Calls

4 calls:

19.0ms	(* (/ 4 x) (* t t))
39.0ms	(* (/ 4 x) (* t t))
47.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
57.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

series893.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (/ 4 x) (* t t))
36.0ms	(* (/ 4 x) (* t t))
405.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
410.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

simplify8.2s

Counts

120 → 120

Iterations

Iter	Nodes
3	9634
2	1744
1	445
0	147

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.0b

localize103.0ms

Local error

Found 4 expressions with local error:

30.2b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
31.1b	(cbrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
31.1b	(cbrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
31.1b	(cbrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-div`
9×	`cbrt-prod` `add-sqr-sqrt`
8×	`-un-lft-identity` `flip3-+` `associate-l/` `frac-add` `associate-*r/` `add-cube-cbrt` `flip-+`
5×	`pow1`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 66

Calls

4 calls:

23.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
18.0ms	(cbrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
18.0ms	(cbrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
32.0ms	(cbrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

408.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
257.0ms	(cbrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
252.0ms	(cbrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
246.0ms	(cbrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

simplify2.7s

Counts

78 → 78

Iterations

Iter	Nodes
3	5154
2	1216
1	355
0	135

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.0b

regimes767.0ms

Accuracy

78.5% (5.1b remaining)

Error of 9.0b against oracle of 3.9b and baseline of 27.8b

bsearch2.3s

Steps

Iters	Range		Point
9	2.4705644922351665e+134	1.0317583027926416e+141	1.1429092917229189e+136
8	2.3578502464846e-162	1.1338586686334638e-159	1.351904254863679e-161
8	4.909230640994137e-244	6.457075559216039e-240	5.047696061686955e-240
10	-1.4127051641121057e-275	-9.154157246979375e-288	-3.737726633798208e-276
8	-8.464715529728638e-167	-8.94496705084197e-170	-1.8034323523291548e-167
8	-1.9308205073062745e+67	-1.8562285193930908e+64	-1.429472263354247e+67

simplify49.0ms

Iterations

Iter	Nodes
4	71
3	71
2	68
1	65
0	51

end0.0ms

sample9.0s

Algorithm

intervals

Results

2.2s	10140×	body	80	nan
1.7s	5168×	body	80	valid
1.3s	865×	body	1280	valid
891.0ms	990×	body	640	valid
753.0ms	600×	body	1280	nan
502.0ms	593×	body	640	nan
459.0ms	621×	body	320	valid
325.0ms	387×	body	320	nan
139.0ms	356×	body	160	valid
91.0ms	177×	body	160	nan