Details

sample491.0ms

Algorithm

intervals

Results

127.0ms	358×	body	80	nan
36.0ms	30×	body	1280	valid
36.0ms	154×	body	80	valid
30.0ms	32×	body	640	valid
29.0ms	24×	body	1280	nan
17.0ms	24×	body	320	valid
15.0ms	16×	body	640	nan
10.0ms	14×	body	320	nan
8.0ms	16×	body	160	valid
5.0ms	11×	body	160	nan

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
6	2002
5	1119
4	393
3	181
2	93
1	42
0	18

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.6b

localize49.0ms

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)
15.3b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.1b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite173.0ms

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:

59.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
12.0ms	(* (sqrt 2) t)
53.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
41.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

449.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
77.0ms	(* (sqrt 2) t)
242.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.6s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.4s

Counts

96 → 96

Iterations

Iter	Nodes
done	2022
3	2022
2	1525
1	458
0	170

prune607.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.1b

localize66.0ms

Local error

Found 4 expressions with local error:

3.0b	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
6.6b	(/ (* l l) x)
9.9b	(/ (* t t) x)
26.5b	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `associate-l/` `frac-add` `associate-r/` `flip-+` `insert-posit16`
3×	`sqrt-prod`
2×	`associate-+l+` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 78

Calls

4 calls:

30.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
9.0ms	(/ (* l l) x)
8.0ms	(/ (* t t) x)
44.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
36.0ms	(/ (* l l) x)
21.0ms	(/ (* t t) x)
353.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	2000
2	2000
1	536
0	172

prune539.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* t t) (/ l (/ x l)))
3.0b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
9.9b	(/ (* t t) x)
26.5b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `associate-l/` `frac-add` `associate-r/` `insert-posit16`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+l+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

20.0ms	(+ (* t t) (/ l (/ x l)))
45.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
23.0ms	(/ (* t t) x)
63.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* t t) (/ l (/ x l)))
88.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
20.0ms	(/ (* t t) x)
379.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify1.4s

Counts

80 → 80

Iterations

Iter	Nodes
done	2002
3	2002
2	1831
1	462
0	155

prune515.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* t t) (* l (/ l x)))
3.0b	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
9.9b	(/ (* t t) x)
26.5b	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `associate-l/` `frac-add` `associate-r/` `insert-posit16`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+l+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

8.0ms	(+ (* t t) (* l (/ l x)))
36.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
18.0ms	(/ (* t t) x)
36.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* t t) (* l (/ l x)))
83.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
21.0ms	(/ (* t t) x)
273.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
done	2003
3	2003
2	1889
1	465
0	155

prune506.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.9b

regimes908.0ms

Accuracy

77.6% (5.2b remaining)

Error of 8.9b against oracle of 3.7b and baseline of 26.8b

bsearch928.0ms

Steps

Iters	Range		Point
9	3.418485680637394e+69	2.5394452178869736e+75	1.190119698582846e+73
5	3.7309912156633627e-165	7.625611042088009e-165	3.9773559035809034e-165
8	1.5881823628500624e-279	7.641349737140096e-275	7.466234522592741e-275
9	-3.571300126685226e+102	-1.3399686220244182e+97	-1.3258761248569655e+101

simplify74.0ms

Iterations

Iter	Nodes
done	94
4	94
3	88
2	86
1	77
0	56

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.1s	10227×	body	80	nan
1.3s	835×	body	1280	valid
1.0s	5158×	body	80	valid
915.0ms	1024×	body	640	valid
625.0ms	614×	body	1280	nan
451.0ms	594×	body	640	nan
419.0ms	628×	body	320	valid
180.0ms	307×	body	320	nan
152.0ms	355×	body	160	valid
145.0ms	184×	body	160	nan