Details

sample319.0ms

Algorithm

intervals

Results

50.0ms	15×	body	160	valid
37.0ms	331×	body	80	nan
21.0ms	33×	body	1280	valid
19.0ms	161×	body	80	valid
11.0ms	20×	body	1280	nan
10.0ms	25×	body	640	valid
8.0ms	21×	body	640	nan
7.0ms	22×	body	320	valid
5.0ms	11×	body	320	nan
2.0ms	7×	body	160	nan

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4473
5	1119
4	393
3	181
2	93
1	42
0	18

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize80.0ms

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)
11.3b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
19.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite180.0ms

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:

45.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
10.0ms	(* (sqrt 2) t)
55.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
65.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

502.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
59.0ms	(* (sqrt 2) t)
248.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1525
1	458
0	170

prune658.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.1b

localize45.0ms

Local error

Found 4 expressions with local error:

2.6b	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
5.3b	(/ (* l l) x)
10.7b	(/ (* t t) x)
26.1b	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

rewrite116.0ms

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:

40.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
17.0ms	(/ (* l l) x)
17.0ms	(/ (* t t) x)
40.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
20.0ms	(/ (* l l) x)
34.0ms	(/ (* t t) x)
304.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify1.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5004
2	2246
1	536
0	172

prune521.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* t t) (/ l (/ x l)))
2.6b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
10.7b	(/ (* t t) x)
26.1b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite142.0ms

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:

10.0ms	(+ (* t t) (/ l (/ x l)))
45.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
17.0ms	(/ (* t t) x)
69.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* t t) (/ l (/ x l)))
89.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
33.0ms	(/ (* t t) x)
392.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
done	5003
2	1831
1	462
0	155

prune553.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.2b

localize57.0ms

Local error

Found 4 expressions with local error:

10.7b	(/ (* t t) x)
10.7b	(/ (* t t) x)
26.1b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))
26.1b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
6×	`pow1` `associate-/r*` `times-frac` `sqrt-prod`
4×	`cbrt-undiv` `flip3-+` `div-exp` `associate-l/` `frac-add` `associate-r/` `flip-+` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

17.0ms	(/ (* t t) x)
16.0ms	(/ (* t t) x)
67.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))
64.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series745.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (* t t) x)
35.0ms	(/ (* t t) x)
334.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))
339.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify1.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5002
2	1554
1	373
0	124

prune766.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.2b

regimes731.0ms

Accuracy

74.3% (6.2b remaining)

Error of 10.0b against oracle of 3.9b and baseline of 27.9b

bsearch1.6s

Steps

Iters	Range		Point
5	6.364793754454402e+60	1.7652923151240752e+61	1.6254114022993327e+61
9	4.178826324149685e-184	4.985769453538649e-178	8.801957257978148e-180
10	-5.87551456151423e-303	2.02503051581541e-296	1.0361466531567994e-296
9	-8.029424359520944e-243	-2.0952165801168822e-249	-2.9098210944374083e-243
5	-1.82407131439873e-220	-6.727441174307589e-221	-8.085409915535338e-221
7	-5.3142180222849325e+81	-2.3483171863989254e+79	-2.1951411765329485e+80

simplify33.0ms

Iterations

Iter	Nodes
done	67
1	67
0	54

end0.0ms

sample6.3s

Algorithm

intervals

Results

1.8s	10063×	body	80	nan
948.0ms	850×	body	1280	valid
924.0ms	5088×	body	80	valid
653.0ms	1061×	body	640	valid
545.0ms	624×	body	1280	nan
348.0ms	616×	body	640	nan
211.0ms	639×	body	320	valid
102.0ms	362×	body	160	valid
100.0ms	310×	body	320	nan
40.0ms	189×	body	160	nan