Details

sample84.0ms

Algorithm

intervals

Results

15.0ms	317×	body	80	nan
11.0ms	12×	body	320	nan
9.0ms	160×	body	80	valid
6.0ms	23×	body	1280	valid
6.0ms	28×	body	640	valid
5.0ms	36×	body	320	valid
4.0ms	19×	body	640	nan
4.0ms	14×	body	1280	nan
1.0ms	9×	body	160	nan
1.0ms	9×	body	160	valid

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	18	27
1	41	26
2	94	26
3	214	26
4	433	26
5	834	26
6	1339	26
7	2242	26
8	4931	26
done	5000	26

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize26.0ms

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)
13.6b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite67.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

24.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

419.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
46.0ms	(* (sqrt 2.0) t)
210.0ms	(- (* (/ (+ 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)))

simplify720.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (172.0ms)

Iter	Nodes	Cost
0	179	2660
1	444	2367
2	1707	2182
done	5000	2182

prune384.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.9b

localize19.0ms

Local error

Found 4 expressions with local error:

4.8b	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
8.8b	(/ (pow l 2) x)
11.1b	(/ (pow t 2) x)
26.9b	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite17.0ms

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×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow l 2) x)
4.0ms	(/ (pow t 2) x)
5.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series380.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
272.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify1.4s

Counts

139 → 139

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	218	1816
1	376	1665
2	1155	1462
3	3829	1406
done	5001	1405

prune504.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
4.8b	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
11.1b	(/ (pow t 2) x)
26.9b	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite12.0ms

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`
8×	`add-cbrt-cube` `associate-/l*`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
0.0ms	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (sqrt 2.0) t)
61.0ms	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
151.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify911.0ms

Counts

112 → 112

Iterations

Useful iterations: done (908.0ms)

Iter	Nodes	Cost
0	186	1525
1	355	1379
2	1148	1249
done	5001	1245

prune449.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
4.8b	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
11.1b	(/ (pow t 2) x)
26.9b	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
14×	`add-exp-log`
12×	`unpow-prod-down` `sqrt-prod`
11×	`add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `pow-exp` `clear-num` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 102

Calls

4 calls:

16.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
0.0ms	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
62.0ms	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
148.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify950.0ms

Counts

114 → 114

Iterations

Useful iterations: done (946.0ms)

Iter	Nodes	Cost
0	195	1685
1	395	1428
2	1254	1272
done	5000	1269

prune425.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 2.8b

regimes420.0ms

Accuracy

76.7% (5.5b remaining)

Error of 9.3b against oracle of 3.8b and baseline of 27.6b

bsearch514.0ms

Steps

Iters	Range		Point
8	1.4208256029707195e+117	1.7793028727278986e+120	3.3425130247455635e+119
8	-6.458455904138903e-289	-3.5220671154407477e-293	-6.34487891906004e-289
11	-9.166642237663663e-233	-1.562746242727e-252	-9.431458294677752e-250
10	-1.1264209325184682e+126	-7.95573321924467e+112	-5.627772131442995e+125

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	183
1	68	183
done	68	183

end0.0ms

sample2.1s

Algorithm

intervals

Results

494.0ms	9832×	body	80	nan
270.0ms	5148×	body	80	valid
215.0ms	830×	body	1280	valid
207.0ms	1009×	body	640	valid
145.0ms	587×	body	1280	nan
108.0ms	556×	body	640	nan
100.0ms	641×	body	320	valid
51.0ms	354×	body	320	nan
37.0ms	372×	body	160	valid
18.0ms	187×	body	160	nan