Details

sample297.0ms

Algorithm

intervals

Results

68.0ms	34×	body	640	valid
33.0ms	320×	body	80	nan
19.0ms	156×	body	80	valid
13.0ms	21×	body	1280	valid
12.0ms	31×	body	320	valid
12.0ms	22×	body	1280	nan
8.0ms	17×	body	640	nan
6.0ms	16×	body	320	nan
3.0ms	14×	body	160	valid
1.0ms	6×	body	160	nan

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	18	27
1	41	26
2	100	26
3	224	26
4	497	26
5	941	26
6	1555	26
7	3305	26
done	5001	26

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
0.4b	(* (sqrt 2.0) t)
14.5b	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
19.5b	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite209.0ms

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-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 88

Calls

4 calls:

82.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
11.0ms	(* (sqrt 2.0) t)
41.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
67.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

745.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
77.0ms	(* (sqrt 2.0) t)
788.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
562.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify3.5s

Counts

100 → 100

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	155	2445
1	345	2250
2	1195	2062
3	4993	2025
done	5000	2025

prune496.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 29.5b

localize44.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
8.1b	(/ (pow l 2) x)
10.2b	(/ (pow t 2) x)
26.7b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite33.0ms

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 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
9.0ms	(/ (pow l 2) x)
16.0ms	(/ (pow t 2) x)
4.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series647.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
27.0ms	(/ (pow l 2) x)
28.0ms	(/ (pow t 2) x)
470.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify2.4s

Counts

139 → 139

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	217	1761
1	376	1614
2	912	1411
3	3182	1411
done	5000	1410

prune751.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

localize28.0ms

Local error

Found 4 expressions with local error:

2.0b	(fma t t (* l (/ l x)))
4.4b	(fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))
10.2b	(/ (pow t 2) x)
26.7b	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

rewrite19.0ms

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

Counts

4 → 86

Calls

4 calls:

1.0ms	(fma t t (* l (/ l x)))
1.0ms	(fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))
10.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma t t (* l (/ l x)))
95.0ms	(fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))
29.0ms	(/ (pow t 2) x)
396.0ms	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

simplify1.8s

Counts

98 → 98

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	159	1358
1	276	1256
2	666	1108
3	2289	1108
done	5000	1107

prune520.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

localize27.0ms

Local error

Found 4 expressions with local error:

10.2b	(/ (pow t 2) x)
26.7b	(sqrt (fma 2.0 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (* 4.0 (/ (pow t 2) x))))
26.8b	(sqrt (fma t t (* l (/ l x))))
26.8b	(sqrt (fma t t (* l (/ l x))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
12×	`unpow-prod-down`
9×	`add-exp-log` `sqrt-prod`
8×	`associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/r*`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

18.0ms	(/ (pow t 2) x)
3.0ms	(sqrt (fma 2.0 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (* 4.0 (/ (pow t 2) x))))
3.0ms	(sqrt (fma t t (* l (/ l x))))
4.0ms	(sqrt (fma t t (* l (/ l x))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (pow t 2) x)
391.0ms	(sqrt (fma 2.0 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (* 4.0 (/ (pow t 2) x))))
119.0ms	(sqrt (fma t t (* l (/ l x))))
144.0ms	(sqrt (fma t t (* l (/ l x))))

simplify1.6s

Counts

108 → 108

Iterations

Useful iterations: 3 (676.0ms)

Iter	Nodes	Cost
0	154	1527
1	272	1184
2	632	1074
3	1928	1071
done	5000	1071

prune512.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.1b

regimes599.0ms

Accuracy

73.2% (6.4b remaining)

Error of 10.1b against oracle of 3.7b and baseline of 27.6b

bsearch805.0ms

Steps

Iters	Range		Point
7	5.438827393303272e-47	3.255422209678199e-45	3.190616919639676e-45
9	-9.099259929633761e-243	-1.1388205652005344e-250	-4.3039381620799786e-243
8	-4.709429137726002e-147	-1.2135677083227269e-149	-1.2300651500007749e-149
8	-7.002515132037965e+150	-1.149067304892884e+146	-2.3034608226733973e+149

simplify28.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	137
1	43	137
done	43	137

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.0s	10338×	body	80	nan
962.0ms	332×	body	160	valid
705.0ms	910×	body	1280	valid
620.0ms	5100×	body	80	valid
494.0ms	1003×	body	640	valid
385.0ms	564×	body	1280	nan
336.0ms	645×	body	640	nan
259.0ms	655×	body	320	valid
101.0ms	365×	body	320	nan
29.0ms	149×	body	160	nan