Details

sample202.0ms

Algorithm

intervals

Results

57.0ms	156×	body	80	valid
24.0ms	338×	body	80	nan
12.0ms	40×	body	640	valid
10.0ms	24×	body	1280	valid
7.0ms	19×	body	1280	nan
5.0ms	20×	body	320	nan
5.0ms	24×	body	320	valid
4.0ms	14×	body	640	nan
2.0ms	12×	body	160	valid
1.0ms	5×	body	160	nan

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 1 (10.0ms)

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

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
0.5b	(* (sqrt 2.0) t)
13.9b	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
21.6b	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite158.0ms

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:

55.0ms	(/ (* (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)
36.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
50.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.5s

Counts

4 → 12

Calls

4 calls:

712.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
44.0ms	(* (sqrt 2.0) t)
281.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
462.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify3.7s

Counts

100 → 100

Iterations

Useful iterations: 3 (2.0s)

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

prune513.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 30.8b

localize29.0ms

Local error

Found 4 expressions with local error:

5.3b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
6.9b	(/ (pow l 2) x)
9.5b	(/ (pow t 2) x)
28.2b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite37.0ms

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:

1.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
17.0ms	(/ (pow l 2) x)
9.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series592.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
34.0ms	(/ (pow l 2) x)
26.0ms	(/ (pow t 2) x)
432.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify2.2s

Counts

139 → 139

Iterations

Useful iterations: done (2.2s)

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

prune764.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma t t (* l (/ l x)))
5.3b	(fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))
9.5b	(/ (pow t 2) x)
28.2b	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

rewrite27.0ms

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

series1.1s

Counts

4 → 12

Calls

4 calls:

86.0ms	(fma t t (* l (/ l x)))
97.0ms	(fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))
21.0ms	(/ (pow t 2) x)
854.0ms	(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

prune534.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize49.0ms

Local error

Found 4 expressions with local error:

9.5b	(/ (pow t 2) x)
28.2b	(sqrt (fma 2.0 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (* 4.0 (/ (pow t 2) x))))
28.4b	(sqrt (fma t t (* l (/ l x))))
28.4b	(sqrt (fma t t (* l (/ l x))))

rewrite31.0ms

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))))
3.0ms	(sqrt (fma t t (* l (/ l x))))

series706.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (pow t 2) x)
399.0ms	(sqrt (fma 2.0 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (* 4.0 (/ (pow t 2) x))))
140.0ms	(sqrt (fma t t (* l (/ l x))))
129.0ms	(sqrt (fma t t (* l (/ l x))))

simplify1.5s

Counts

108 → 108

Iterations

Useful iterations: 3 (734.0ms)

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

prune589.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

regimes429.0ms

Accuracy

76.5% (5.6b remaining)

Error of 9.6b against oracle of 4.0b and baseline of 27.9b

bsearch453.0ms

Steps

Iters	Range		Point
9	9.324172023423285e+142	1.1012045087961449e+149	1.6421833813677545e+146
10	-1.1979006433782284e+85	-5.09199279650327e+67	-2.8442338941596414e+80

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	77
1	37	77
done	37	77

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.0s	10110×	body	80	nan
689.0ms	5091×	body	80	valid
574.0ms	376×	body	160	valid
499.0ms	1030×	body	640	valid
490.0ms	847×	body	1280	valid
337.0ms	601×	body	1280	nan
313.0ms	656×	body	320	valid
207.0ms	584×	body	640	nan
150.0ms	381×	body	320	nan
33.0ms	183×	body	160	nan