Details

sample334.0ms

Algorithm

intervals

Results

78.0ms	168×	body	80	valid
37.0ms	299×	body	80	nan
17.0ms	24×	body	1280	valid
11.0ms	26×	body	640	valid
8.0ms	15×	body	1280	nan
7.0ms	19×	body	640	nan
6.0ms	20×	body	320	valid
6.0ms	18×	body	320	nan
5.0ms	18×	body	160	valid
2.0ms	8×	body	160	nan

simplify5.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (18.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize40.0ms

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))))
0.4b	(* (sqrt 2.0) t)
13.6b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.4b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite297.0ms

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:

120.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
21.0ms	(* (sqrt 2.0) t)
74.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
74.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

630.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
54.0ms	(* (sqrt 2.0) t)
342.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.7s

Counts

102 → 102

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	179	2660
1	442	2367
2	1680	2178
done	5001	2125

prune560.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize26.0ms

Local error

Found 4 expressions with local error:

5.2b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
6.7b	(/ (pow t 2) x)
6.7b	(/ (pow l 2) x)
29.0b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite41.0ms

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

series672.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
37.0ms	(/ (pow t 2) x)
36.0ms	(/ (pow l 2) x)
473.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify2.1s

Counts

139 → 139

Iterations

Useful iterations: done (2.1s)

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

prune777.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma t t (* l (/ l x)))
5.2b	(fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))
6.7b	(/ (pow t 2) x)
29.0b	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

rewrite32.0ms

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)))
16.0ms	(/ (pow t 2) x)
10.0ms	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

series585.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma t t (* l (/ l x)))
117.0ms	(fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x)))
29.0ms	(/ (pow t 2) x)
367.0ms	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: done (1.6s)

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

prune558.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize57.0ms

Local error

Found 4 expressions with local error:

6.7b	(/ (pow t 2) x)
6.7b	(/ (pow t 2) x)
29.0b	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))
29.0b	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`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×	`pow1` `div-exp` `associate-/r*` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 132

Calls

4 calls:

18.0ms	(/ (pow t 2) x)
11.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))
2.0ms	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

series790.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (pow t 2) x)
44.0ms	(/ (pow t 2) x)
336.0ms	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))
377.0ms	(sqrt (fma 2.0 (fma t t (* l (/ l x))) (* 4.0 (/ (pow t 2) x))))

simplify1.8s

Counts

144 → 144

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	133	1862
1	234	1676
2	558	1492
3	1786	1492
done	5000	1490

prune992.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

regimes491.0ms

Accuracy

75.5% (5.9b remaining)

Error of 9.7b against oracle of 3.8b and baseline of 27.9b

bsearch634.0ms

Steps

Iters	Range		Point
8	7.407251155982859e+145	4.879894848387411e+149	6.335165898555757e+148
6	-1.4231360660802614e-302	-2.7726430826687857e-303	-1.4020051272573528e-302
8	-2.3731648380204055e-262	-6.820981679032075e-265	-8.549619549454068e-265
5	-1.5004718450719783e+25	-4.978593612221029e+24	-8.54333635658851e+24

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	46	209
1	51	209
done	51	209

end0.0ms

sample6.6s

Algorithm

intervals

Results

1.4s	10248×	body	80	nan
1.1s	851×	body	1280	valid
999.0ms	5159×	body	80	valid
778.0ms	576×	body	1280	nan
544.0ms	1001×	body	640	valid
273.0ms	591×	body	640	nan
239.0ms	635×	body	320	valid
98.0ms	334×	body	320	nan
81.0ms	354×	body	160	valid
37.0ms	180×	body	160	nan