Details

sample76.0ms

Algorithm

intervals

Results

15.0ms	322×	body	80	nan
8.0ms	163×	body	80	valid
7.0ms	32×	body	1280	nan
7.0ms	36×	body	640	valid
6.0ms	24×	body	1280	valid
4.0ms	20×	body	640	nan
3.0ms	22×	body	320	valid
1.0ms	10×	body	320	nan
1.0ms	11×	body	160	valid
1.0ms	7×	body	160	nan

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	18	27
1	39	27
2	86	27
3	177	27
4	344	27
5	550	27
6	899	27
7	1592	27
8	3229	27
done	5001	27

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.5b

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))))
0.4b	(* (sqrt 2.0) t)
13.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.1b	(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×	`sqrt-div`
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` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

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))
22.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

443.0ms	(/ (* (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)
215.0ms	(- (* (/ (+ 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)))

simplify807.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (160.0ms)

Iter	Nodes	Cost
0	168	2472
1	416	2287
2	1604	2081
done	5000	2081

prune313.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.7b

localize22.0ms

Local error

Found 4 expressions with local error:

5.3b	(/ (pow t 2) x)
5.4b	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
6.7b	(/ (pow l 2) x)
23.8b	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite55.0ms

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`
9×	`add-log-exp`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
3×	`sum-log` `sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `sqrt-div` `pow-exp` `clear-num` `flip-+` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `associate-+r+` `sqrt-pow1` `pow1/2`

Counts

4 → 126

Calls

4 calls:

4.0ms	(/ (pow t 2) x)
15.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow l 2) x)
27.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (pow t 2) x)
66.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
20.0ms	(/ (pow l 2) x)
288.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

simplify714.0ms

Counts

138 → 138

Iterations

Useful iterations: done (710.0ms)

Iter	Nodes	Cost
0	229	2129
1	453	1871
2	1503	1664
done	5002	1660

prune467.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
5.3b	(/ (pow t 2) x)
5.4b	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
23.8b	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

rewrite89.0ms

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`
9×	`add-log-exp`
8×	`add-cbrt-cube` `associate-/l*`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`unpow2` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*` `sum-log`
2×	`flip3-+` `sqrt-div` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `associate-+r+` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 99

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
4.0ms	(/ (pow t 2) x)
28.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
49.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sqrt 2.0) t)
19.0ms	(/ (pow t 2) x)
62.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
150.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

simplify880.0ms

Counts

111 → 111

Iterations

Useful iterations: done (877.0ms)

Iter	Nodes	Cost
0	200	1866
1	438	1600
2	1583	1451
done	5001	1450

prune402.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
5.3b	(/ (pow t 2) x)
5.4b	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
23.8b	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

rewrite99.0ms

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` `add-log-exp`
8×	`associate-/l*`
4×	`unpow2` `sqr-pow`
3×	`div-exp` `pow-prod-down` `prod-exp` `associate-/r*` `sum-log` `cbrt-unprod`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `associate-+r+` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `pow-exp` `clear-num` `*-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

16.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
4.0ms	(/ (pow t 2) x)
27.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
48.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

series279.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
19.0ms	(/ (pow t 2) x)
63.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
148.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

simplify909.0ms

Counts

113 → 113

Iterations

Useful iterations: done (906.0ms)

Iter	Nodes	Cost
0	209	2016
1	478	1649
2	1597	1474
done	5001	1473

prune403.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.2b

regimes421.0ms

Accuracy

76.9% (5.5b remaining)

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

bsearch452.0ms

Steps

Iters	Range		Point
8	2.2751938498197737e+94	4.76303649330398e+98	3.4577470562944996e+98
8	2.5603887409626556e-253	4.167559130856697e-249	2.5976520530279296e-253
9	3.512144195931097e-279	7.021214941300326e-270	2.048999071991341e-272
7	-3.6364283768276295e+126	-2.0040148580114575e+125	-3.647549170547215e+125

simplify11.0ms

Iterations

Useful iterations: done (10.0ms)

Iter	Nodes	Cost
0	50	194
1	67	155
2	70	127
3	73	127
done	73	126

end0.0ms

sample2.1s

Algorithm

intervals

Results

470.0ms	9936×	body	80	nan
336.0ms	1026×	body	640	valid
264.0ms	5084×	body	80	valid
216.0ms	861×	body	1280	valid
141.0ms	601×	body	1280	nan
105.0ms	570×	body	640	nan
97.0ms	661×	body	320	valid
45.0ms	333×	body	320	nan
37.0ms	368×	body	160	valid
16.0ms	172×	body	160	nan