Details

sample61.0ms

Algorithm

intervals

Results

22.0ms	54×	body	1280	valid
12.0ms	51×	body	640	valid
6.0ms	149×	body	80	valid
4.0ms	28×	body	320	valid
2.0ms	87×	body	80	nan
1.0ms	8×	body	160	valid

simplify112.0ms

Counts

1 → 1

Iterations

Useful iterations: 4 (7.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4
done	5001	4

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
4.6b	(pow (/ x (+ x y)) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 66

Calls

2 calls:

11.0ms	(/ x (+ x y))
13.0ms	(pow (/ x (+ x y)) x)

series278.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ x (+ x y))
232.0ms	(pow (/ x (+ x y)) x)

simplify39.0ms

Counts

72 → 72

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	309	402
1	1244	387
2	5002	386
done	5002	386

prune147.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log`
1×	`pow1` `cbrt-undiv` `exp-neg` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

9.0ms

(/ (exp (* -1 y)) x)

series21.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(/ (exp (* -1 y)) x)

simplify49.0ms

Counts

31 → 31

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	114	186
1	303	172
2	1465	170
3	5003	170
done	5003	170

prune66.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (exp (* -1 y)) x)) (cbrt (/ (exp (* -1 y)) x)))
0.4b	(cbrt (/ (exp (* -1 y)) x))
0.4b	(cbrt (/ (exp (* -1 y)) x))
0.4b	(cbrt (/ (exp (* -1 y)) x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 144

Calls

4 calls:

33.0ms	(* (cbrt (/ (exp (* -1 y)) x)) (cbrt (/ (exp (* -1 y)) x)))
3.0ms	(cbrt (/ (exp (* -1 y)) x))
3.0ms	(cbrt (/ (exp (* -1 y)) x))
3.0ms	(cbrt (/ (exp (* -1 y)) x))

series311.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (cbrt (/ (exp (* -1 y)) x)) (cbrt (/ (exp (* -1 y)) x)))
68.0ms	(cbrt (/ (exp (* -1 y)) x))
74.0ms	(cbrt (/ (exp (* -1 y)) x))
72.0ms	(cbrt (/ (exp (* -1 y)) x))

simplify49.0ms

Counts

156 → 156

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	325	1726
1	1140	1658
2	5001	1578
done	5001	1578

prune440.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (pow (/ (sqrt x) (sqrt (+ x y))) x) (pow (/ (sqrt x) (sqrt (+ x y))) x))
0.1b	(/ (sqrt x) (sqrt (+ x y)))
0.1b	(/ (sqrt x) (sqrt (+ x y)))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

450×	`sqrt-prod`
415×	`add-sqr-sqrt`
400×	`times-frac`
354×	`unpow-prod-down`
331×	`*-un-lft-identity`
199×	`add-cube-cbrt`
98×	`swap-sqr`
58×	`distribute-lft-out`
52×	`associate-r` `associate-l`
49×	`unswap-sqr`
39×	`add-exp-log`
18×	`sqr-pow`
16×	`pow-exp` `prod-exp`
14×	`associate-/r*`
12×	`sqrt-div` `associate-/r/` `associate-/l*`
10×	`div-exp`
9×	`add-cbrt-cube`
8×	`pow-to-exp`
6×	`flip3-+` `flip-+` `div-inv`
3×	`pow1` `add-log-exp`
2×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `clear-num`
1×	`pow2` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

3 → 420

Calls

3 calls:

191.0ms	(* (pow (/ (sqrt x) (sqrt (+ x y))) x) (pow (/ (sqrt x) (sqrt (+ x y))) x))
14.0ms	(/ (sqrt x) (sqrt (+ x y)))
15.0ms	(/ (sqrt x) (sqrt (+ x y)))

series357.0ms

Counts

3 → 9

Calls

3 calls:

228.0ms	(* (pow (/ (sqrt x) (sqrt (+ x y))) x) (pow (/ (sqrt x) (sqrt (+ x y))) x))
60.0ms	(/ (sqrt x) (sqrt (+ x y)))
69.0ms	(/ (sqrt x) (sqrt (+ x y)))

simplify136.0ms

Counts

429 → 429

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	926	5469
1	4917	5142
2	5001	5142
done	5001	5142

prune689.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.8b

regimes72.0ms

Accuracy

87.7% (1.4b remaining)

Error of 1.9b against oracle of 0.4b and baseline of 12.2b

bsearch64.0ms

Steps

Iters	Range		Point
7	3.250284779123594e-16	2.925089333066609e-14	2.852199015031174e-14
9	-1418669.5161722333	-0.15939393977811658	-7.006483848542437

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16
done	31	16

end0.0ms

sample1.8s

Algorithm

intervals

Results

621.0ms	1481×	body	1280	valid
365.0ms	1490×	body	640	valid
193.0ms	4783×	body	80	valid
127.0ms	836×	body	320	valid
86.0ms	2967×	body	80	nan
45.0ms	472×	body	160	valid