Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
3.0ms	28×	body	640	valid
2.0ms	11×	body	1280	valid
2.0ms	19×	body	320	valid
1.0ms	15×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	203
1	16	203
2	35	203
3	74	203
4	152	203
5	419	203
6	1686	203
done	5000	203

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
3.4b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.3b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`add-cbrt-cube` `add-exp-log`
7×	`add-cube-cbrt`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-/r` `times-frac` `associate-l/`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `-commutative` `flip-+` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

19.0ms	(* (- 1.0 x) y)
15.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
21.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series205.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (- 1.0 x) y)
103.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
66.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.3s

Counts

72 → 72

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	128	16962
1	347	15213
2	2052	14931
done	5000	14691

prune320.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize304.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ y 1.0) y)
0.1b	(/ (- 1.0 x) (/ (+ y 1.0) y))
3.4b	(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

167×	`times-frac`
157×	`*-un-lft-identity`
120×	`add-sqr-sqrt`
77×	`add-cube-cbrt`
22×	`distribute-lft-out`
20×	`difference-of-squares`
19×	`associate-/r*`
18×	`distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1`
2×	`clear-num` `frac-2neg` `flip3--` `div-sub` `flip--`
1×	`sub-neg` `flip3-+` `diff-log` `associate-/r/` `flip-+` `associate--r-`

Counts

3 → 169

Calls

3 calls:

19.0ms	(/ (+ y 1.0) y)
31.0ms	(/ (- 1.0 x) (/ (+ y 1.0) y))
56.0ms	(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

series213.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (+ y 1.0) y)
52.0ms	(/ (- 1.0 x) (/ (+ y 1.0) y))
86.0ms	(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

simplify2.0s

Counts

178 → 178

Iterations

Useful iterations: 2 (941.0ms)

Iter	Nodes	Cost
0	249	64917
1	760	61104
2	3792	59233
done	5001	59233

prune640.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.0b	(/ 1 (+ y 1.0))
6.4b	(* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))
6.5b	(- 1.0 (* (/ 1 (+ y 1.0)) (* (- 1.0 x) y)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
32×	`add-exp-log`
27×	`add-sqr-sqrt`
24×	`times-frac`
23×	`associate-l` `add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
7×	`associate-*l/` `cbrt-unprod` `distribute-lft-out`
6×	`div-exp` `add-log-exp`
4×	`associate-/r` `flip3--` `associate-r*` `pow-prod-down` `associate-/r/` `flip--`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*`
2×	`frac-times` `flip3-+` `associate-r/` `-commutative` `flip-+` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-flip` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

18.0ms	(* (- 1.0 x) y)
10.0ms	(/ 1 (+ y 1.0))
62.0ms	(* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))
5.0ms	(- 1.0 (* (/ 1 (+ y 1.0)) (* (- 1.0 x) y)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (- 1.0 x) y)
37.0ms	(/ 1 (+ y 1.0))
42.0ms	(* (/ 1 (+ y 1.0)) (* (- 1.0 x) y))
96.0ms	(- 1.0 (* (/ 1 (+ y 1.0)) (* (- 1.0 x) y)))

simplify2.9s

Counts

129 → 129

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	188	34247
1	525	27244
2	3745	24833
done	5002	24312

prune563.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 x) (/ (+ y 1.0) y))
0.1b	(* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y)))
3.3b	(- (* 1.0 1.0) (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y))))
8.0b	(/ (- (* 1.0 1.0) (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y)))) (+ 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y))))

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

1026×	`times-frac`
1013×	`*-un-lft-identity`
601×	`add-sqr-sqrt`
379×	`add-cube-cbrt`
159×	`swap-sqr`
137×	`distribute-lft-out` `distribute-lft-out--`
99×	`difference-of-squares`
85×	`associate-r` `associate-l`
47×	`add-cbrt-cube` `add-exp-log`
36×	`div-inv`
22×	`cbrt-undiv` `div-exp`
20×	`associate-/r*`
11×	`pow1`
9×	`prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
7×	`associate-/r/`
6×	`add-log-exp`
4×	`associate-/l/`
3×	`flip3--` `flip--`
2×	`clear-num` `frac-2neg` `div-sub`
1×	`pow2` `frac-times` `sub-neg` `flip3-+` `pow-plus` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+`

Counts

4 → 545

Calls

4 calls:

22.0ms	(/ (- 1.0 x) (/ (+ y 1.0) y))
268.0ms	(* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y)))
6.0ms	(- (* 1.0 1.0) (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y))))
192.0ms	(/ (- (* 1.0 1.0) (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y)))) (+ 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y))))

series857.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (- 1.0 x) (/ (+ y 1.0) y))
78.0ms	(* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y)))
122.0ms	(- (* 1.0 1.0) (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y))))
584.0ms	(/ (- (* 1.0 1.0) (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y)))) (+ 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y))))

simplify2.4s

Counts

557 → 557

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	545	251597
1	2234	233825
done	5000	223775

prune2.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes350.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.6b

bsearch87.0ms

Steps

Iters	Range		Point
6	64260609.3427585	488997712.5877659	186709514.1052932
9	-3322970397.4786234	-6367.3348759504115	-179455656.42601708

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	706
1	31	706
done	31	706

end0.0ms

sample968.0ms

Algorithm

intervals

Results

420.0ms	6080×	body	80	valid
151.0ms	752×	body	640	valid
76.0ms	364×	body	1280	valid
62.0ms	498×	body	320	valid
48.0ms	306×	body	160	valid