Details

sample15.0ms

Algorithm

intervals

Results

4.0ms	230×	body	80	valid
1.0ms	9×	body	1280	valid
0.0ms	7×	body	320	valid
0.0ms	5×	body	640	valid
0.0ms	3×	body	2560	valid
0.0ms	2×	body	160	valid

simplify131.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	12	7
2	19	7
3	29	7
4	39	7
5	50	7
6	78	7
7	127	7
8	147	7
9	165	7
10	177	7
11	189	7
done	189	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (- x y) 2.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `associate-+r-` `flip3-+` `div-sub` `sum-log` `add-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

1 → 13

Calls

1 calls:

12.0ms

(+ x (/ (- x y) 2.0))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(+ x (/ (- x y) 2.0))

simplify803.0ms

Counts

16 → 16

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	34	178
1	92	171
2	216	157
3	637	157
4	2495	157
done	5001	157

prune36.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (+ x (/ x 2.0)) (/ y 2.0))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`diff-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `flip3-+` `times-frac` `associate--l+` `sum-log` `add-cbrt-cube` `flip--` `flip-+` `distribute-lft-out`

Counts

1 → 20

Calls

1 calls:

58.0ms

(- (+ x (/ x 2.0)) (/ y 2.0))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(- (+ x (/ x 2.0)) (/ y 2.0))

simplify471.0ms

Counts

23 → 23

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	66	371
1	161	356
2	445	338
3	1461	330
done	5000	330

prune48.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0))))
0.5b	(cbrt (+ x (/ (- x y) 2.0)))
0.5b	(cbrt (+ x (/ (- x y) 2.0)))
0.5b	(cbrt (+ x (/ (- x y) 2.0)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

98.0ms	(* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0))))
12.0ms	(cbrt (+ x (/ (- x y) 2.0)))
11.0ms	(cbrt (+ x (/ (- x y) 2.0)))
12.0ms	(cbrt (+ x (/ (- x y) 2.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

384.0ms	(* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0))))
413.0ms	(cbrt (+ x (/ (- x y) 2.0)))
410.0ms	(cbrt (+ x (/ (- x y) 2.0)))
409.0ms	(cbrt (+ x (/ (- x y) 2.0)))

simplify928.0ms

Counts

107 → 107

Iterations

Useful iterations: 3 (267.0ms)

Iter	Nodes	Cost
0	129	2124
1	266	1971
2	721	1841
3	2132	1650
done	5001	1650

prune246.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ x (/ x 2.0)) (/ y 2.0))
0.0b	(sqrt (- (+ x (/ x 2.0)) (/ y 2.0)))
0.0b	(sqrt (- (+ x (/ x 2.0)) (/ y 2.0)))
0.3b	(* (sqrt (- (+ x (/ x 2.0)) (/ y 2.0))) (sqrt (- (+ x (/ x 2.0)) (/ y 2.0))))

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
63×	`add-sqr-sqrt`
60×	`sqrt-prod`
48×	`sqrt-div`
26×	`frac-sub`
22×	`distribute-lft-out--`
21×	`pow1`
18×	`swap-sqr`
16×	`frac-times`
14×	`add-cube-cbrt` `difference-of-squares`
13×	`flip3--` `flip3-+` `flip--` `flip-+`
11×	`distribute-lft-out`
10×	`sqrt-pow1` `pow1/2` `associate-r` `associate-l`
9×	`add-log-exp`
7×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`associate-r/` `associate-l/` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `diff-log`
1×	`pow2` `sub-neg` `pow-plus` `sqrt-unprod` `prod-exp` `associate--l+` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 153

Calls

4 calls:

58.0ms	(- (+ x (/ x 2.0)) (/ y 2.0))
53.0ms	(sqrt (- (+ x (/ x 2.0)) (/ y 2.0)))
54.0ms	(sqrt (- (+ x (/ x 2.0)) (/ y 2.0)))
223.0ms	(* (sqrt (- (+ x (/ x 2.0)) (/ y 2.0))) (sqrt (- (+ x (/ x 2.0)) (/ y 2.0))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (+ x (/ x 2.0)) (/ y 2.0))
90.0ms	(sqrt (- (+ x (/ x 2.0)) (/ y 2.0)))
290.0ms	(sqrt (- (+ x (/ x 2.0)) (/ y 2.0)))
38.0ms	(* (sqrt (- (+ x (/ x 2.0)) (/ y 2.0))) (sqrt (- (+ x (/ x 2.0)) (/ y 2.0))))

simplify551.0ms

Counts

165 → 165

Iterations

Useful iterations: done (545.0ms)

Iter	Nodes	Cost
0	190	4579
1	353	3474
2	1122	3336
done	5000	3224

prune302.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	7	7
done	7	7

end0.0ms

sample309.0ms

Algorithm

intervals

Results

134.0ms	7349×	body	80	valid
22.0ms	246×	body	1280	valid
10.0ms	161×	body	640	valid
9.0ms	97×	body	2560	valid
5.0ms	99×	body	320	valid
2.0ms	51×	body	160	valid