Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

356×

body

valid

simplify37.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	8	15
1	15	15
2	25	13
3	38	9
4	47	9
5	54	9
6	72	9
7	125	9
8	141	9
9	153	9
10	256	9
11	672	9
12	3513	9
done	5000	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ (* x y) (* z z)) (* z z))
0.2b	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-log-exp`
9×	`sum-log`
2×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `associate-+l+` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `flip-+`

Counts

2 → 27

Calls

2 calls:

10.0ms	(+ (+ (* x y) (* z z)) (* z z))
44.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series92.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(+ (+ (* x y) (* z z)) (* z z))
45.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify1.5s

Counts

33 → 33

Iterations

Useful iterations: 3 (282.0ms)

Iter	Nodes	Cost
0	56	625
1	166	520
2	675	460
3	2632	382
done	5000	382

prune81.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 2 (pow z 2)) (* x y))) (cbrt (+ (* 2 (pow z 2)) (* x y))))
3.5b	(cbrt (+ (* 2 (pow z 2)) (* x y)))
3.5b	(cbrt (+ (* 2 (pow z 2)) (* x y)))
3.5b	(cbrt (+ (* 2 (pow z 2)) (* x y)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
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 → 87

Calls

4 calls:

28.0ms	(* (cbrt (+ (* 2 (pow z 2)) (* x y))) (cbrt (+ (* 2 (pow z 2)) (* x y))))
3.0ms	(cbrt (+ (* 2 (pow z 2)) (* x y)))
3.0ms	(cbrt (+ (* 2 (pow z 2)) (* x y)))
3.0ms	(cbrt (+ (* 2 (pow z 2)) (* x y)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (cbrt (+ (* 2 (pow z 2)) (* x y))) (cbrt (+ (* 2 (pow z 2)) (* x y))))
109.0ms	(cbrt (+ (* 2 (pow z 2)) (* x y)))
109.0ms	(cbrt (+ (* 2 (pow z 2)) (* x y)))
109.0ms	(cbrt (+ (* 2 (pow z 2)) (* x y)))

simplify2.7s

Counts

99 → 99

Iterations

Useful iterations: 3 (489.0ms)

Iter	Nodes	Cost
0	124	2420
1	288	2235
2	977	2017
3	4289	1786
done	5000	1786

prune319.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 3 (pow z 2)) (* x y))) (cbrt (+ (* 3 (pow z 2)) (* x y))))
3.4b	(cbrt (+ (* 3 (pow z 2)) (* x y)))
3.4b	(cbrt (+ (* 3 (pow z 2)) (* x y)))
3.4b	(cbrt (+ (* 3 (pow z 2)) (* x y)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
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 → 87

Calls

4 calls:

24.0ms	(* (cbrt (+ (* 3 (pow z 2)) (* x y))) (cbrt (+ (* 3 (pow z 2)) (* x y))))
2.0ms	(cbrt (+ (* 3 (pow z 2)) (* x y)))
2.0ms	(cbrt (+ (* 3 (pow z 2)) (* x y)))
3.0ms	(cbrt (+ (* 3 (pow z 2)) (* x y)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (cbrt (+ (* 3 (pow z 2)) (* x y))) (cbrt (+ (* 3 (pow z 2)) (* x y))))
111.0ms	(cbrt (+ (* 3 (pow z 2)) (* x y)))
110.0ms	(cbrt (+ (* 3 (pow z 2)) (* x y)))
111.0ms	(cbrt (+ (* 3 (pow z 2)) (* x y)))

simplify2.3s

Counts

99 → 99

Iterations

Useful iterations: 3 (451.0ms)

Iter	Nodes	Cost
0	122	2414
1	284	2229
2	923	2011
3	3922	1780
done	5000	1780

prune311.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3 (pow z 2))
0.3b	(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* 3 (pow z 2)) (* x y))))
2.9b	(sqrt (+ (* 3 (pow z 2)) (* x y)))
2.9b	(sqrt (+ (* 3 (pow z 2)) (* x y)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
17×	`add-cube-cbrt` `*-un-lft-identity`
16×	`sqrt-div`
14×	`associate-r`
11×	`add-exp-log`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-l`
8×	`flip3-+` `swap-sqr` `add-cbrt-cube` `flip-+` `unswap-sqr`
5×	`pow-prod-up`
4×	`frac-times` `unpow-prod-down` `prod-exp` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `*-commutative` `cbrt-unprod` `unpow2` `sqr-pow`
1×	`pow2` `pow-to-exp` `pow-plus` `sqrt-unprod` `pow-exp` `rem-square-sqrt`

Counts

4 → 114

Calls

4 calls:

5.0ms	(* 3 (pow z 2))
22.0ms	(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* 3 (pow z 2)) (* x y))))
4.0ms	(sqrt (+ (* 3 (pow z 2)) (* x y)))
4.0ms	(sqrt (+ (* 3 (pow z 2)) (* x y)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 3 (pow z 2))
39.0ms	(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* 3 (pow z 2)) (* x y))))
104.0ms	(sqrt (+ (* 3 (pow z 2)) (* x y)))
103.0ms	(sqrt (+ (* 3 (pow z 2)) (* x y)))

simplify740.0ms

Counts

126 → 126

Iterations

Useful iterations: done (737.0ms)

Iter	Nodes	Cost
0	132	2492
1	284	1715
2	1153	1576
done	5001	1574

prune277.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes216.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	12	15
done	12	15

end0.0ms

sample514.0ms

Algorithm

intervals

Results

281.0ms

12061×

body

valid