Details

sample110.0ms

Algorithm

intervals

Results

75.0ms

650×

body

valid

simplify6.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	53	31
2	160	31
3	451	31
4	1223	31
5	2469	31
6	4618	31
done	5001	31

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.1b	(* (* a a) (+ 1.0 a))
0.2b	(* (* b b) (- 1.0 (* 3.0 a)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`associate-*r/`
3×	`distribute-rgt-in` `unpow-prod-down` `pow-unpow` `distribute-lft-in`
2×	`sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

17.0ms	(+ (* a a) (* b b))
66.0ms	(* (* a a) (+ 1.0 a))
44.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
23.0ms	(pow (+ (* a a) (* b b)) 2.0)

series334.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* a a) (* b b))
84.0ms	(* (* a a) (+ 1.0 a))
86.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
127.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify1.7s

Counts

89 → 89

Iterations

Useful iterations: 2 (516.0ms)

Iter	Nodes	Cost
0	155	1076
1	426	997
2	1606	887
done	5001	887

prune377.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
9.3b	(cbrt (+ (* a a) (* b b)))
9.3b	(cbrt (+ (* a a) (* b b)))
9.3b	(cbrt (+ (* a a) (* b b)))

rewrite89.0ms

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:

68.0ms	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
6.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))
6.0ms	(cbrt (+ (* a a) (* b b)))

series619.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
138.0ms	(cbrt (+ (* a a) (* b b)))
145.0ms	(cbrt (+ (* a a) (* b b)))
146.0ms	(cbrt (+ (* a a) (* b b)))

simplify3.0s

Counts

99 → 99

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	102	1926
1	221	1757
2	555	1543
3	1205	1394
4	3224	1384
done	5001	1329

prune644.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

8.6b	(sqrt (+ (* a a) (* b b)))
8.6b	(sqrt (+ (* a a) (* b b)))
9.3b	(cbrt (+ (* a a) (* b b)))
9.3b	(cbrt (+ (* a a) (* b b)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

10.0ms	(sqrt (+ (* a a) (* b b)))
9.0ms	(sqrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt (+ (* a a) (* b b)))
50.0ms	(sqrt (+ (* a a) (* b b)))
136.0ms	(cbrt (+ (* a a) (* b b)))
156.0ms	(cbrt (+ (* a a) (* b b)))

simplify2.1s

Counts

68 → 68

Iterations

Useful iterations: 3 (231.0ms)

Iter	Nodes	Cost
0	65	890
1	144	824
2	313	716
3	670	710
4	1768	710
done	5001	710

prune711.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

8.6b	(sqrt (+ (* a a) (* b b)))
8.6b	(sqrt (+ (* a a) (* b b)))
9.3b	(cbrt (+ (* a a) (* b b)))
9.3b	(cbrt (+ (* a a) (* b b)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

19.0ms	(sqrt (+ (* a a) (* b b)))
10.0ms	(sqrt (+ (* a a) (* b b)))
11.0ms	(cbrt (+ (* a a) (* b b)))
9.0ms	(cbrt (+ (* a a) (* b b)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt (+ (* a a) (* b b)))
46.0ms	(sqrt (+ (* a a) (* b b)))
157.0ms	(cbrt (+ (* a a) (* b b)))
143.0ms	(cbrt (+ (* a a) (* b b)))

simplify2.0s

Counts

68 → 68

Iterations

Useful iterations: 3 (309.0ms)

Iter	Nodes	Cost
0	65	890
1	144	824
2	313	716
3	670	710
4	1768	710
done	5001	710

prune515.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes513.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	27	31
done	27	31

end0.0ms

sample4.2s

Algorithm

intervals

Results

3.4s

20563×

body

valid