Details

sample90.0ms

Algorithm

intervals

Results

55.0ms

709×

body

valid

simplify4.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	29
1	51	29
2	154	29
3	410	29
4	1047	29
5	1929	29
6	3970	29
done	5000	29

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b	(* (* a a) (- 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.4b	(* (* b b) (+ 3.0 a))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*r/`
17×	`pow1` `add-exp-log`
16×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`associate-r`
10×	`add-cube-cbrt`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `frac-add` `flip-+` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

116.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
49.0ms	(* (* a a) (- 1.0 a))
19.0ms	(pow (+ (* a a) (* b b)) 2.0)
57.0ms	(* (* b b) (+ 3.0 a))

series348.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
66.0ms	(* (* a a) (- 1.0 a))
141.0ms	(pow (+ (* a a) (* b b)) 2.0)
51.0ms	(* (* b b) (+ 3.0 a))

simplify1.9s

Counts

106 → 106

Iterations

Useful iterations: 2 (669.0ms)

Iter	Nodes	Cost
0	215	1577
1	617	1468
2	2511	1334
done	5002	1334

prune445.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* b b) (+ 3.0 a))
21.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
9×	`pow1` `add-exp-log` `unpow-prod-down` `add-cbrt-cube`
4×	`associate-r` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-l` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

36.0ms	(* (* b b) (+ 3.0 a))
17.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
10.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
9.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series614.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* b b) (+ 3.0 a))
185.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
197.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
189.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.6s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	105	1185
1	251	1154
2	813	1052
3	3062	1043
done	5001	1043

prune429.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

11.5b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
11.5b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
21.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-prod`
18×	`unpow-prod-down`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

16.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
23.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
11.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
11.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series856.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
220.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
218.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
198.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify1.5s

Counts

78 → 78

Iterations

Useful iterations: 3 (207.0ms)

Iter	Nodes	Cost
0	97	1398
1	172	1356
2	325	1272
3	761	1260
4	2062	1260
done	5000	1260

prune539.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

10.9b	(sqrt (+ (* a a) (* b b)))
11.5b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
21.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
6×	`sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 63

Calls

4 calls:

22.0ms	(sqrt (+ (* a a) (* b b)))
16.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
14.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
14.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series736.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (+ (* a a) (* b b)))
236.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
226.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
220.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.0s

Counts

75 → 75

Iterations

Useful iterations: 3 (338.0ms)

Iter	Nodes	Cost
0	118	1213
1	242	1161
2	509	1079
3	1187	1068
4	3149	1068
done	5001	1068

prune578.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes334.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	25	29
done	25	29

end0.0ms

sample3.8s

Algorithm

intervals

Results

3.1s

20340×

body

valid