Details

sample77.0ms

Algorithm

intervals

Results

47.0ms

709×

body

valid

simplify4.6s

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

localize28.0ms

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)
0.5b	(* (* b b) (+ 3.0 a))

rewrite247.0ms

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:

121.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
55.0ms	(* (* a a) (- 1.0 a))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)
47.0ms	(* (* b b) (+ 3.0 a))

series343.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
63.0ms	(* (* a a) (- 1.0 a))
136.0ms	(pow (+ (* a a) (* b b)) 2.0)
55.0ms	(* (* b b) (+ 3.0 a))

simplify1.8s

Counts

106 → 106

Iterations

Useful iterations: 2 (609.0ms)

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

prune399.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* 4.0 (pow a 2)) (* 12.0 (pow b 2))) (* 4.0 (pow a 3)))
0.0b	(* 4.0 (pow a 2))
0.2b	(* 12.0 (pow b 2))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`unpow-prod-down`
9×	`add-log-exp`
8×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`pow1` `sqr-pow`
4×	`unpow2`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`diff-log` `*-commutative` `cbrt-unprod`
1×	`sub-neg` `flip3--` `pow-pow` `associate--l+` `sum-log` `flip--`

Counts

4 → 85

Calls

4 calls:

60.0ms	(- (+ (* 4.0 (pow a 2)) (* 12.0 (pow b 2))) (* 4.0 (pow a 3)))
22.0ms	(* 4.0 (pow a 2))
22.0ms	(* 12.0 (pow b 2))
11.0ms	(pow (+ (* a a) (* b b)) 2.0)

series266.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (+ (* 4.0 (pow a 2)) (* 12.0 (pow b 2))) (* 4.0 (pow a 3)))
35.0ms	(* 4.0 (pow a 2))
29.0ms	(* 12.0 (pow b 2))
134.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify3.9s

Counts

97 → 97

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	168	1144
1	366	1075
2	987	961
3	4257	921
done	5000	915

prune400.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (+ 3.0 a))
10.3b	(cbrt (+ (* a a) (* b b)))
10.3b	(cbrt (+ (* a a) (* b b)))
10.3b	(cbrt (+ (* a a) (* b b)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

42.0ms	(* (* b b) (+ 3.0 a))
10.0ms	(cbrt (+ (* a a) (* b b)))
10.0ms	(cbrt (+ (* a a) (* b b)))
9.0ms	(cbrt (+ (* a a) (* b b)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* b b) (+ 3.0 a))
125.0ms	(cbrt (+ (* a a) (* b b)))
109.0ms	(cbrt (+ (* a a) (* b b)))
134.0ms	(cbrt (+ (* a a) (* b b)))

simplify2.3s

Counts

75 → 75

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	97	978
1	260	901
2	914	803
3	3349	794
done	5001	794

prune344.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

10.3b	(cbrt (+ (* a a) (* b b)))
10.3b	(cbrt (+ (* a a) (* b b)))
10.3b	(cbrt (+ (* a a) (* b b)))
10.3b	(cbrt (+ (* a a) (* b b)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

5.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))
7.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (+ (* a a) (* b b)))
96.0ms	(cbrt (+ (* a a) (* b b)))
97.0ms	(cbrt (+ (* a a) (* b b)))
101.0ms	(cbrt (+ (* a a) (* b b)))

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: 3 (135.0ms)

Iter	Nodes	Cost
0	51	928
1	125	904
2	286	776
3	612	764
4	1581	764
done	5001	764

prune321.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes137.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	29
1	28	29
done	28	29

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s

20533×

body

valid