Details

sample44.0ms

Algorithm

intervals

Results

25.0ms

699×

body

valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	25	17
2	40	17
3	66	17
4	118	17
5	255	17
6	849	17
7	3688	17
done	5000	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log`
8×	`add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `pow-to-exp` `pow-pow` `flip3-+` `associate-r` `pow-exp` `sum-log` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`

Counts

3 → 47

Calls

3 calls:

54.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
21.0ms	(* 4.0 (* b b))
10.0ms	(pow (+ (* a a) (* b b)) 2.0)

series210.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
25.0ms	(* 4.0 (* b b))
111.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify1.4s

Counts

56 → 56

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	101	765
1	242	693
2	670	647
3	2010	647
done	5001	647

prune132.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
1.4b	(* (pow a 2) (pow b 2))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
28×	`prod-exp`
25×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`-un-lft-identity` `associate-l*` `add-cbrt-cube` `add-log-exp`
10×	`unpow2` `sqr-pow`
9×	`add-cube-cbrt` `associate-r`
6×	`pow1`
4×	`sum-log` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

37.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
13.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
24.0ms	(* 2 (* (pow a 2) (pow b 2)))
18.0ms	(* (pow a 2) (pow b 2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
54.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
43.0ms	(* 2 (* (pow a 2) (pow b 2)))
35.0ms	(* (pow a 2) (pow b 2))

simplify820.0ms

Counts

113 → 113

Iterations

Useful iterations: done (817.0ms)

Iter	Nodes	Cost
0	146	1649
1	373	1431
2	1239	1245
done	5001	1231

prune264.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (* (pow a 2) (pow b 2)))
0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
1.4b	(* (pow a 2) (pow b 2))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
31×	`prod-exp`
27×	`add-sqr-sqrt`
17×	`unswap-sqr`
16×	`add-cbrt-cube`
14×	`unpow-prod-down` `associate-l`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `unpow2` `sqr-pow`
9×	`add-log-exp`
7×	`cbrt-unprod`
5×	`pow-prod-down`
3×	`sum-log` `*-commutative`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Counts

4 → 108

Calls

4 calls:

24.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
54.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
16.0ms	(* 4.0 (* b b))
18.0ms	(* (pow a 2) (pow b 2))

series161.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
66.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
25.0ms	(* 4.0 (* b b))
34.0ms	(* (pow a 2) (pow b 2))

simplify833.0ms

Counts

120 → 120

Iterations

Useful iterations: done (830.0ms)

Iter	Nodes	Cost
0	160	1554
1	385	1400
2	1326	1118
done	5000	1094

prune236.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* b b) (+ (* 2.0 (pow a 2)) 4.0))
1.0b	(* (* b b) (+ (* 2.0 (pow a 2)) 4.0))
20.2b	(sqrt (+ (pow b 4) (* (* b b) (+ (* 2.0 (pow a 2)) 4.0))))
20.2b	(sqrt (+ (pow b 4) (* (* b b) (+ (* 2.0 (pow a 2)) 4.0))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+` `add-log-exp`
2×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

40.0ms	(* (* b b) (+ (* 2.0 (pow a 2)) 4.0))
40.0ms	(* (* b b) (+ (* 2.0 (pow a 2)) 4.0))
15.0ms	(sqrt (+ (pow b 4) (* (* b b) (+ (* 2.0 (pow a 2)) 4.0))))
14.0ms	(sqrt (+ (pow b 4) (* (* b b) (+ (* 2.0 (pow a 2)) 4.0))))

series422.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (* b b) (+ (* 2.0 (pow a 2)) 4.0))
75.0ms	(* (* b b) (+ (* 2.0 (pow a 2)) 4.0))
134.0ms	(sqrt (+ (pow b 4) (* (* b b) (+ (* 2.0 (pow a 2)) 4.0))))
129.0ms	(sqrt (+ (pow b 4) (* (* b b) (+ (* 2.0 (pow a 2)) 4.0))))

simplify952.0ms

Counts

88 → 88

Iterations

Useful iterations: done (949.0ms)

Iter	Nodes	Cost
0	103	1678
1	276	1460
2	1104	1344
done	5000	1340

prune469.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes128.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	15	17
done	15	17

end0.0ms

sample1.2s

Algorithm

intervals

Results

746.0ms

20523×

body

valid