Details

sample60.0ms

Algorithm

intervals

Results

34.0ms

693×

body

valid

simplify3.6s

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	120	17
5	426	17
6	3507	17
done	5001	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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)

rewrite131.0ms

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:

92.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
16.0ms	(* 4.0 (* b b))
20.0ms	(pow (+ (* a a) (* b b)) 2.0)

series271.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
38.0ms	(* 4.0 (* b b))
145.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify1.0s

Counts

56 → 56

Iterations

Useful iterations: 2 (239.0ms)

Iter	Nodes	Cost
0	101	765
1	293	699
2	1405	647
done	5000	647

prune223.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

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)))
2.2b	(* (pow a 2) (pow b 2))

rewrite156.0ms

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:

61.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
18.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
41.0ms	(* 2 (* (pow a 2) (pow b 2)))
31.0ms	(* (pow a 2) (pow b 2))

series234.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
77.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
40.0ms	(* 2 (* (pow a 2) (pow b 2)))
41.0ms	(* (pow a 2) (pow b 2))

simplify2.1s

Counts

113 → 113

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	146	1649
1	386	1443
2	2409	1247
done	5000	1233

prune357.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b	(* 2.0 (* (pow a 2) (pow b 2)))
0.0b	(* 4.0 (* b b))
2.2b	(* (pow a 2) (pow b 2))

rewrite165.0ms

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:

89.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
38.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
17.0ms	(* 4.0 (* b b))
17.0ms	(* (pow a 2) (pow b 2))

series231.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
69.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
27.0ms	(* 4.0 (* b b))
55.0ms	(* (pow a 2) (pow b 2))

simplify2.4s

Counts

120 → 120

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	160	1554
1	435	1422
2	2801	1118
done	5000	1106

prune355.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.2b	(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
28.5b	(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 3))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
11×	`pow1` `add-exp-log`
10×	`add-cbrt-cube`
9×	`unpow-prod-down`
6×	`pow-unpow` `cube-prod`
4×	`cube-div` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `pow-pow` `flip3-+` `unpow3` `pow-exp` `flip-+`
1×	`pow1/3` `associate-r` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

18.0ms	(* 4.0 (* b b))
108.0ms	(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 3)
10.0ms	(pow (+ (* a a) (* b b)) 2.0)
86.0ms	(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 3))

series884.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 4.0 (* b b))
617.0ms	(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 3)
150.0ms	(pow (+ (* a a) (* b b)) 2.0)
81.0ms	(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 3))

simplify1.9s

Counts

96 → 96

Iterations

Useful iterations: 2 (499.0ms)

Iter	Nodes	Cost
0	158	2031
1	469	1793
2	2521	1567
done	5002	1567

prune392.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes224.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.4s

20552×

body

valid