Details

sample151.0ms

Algorithm

intervals

Results

125.0ms

682×

body

valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
5	5568
4	1638
3	539
2	179
1	54
0	19

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a a) a)
0.2b	(* -12 (* a (* b b)))
0.4b	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))
1.1b	(* a (* b b))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

44×	`pow1`
25×	`add-cbrt-cube` `add-exp-log`
15×	`add-sqr-sqrt`
13×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
8×	`associate-r`
7×	`pow-plus` `pow-prod-up`
6×	`flip3-+` `flip-+`
4×	`frac-times` `*-commutative` `insert-posit16` `add-log-exp`
3×	`pow2` `swap-sqr` `pow-sqr` `unswap-sqr`
2×	`associate-l/` `associate-r/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow3`

Counts

4 → 107

Calls

4 calls:

28.0ms	(* (* a a) a)
43.0ms	(* -12 (* a (* b b)))
37.0ms	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))
18.0ms	(* a (* b b))

series193.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* a a) a)
44.0ms	(* -12 (* a (* b b)))
52.0ms	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))
51.0ms	(* a (* b b))

simplify628.0ms

Counts

119 → 119

Iterations

Iter	Nodes
2	2029
1	478
0	147

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* -12 (* a (* b b)))
1.1b	(* a (* b b))
9.1b	(sqrt (+ (* a a) (* b b)))
9.1b	(sqrt (+ (* a a) (* b b)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `sqrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `*-commutative` `flip-+`
1×	`unswap-sqr`

Counts

4 → 74

Calls

4 calls:

67.0ms	(* -12 (* a (* b b)))
16.0ms	(* a (* b b))
6.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* -12 (* a (* b b)))
35.0ms	(* a (* b b))
51.0ms	(sqrt (+ (* a a) (* b b)))
62.0ms	(sqrt (+ (* a a) (* b b)))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
3	3724
2	737
1	235
0	93

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

1.1b	(* a (* b b))
9.1b	(sqrt (+ (* a a) (* b b)))
9.1b	(sqrt (+ (* a a) (* b b)))
18.8b	(cbrt (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1`
10×	`sqrt-div`
9×	`add-cbrt-cube` `add-exp-log`
8×	`cbrt-div` `flip3-+` `flip-+`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/`
1×	`cbrt-prod` `pow1/3` `cube-unmult` `associate-r` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

14.0ms	(* a (* b b))
6.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))
15.0ms	(cbrt (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* a (* b b))
49.0ms	(sqrt (+ (* a a) (* b b)))
41.0ms	(sqrt (+ (* a a) (* b b)))
44.0ms	(cbrt (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))

simplify3.2s

Counts

83 → 83

Iterations

Iter	Nodes
3	4958
2	915
1	275
0	106

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

9.1b	(sqrt (+ (* a a) (* b b)))
9.1b	(sqrt (+ (* a a) (* b b)))
18.8b	(cbrt (* (cbrt (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b)))) (+ (* a a) (* b b))))
18.8b	(cbrt (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

58×	`cbrt-div`
35×	`flip3-+` `flip-+`
32×	`frac-times`
28×	`sqrt-div`
16×	`associate-*l/`
10×	`associate-*r/`
9×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`
1×	`cube-unmult` `rem-cbrt-cube`

Counts

4 → 87

Calls

4 calls:

6.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))
42.0ms	(cbrt (* (cbrt (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b)))) (+ (* a a) (* b b))))
29.0ms	(cbrt (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (+ (* a a) (* b b)))
39.0ms	(sqrt (+ (* a a) (* b b)))
57.0ms	(cbrt (* (cbrt (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b)))) (+ (* a a) (* b b))))
60.0ms	(cbrt (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))

simplify2.3s

Counts

99 → 99

Iterations

Iter	Nodes
3	4559
2	1436
1	490
0	179

prune1.7s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes232.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	29
1	29
0	19

end0.0ms

sample5.8s

Algorithm

intervals

Results

5.3s

20643×

body

valid