Details

sample220.0ms

Algorithm

intervals

Results

68.0ms	510×	pre	80	true
50.0ms	157×	body	160	valid
41.0ms	254×	body	80	nan
21.0ms	43×	body	320	valid
9.0ms	56×	body	80	valid

simplify93.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* c a) 4)))
0.1b	(- (* b b) (* (* c a) 4))
0.2b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
39.6b	(- (sqrt (- (* b b) (* (* c a) 4))) b)

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

15.0ms	(sqrt (- (* b b) (* (* c a) 4)))
15.0ms	(- (* b b) (* (* c a) 4))
83.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
77.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)

series378.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (- (* b b) (* (* c a) 4)))
56.0ms	(- (* b b) (* (* c a) 4))
119.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
97.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)

simplify2.2s

Counts

100 → 100

Iterations

Iter	Nodes
3	3594
2	1093
1	398
0	161

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.1b

localize18.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
1	0
0	0

prune104.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.1b

localize31.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* -2 (/ (* a c) b)) a)
0.2b	(/ (* a c) b)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-cbrt-cube` `add-exp-log`
8×	`cbrt-undiv` `div-exp`
6×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `times-frac` `add-cube-cbrt`
5×	`prod-exp` `cbrt-unprod`
2×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 49

Calls

2 calls:

21.0ms	(/ (* -2 (/ (* a c) b)) a)
18.0ms	(/ (* a c) b)

series46.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(/ (* -2 (/ (* a c) b)) a)
22.0ms	(/ (* a c) b)

simplify2.8s

Counts

55 → 55

Iterations

Iter	Nodes
3	6587
2	1060
1	263
0	99

prune555.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 4.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
0.2b	(/ (* a c) b)
0.2b	(/ (* a c) b)
0.5b	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `sqrt-prod`
25×	`add-cbrt-cube` `add-exp-log`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`times-frac`
19×	`pow1`
12×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`associate-/r*`
8×	`sqrt-pow1` `pow1/2` `sqrt-div`
7×	`cbrt-undiv` `div-exp` `div-inv`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-*r/` `pow-prod-up`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `pow-prod-down` `pow-sqr` `associate-/l*` `associate-/l/`
2×	`frac-times` `associate-*l/`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `*-commutative`

Counts

4 → 136

Calls

4 calls:

79.0ms	(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
21.0ms	(/ (* a c) b)
17.0ms	(/ (* a c) b)
44.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
22.0ms	(/ (* a c) b)
27.0ms	(/ (* a c) b)
63.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

simplify2.5s

Counts

148 → 148

Iterations

Iter	Nodes
3	5922
2	1197
1	383
0	167

prune1.5s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 4.0b

regimes646.0ms

Accuracy

10.8% (6.2b remaining)

Error of 11.3b against oracle of 5.1b and baseline of 12.0b

bsearch58.0ms

Steps

Iters	Range		Point
4	4.107563431783021e-05	7.864768175661588e-05	4.197456508925139e-05

simplify6.0ms

Iterations

Iter	Nodes
2	35
1	35
0	26

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.4s	4781×	body	160	valid
1.3s	1405×	body	320	valid
1.1s	8361×	body	80	nan
979.0ms	16361×	pre	80	true
292.0ms	1814×	body	80	valid