Details

sample84.0ms

Algorithm

intervals

Results

26.0ms	523×	pre	80	true
16.0ms	149×	body	160	valid
14.0ms	267×	body	80	nan
8.0ms	46×	body	320	valid
3.0ms	61×	body	80	valid

simplify78.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize24.0ms

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)
38.6b	(- (sqrt (- (* b b) (* (* c a) 4))) b)

rewrite151.0ms

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:

9.0ms	(sqrt (- (* b b) (* (* c a) 4)))
8.0ms	(- (* b b) (* (* c a) 4))
80.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
50.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)

series379.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (- (* b b) (* (* c a) 4)))
57.0ms	(- (* b b) (* (* c a) 4))
121.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
110.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)

simplify2.6s

Counts

100 → 100

Iterations

Iter	Nodes
done	5002
3	4569
2	1103
1	400
0	161

prune547.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.3b

localize10.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune78.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* -2 (/ (* a c) b)) a)
0.3b	(/ (* a c) b)

rewrite58.0ms

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:

40.0ms	(/ (* -2 (/ (* a c) b)) a)
15.0ms	(/ (* a c) b)

series64.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (* -2 (/ (* a c) b)) a)
38.0ms	(/ (* a c) b)

simplify1.0s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
2	1429
1	278
0	99

prune312.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
0.3b	(/ (* a c) b)
0.3b	(/ (* a c) b)
0.6b	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

rewrite180.0ms

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:

103.0ms	(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
15.0ms	(/ (* a c) b)
10.0ms	(/ (* a c) b)
46.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
39.0ms	(/ (* a c) b)
29.0ms	(/ (* a c) b)
65.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

simplify1.2s

Counts

148 → 148

Iterations

Iter	Nodes
done	5027
2	1508
1	403
0	167

prune554.0ms

Pruning

28 alts after pruning (26 fresh and 2 done)

Merged error: 5.2b

regimes617.0ms

Accuracy

4.4% (6.4b remaining)

Error of 11.7b against oracle of 5.3b and baseline of 12.0b

bsearch56.0ms

Steps

Iters	Range		Point
5	0.8976043504807807	2.718412628430079	0.9098230818343235

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.2s	16089×	pre	80	true
939.0ms	4872×	body	160	valid
706.0ms	1347×	body	320	valid
695.0ms	8089×	body	80	nan
186.0ms	1781×	body	80	valid