Details

sample163.0ms

Algorithm

intervals

Results

49.0ms	516×	pre	80	true
38.0ms	156×	body	160	valid
30.0ms	260×	body	80	nan
17.0ms	50×	body	320	valid
6.0ms	50×	body	80	valid

simplify518.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.2b

localize40.0ms

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)
40.5b	(- (sqrt (- (* b b) (* (* c a) 4))) b)

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

127×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
40×	`difference-of-squares`
36×	`unswap-sqr`
29×	`sqrt-prod`
18×	`times-frac` `associate-l`
17×	`distribute-lft-out--`
16×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`add-cbrt-cube` `swap-sqr` `add-exp-log` `-commutative` `associate-/l`
5×	`pow1`
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 → 130

Calls

4 calls:

140.0ms	(sqrt (- (* b b) (* (* c a) 4)))
105.0ms	(- (* b b) (* (* c a) 4))
1.4s	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
796.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)

series383.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(sqrt (- (* b b) (* (* c a) 4)))
48.0ms	(- (* b b) (* (* c a) 4))
127.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
109.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)

simplify1.4s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	1344
1	492
0	206

prune775.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.0b

localize20.0ms

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

prune74.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.0b

localize34.0ms

Local error

Found 2 expressions with local error:

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

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

341×	`times-frac`
249×	`add-sqr-sqrt`
211×	`associate-r`
181×	`*-un-lft-identity`
179×	`add-cube-cbrt`
77×	`associate-/l*`
64×	`associate-l`
33×	`unswap-sqr`
21×	`add-cbrt-cube` `add-exp-log` `*-commutative` `associate-/l/`
18×	`associate-*r/`
9×	`associate-/r*`
8×	`cbrt-undiv` `div-exp`
6×	`div-inv`
5×	`prod-exp` `cbrt-unprod`
4×	`clear-num`
3×	`frac-2neg` `un-div-inv`
2×	`pow1` `insert-posit16` `add-log-exp`

Counts

2 → 313

Calls

2 calls:

154.0ms	(/ (* -2 (/ (* a c) b)) a)
31.0ms	(/ (* a c) b)

series57.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (* -2 (/ (* a c) b)) a)
21.0ms	(/ (* a c) b)

simplify1.6s

Counts

319 → 319

Iterations

Iter	Nodes
done	5001
1	1535
0	523

prune1.6s

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 3.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (/ (* (sqrt a) c) b))
0.2b	(* (sqrt a) c)
0.3b	(/ (* (sqrt a) c) b)
0.3b	(/ (* -2 (/ (sqrt a) 1)) (/ a (/ (* (sqrt a) c) b)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

21640×	`times-frac`
11932×	`add-sqr-sqrt`
8579×	`*-un-lft-identity`
8212×	`add-cube-cbrt`
5169×	`associate-r`
3540×	`sqrt-prod`
2835×	`associate-l`
1677×	`unswap-sqr`
872×	`associate-/r/`
656×	`associate-/l*`
564×	`*-commutative`
403×	`associate-/r*`
335×	`div-inv`
92×	`add-exp-log`
74×	`add-cbrt-cube`
51×	`div-exp`
43×	`clear-num`
42×	`frac-2neg`
38×	`cbrt-undiv`
19×	`prod-exp`
14×	`cbrt-unprod` `associate-/l/`
12×	`associate-*r/`
6×	`pow1`
4×	`1-exp` `insert-posit16` `add-log-exp`
2×	`un-div-inv`
1×	`pow-prod-down`

Counts

4 → 7053

Calls

4 calls:

38.0ms	(/ a (/ (* (sqrt a) c) b))
11.0ms	(* (sqrt a) c)
48.0ms	(/ (* (sqrt a) c) b)
337.0ms	(/ (* -2 (/ (sqrt a) 1)) (/ a (/ (* (sqrt a) c) b)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ a (/ (* (sqrt a) c) b))
65.0ms	(* (sqrt a) c)
94.0ms	(/ (* (sqrt a) c) b)
79.0ms	(/ (* -2 (/ (sqrt a) 1)) (/ a (/ (* (sqrt a) c) b)))

simplify11.4s

Counts

7065 → 7065

Iterations

Iter	Nodes
done	8223
0	8223

prune36.0s

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 3.9b

regimes716.0ms

Accuracy

11.2% (6.0b remaining)

Error of 11.1b against oracle of 5.1b and baseline of 11.8b

bsearch67.0ms

Steps

Iters	Range		Point
5	1.5870254657342646e-05	4.458333025154689e-05	1.6209007775013438e-05

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample5.9s

Algorithm

intervals

Results

1.6s	4880×	body	160	valid
1.4s	16170×	pre	80	true
1.1s	1367×	body	320	valid
1.1s	8170×	body	80	nan
272.0ms	1753×	body	80	valid