Details

sample128.0ms

Algorithm

intervals

Results

43.0ms	162×	body	160	valid
17.0ms	242×	body	80	nan
16.0ms	498×	pre	80	true
9.0ms	42×	body	320	valid
4.0ms	52×	body	80	valid

simplify87.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
40.7b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(- (* b b) (* (* 4.0 a) c))
152.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
56.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series461.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(- (* b b) (* (* 4.0 a) c))
165.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
101.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.9s

Counts

118 → 118

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	195	2476
1	518	2183
2	2466	1866
done	5002	1794

prune390.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.3b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune43.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* a c) b)
0.3b	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/r`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 55

Calls

2 calls:

20.0ms	(/ (* a c) b)
47.0ms	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

series63.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (* a c) b)
32.0ms	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

simplify1.2s

Counts

61 → 61

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	111	818
1	353	787
2	2537	605
done	5001	575

prune236.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(* a (/ c b))
0.3b	(/ (* -2.0 (* a (/ c b))) (* 2.0 a))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
16×	`prod-exp` `cbrt-unprod`
15×	`add-sqr-sqrt`
13×	`associate-r`
11×	`cbrt-undiv` `times-frac` `div-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l/` `associate-/l*`

Counts

2 → 66

Calls

2 calls:

27.0ms	(* a (/ c b))
53.0ms	(/ (* -2.0 (* a (/ c b))) (* 2.0 a))

series45.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(* a (/ c b))
24.0ms	(/ (* -2.0 (* a (/ c b))) (* 2.0 a))

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: 2 (386.0ms)

Iter	Nodes	Cost
0	132	909
1	411	872
2	2773	680
done	5002	680

prune179.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 5.2b

regimes480.0ms

Accuracy

14.3% (6.1b remaining)

Error of 11.0b against oracle of 4.9b and baseline of 12.0b

bsearch34.0ms

Steps

Iters	Range		Point
3	0.00035791103598314976	0.0004692793959918333	0.00036487155848369246

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	38
1	27	38
done	27	38

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.1s	8174×	body	80	nan
948.0ms	4827×	body	160	valid
627.0ms	16174×	pre	80	true
613.0ms	1810×	body	80	valid
401.0ms	1363×	body	320	valid