Details

sample119.0ms

Algorithm

intervals

Results

30.0ms	145×	body	160	valid
19.0ms	278×	body	80	nan
18.0ms	534×	pre	80	true
10.0ms	44×	body	320	valid
5.0ms	67×	body	80	valid

simplify133.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
39.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

18.0ms	(- (* b b) (* (* 3.0 a) c))
25.0ms	(* (* 3.0 a) c)
135.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
75.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series372.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* b b) (* (* 3.0 a) c))
27.0ms	(* (* 3.0 a) c)
156.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
127.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.9s

Counts

121 → 121

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	201	2338
1	495	2065
2	1668	1747
done	5000	1676

prune437.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.5b

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune74.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.5b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (* a c) b)
0.3b	(* -1.5 (/ (* a c) b))
0.4b	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

18.0ms	(/ (* a c) b)
36.0ms	(* -1.5 (/ (* a c) b))
31.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series116.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ (* a c) b)
61.0ms	(* -1.5 (/ (* a c) b))
27.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify1.0s

Counts

93 → 93

Iterations

Useful iterations: 2 (320.0ms)

Iter	Nodes	Cost
0	129	1138
1	353	1097
2	1740	813
done	5000	813

prune284.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ b (* a c))
0.3b	(* -1.5 (/ 1 (/ b (* a c))))
0.3b	(/ 1 (/ b (* a c)))
0.4b	(/ (* -1.5 (/ 1 (/ b (* a c)))) (* 3.0 a))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-exp-log`
77×	`add-cbrt-cube`
72×	`div-exp`
69×	`times-frac`
54×	`prod-exp`
44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
37×	`add-cube-cbrt`
32×	`cbrt-undiv`
26×	`associate-r`
22×	`cbrt-unprod`
12×	`rec-exp` `1-exp`
11×	`div-inv`
9×	`associate-/r*`
7×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num` `unswap-sqr`
2×	`associate-*r/` `associate-/r/` `un-div-inv` `associate-/l/`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 189

Calls

4 calls:

16.0ms	(/ b (* a c))
59.0ms	(* -1.5 (/ 1 (/ b (* a c))))
27.0ms	(/ 1 (/ b (* a c)))
55.0ms	(/ (* -1.5 (/ 1 (/ b (* a c)))) (* 3.0 a))

series120.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ b (* a c))
37.0ms	(* -1.5 (/ 1 (/ b (* a c))))
25.0ms	(/ 1 (/ b (* a c)))
21.0ms	(/ (* -1.5 (/ 1 (/ b (* a c)))) (* 3.0 a))

simplify2.0s

Counts

201 → 201

Iterations

Useful iterations: 2 (558.0ms)

Iter	Nodes	Cost
0	246	2699
1	608	2209
2	2168	1703
done	5000	1703

prune352.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.5b

regimes691.0ms

Accuracy

10.7% (6.4b remaining)

Error of 11.5b against oracle of 5.0b and baseline of 12.2b

bsearch33.0ms

Steps

Iters	Range		Point
4	0.3765543169386318	0.509031623797797	0.4445338611362734

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	38
1	24	38
done	24	38

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.2s	8430×	body	80	nan
848.0ms	16430×	pre	80	true
721.0ms	4767×	body	160	valid
303.0ms	1363×	body	320	valid
129.0ms	1870×	body	80	valid