Details

sample77.0ms

Algorithm

intervals

Results

17.0ms	299×	body	80	nan
16.0ms	555×	pre	80	true
16.0ms	141×	body	160	valid
6.0ms	115×	body	80	valid

simplify133.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (28.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* 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))
29.1b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite252.0ms

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:

17.0ms	(- (* b b) (* (* 3.0 a) c))
19.0ms	(* (* 3.0 a) c)
128.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
84.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series371.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(* (* 3.0 a) c)
155.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
120.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify2.1s

Counts

121 → 121

Iterations

Useful iterations: done (2.1s)

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

prune469.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.3b

localize9.0ms

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

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* a c) b)
0.3b	(* -1.5 (/ (* a c) b))
0.3b	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

rewrite92.0ms

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:

20.0ms	(/ (* a c) b)
32.0ms	(* -1.5 (/ (* a c) b))
33.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series137.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (* a c) b)
53.0ms	(* -1.5 (/ (* a c) b))
41.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify992.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (315.0ms)

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

prune360.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 9.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ -1.5 (/ (* 3.0 a) (/ (* a c) b)))
0.2b	(/ (* a c) b)
0.3b	(/ (* 3.0 a) (/ (* a c) b))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
58×	`add-exp-log` `add-cbrt-cube`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
29×	`cbrt-undiv` `div-exp`
22×	`associate-/r*`
13×	`div-inv`
11×	`prod-exp` `cbrt-unprod`
6×	`associate-/r/`
5×	`associate-/l*`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`

Counts

3 → 141

Calls

3 calls:

21.0ms	(/ -1.5 (/ (* 3.0 a) (/ (* a c) b)))
11.0ms	(/ (* a c) b)
23.0ms	(/ (* 3.0 a) (/ (* a c) b))

series108.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ -1.5 (/ (* 3.0 a) (/ (* a c) b)))
37.0ms	(/ (* a c) b)
34.0ms	(/ (* 3.0 a) (/ (* a c) b))

simplify1.4s

Counts

150 → 150

Iterations

Useful iterations: 2 (510.0ms)

Iter	Nodes	Cost
0	229	2237
1	549	2149
2	2326	1475
done	5000	1475

prune399.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 9.2b

regimes733.0ms

Accuracy

38.7% (8.3b remaining)

Error of 17.4b against oracle of 9.1b and baseline of 22.7b

bsearch48.0ms

Steps

Iters	Range		Point
3	22.362890977079257	29.634246312554687	22.81735068554647

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	4511×	body	160	valid
770.0ms	16384×	pre	80	true
692.0ms	8384×	body	80	nan
341.0ms	3489×	body	80	valid