Details

sample53.0ms

Algorithm

intervals

Results

12.0ms	326×	body	80	nan
10.0ms	582×	pre	80	true
10.0ms	152×	body	160	valid
4.0ms	104×	body	80	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	83	16
4	102	16
5	110	16
done	110	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.4b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
29.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite76.0ms

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:

3.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(* (* 3.0 a) c)
42.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
21.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series239.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(* (* 3.0 a) c)
100.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
76.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify766.0ms

Counts

121 → 121

Iterations

Useful iterations: done (763.0ms)

Iter	Nodes	Cost
0	201	2338
1	517	2065
2	2220	1729
done	5000	1728

prune254.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.7b

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune40.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.7b

localize7.0ms

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))

rewrite23.0ms

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:

3.0ms	(/ (* a c) b)
8.0ms	(* -1.5 (/ (* a c) b))
8.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series70.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ (* a c) b)
26.0ms	(* -1.5 (/ (* a c) b))
25.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify934.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	129	1138
1	394	1097
2	2297	813
done	5000	813

prune180.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 9.6b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 71

Calls

2 calls:

10.0ms	(* (* a -1.5) (/ c b))
10.0ms	(/ (* (* a -1.5) (/ c b)) (* 3.0 a))

series49.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(* (* a -1.5) (/ c b))
19.0ms	(/ (* (* a -1.5) (/ c b)) (* 3.0 a))

simplify950.0ms

Counts

77 → 77

Iterations

Useful iterations: 2 (160.0ms)

Iter	Nodes	Cost
0	133	1116
1	439	1063
2	2781	751
done	5000	751

prune91.0ms

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 9.6b

regimes570.0ms

Accuracy

45% (7.4b remaining)

Error of 16.4b against oracle of 9.0b and baseline of 22.4b

bsearch2.0ms

Steps

Iters	Range		Point
0	228.11766252751497	228.40791225309218	228.26278739030357

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	38
1	24	38
done	24	38

end0.0ms

sample1.3s

Algorithm

intervals

Results

300.0ms	4522×	body	160	valid
299.0ms	16462×	pre	80	true
264.0ms	8462×	body	80	nan
118.0ms	3478×	body	80	valid