Details

sample46.0ms

Algorithm

intervals

Results

10.0ms	152×	body	160	valid
9.0ms	523×	pre	80	true
8.0ms	267×	body	80	nan
3.0ms	104×	body	80	valid

simplify51.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* 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))
29.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite77.0ms

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))
7.0ms	(* (* 3.0 a) c)
42.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
22.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series258.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
20.0ms	(* (* 3.0 a) c)
114.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
80.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify821.0ms

Counts

121 → 121

Iterations

Useful iterations: done (817.0ms)

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

prune270.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 9.3b

localize4.0ms

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

prune49.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.3b

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))
9.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series69.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ (* a c) b)
30.0ms	(* -1.5 (/ (* a c) b))
21.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify797.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (144.0ms)

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

prune204.0ms

Pruning

38 alts after pruning (37 fresh and 1 done)

Merged error: 9.2b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

1131×	`times-frac`
457×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
111×	`associate-/r*`
76×	`div-inv`
52×	`add-exp-log` `add-cbrt-cube`
30×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

4 → 543

Calls

4 calls:

12.0ms	(/ 3.0 (/ (/ (* a c) b) a))
23.0ms	(/ -1.5 (/ 3.0 (/ (/ (* a c) b) a)))
5.0ms	(/ (/ (* a c) b) a)
3.0ms	(/ (* a c) b)

series72.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 3.0 (/ (/ (* a c) b) a))
20.0ms	(/ -1.5 (/ 3.0 (/ (/ (* a c) b) a)))
7.0ms	(/ (/ (* a c) b) a)
25.0ms	(/ (* a c) b)

simplify642.0ms

Counts

555 → 555

Iterations

Useful iterations: done (619.0ms)

Iter	Nodes	Cost
0	893	11463
1	2132	10679
done	5000	10651

prune1.4s

Pruning

47 alts after pruning (47 fresh and 0 done)

Merged error: 9.1b

regimes785.0ms

Accuracy

39.6% (8.3b remaining)

Error of 17.3b against oracle of 8.9b and baseline of 22.7b

bsearch3.0ms

Steps

Iters	Range		Point
0	17.302597776335716	18.126688132261577	17.714642954298647

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	54
1	36	54
done	36	54

end0.0ms

sample1.3s

Algorithm

intervals

Results

305.0ms	16491×	pre	80	true
290.0ms	4519×	body	160	valid
257.0ms	8491×	body	80	nan
112.0ms	3481×	body	80	valid