Details

sample125.0ms

Algorithm

intervals

Results

26.0ms	141×	body	160	valid
21.0ms	239×	body	80	nan
19.0ms	495×	pre	80	true
14.0ms	50×	body	320	valid
6.0ms	65×	body	80	valid

simplify150.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(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))
36.0b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
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 → 72

Calls

4 calls:

9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
128.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
85.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series499.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(- (* b b) (* (* 4.0 a) c))
186.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
120.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify3.0s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	154	1592
1	386	1488
2	1234	1332
3	4646	1324
done	5000	1324

prune415.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize8.0ms

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

prune63.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
0.3b	(/ (* a c) b)

rewrite39.0ms

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` `frac-2neg` `clear-num` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 51

Calls

2 calls:

23.0ms	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
13.0ms	(/ (* a c) b)

series70.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
23.0ms	(/ (* a c) b)

simplify905.0ms

Counts

57 → 57

Iterations

Useful iterations: 2 (319.0ms)

Iter	Nodes	Cost
0	107	782
1	310	751
2	1621	523
done	5001	523

prune152.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* -2.0 (* (* a c) (/ 1 b))) (* 2.0 a))
0.4b	(* (* a c) (/ 1 b))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-exp-log`
70×	`add-cbrt-cube`
64×	`prod-exp`
34×	`cbrt-unprod`
32×	`div-exp`
18×	`cbrt-undiv`
13×	`associate-r`
10×	`times-frac`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`rec-exp` `1-exp`
4×	`associate-*r/`
3×	`pow-prod-down`
2×	`un-div-inv` `div-inv` `associate-/l/` `add-log-exp`
1×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

2 → 85

Calls

2 calls:

76.0ms	(/ (* -2.0 (* (* a c) (/ 1 b))) (* 2.0 a))
33.0ms	(* (* a c) (/ 1 b))

series57.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(/ (* -2.0 (* (* a c) (/ 1 b))) (* 2.0 a))
33.0ms	(* (* a c) (/ 1 b))

simplify1.4s

Counts

91 → 91

Iterations

Useful iterations: 2 (531.0ms)

Iter	Nodes	Cost
0	167	1486
1	479	1199
2	2749	813
done	5001	813

prune96.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 5.4b

regimes302.0ms

Accuracy

3.6% (6.7b remaining)

Error of 11.7b against oracle of 5.0b and baseline of 12.0b

bsearch58.0ms

Steps

Iters	Range		Point
5	5.783021591474238	12.498921350077156	5.85280970215493

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	39
1	26	39
done	26	39

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.6s	16396×	pre	80	true
844.0ms	4869×	body	160	valid
752.0ms	8396×	body	80	nan
355.0ms	1350×	body	320	valid
119.0ms	1781×	body	80	valid