Details

sample163.0ms

Algorithm

intervals

Results

58.0ms	118×	body	320	valid
12.0ms	213×	body	80	nan
11.0ms	469×	pre	80	true
9.0ms	98×	body	160	valid
2.0ms	11×	body	640	valid
2.0ms	29×	body	80	valid

simplify89.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
28.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite368.0ms

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:

52.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(- (* b b) (* (* 4.0 a) c))
228.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
58.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series644.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(- (* b b) (* (* 4.0 a) c))
179.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
306.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify3.5s

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

prune497.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.4b

localize8.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune50.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.4b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite62.0ms

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:

10.0ms	(/ (* a c) b)
49.0ms	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

series48.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(/ (* a c) b)
26.0ms	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

simplify1.0s

Counts

57 → 57

Iterations

Useful iterations: 2 (248.0ms)

Iter	Nodes	Cost
0	107	782
1	310	751
2	1631	523
done	5000	523

prune190.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 2.4b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
85×	`times-frac`
76×	`add-exp-log` `add-cbrt-cube`
60×	`add-cube-cbrt` `*-un-lft-identity`
48×	`sqrt-prod`
28×	`prod-exp` `cbrt-unprod`
26×	`cbrt-undiv` `div-exp`
22×	`associate-r` `associate-l`
13×	`associate-/r*`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`pow1`
5×	`associate-*r/` `div-inv`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`frac-times` `associate-*l/`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 191

Calls

4 calls:

14.0ms	(/ a (sqrt b))
13.0ms	(/ c (sqrt b))
85.0ms	(/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2.0 a))
50.0ms	(* (/ a (sqrt b)) (/ c (sqrt b)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ a (sqrt b))
78.0ms	(/ c (sqrt b))
76.0ms	(/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2.0 a))
72.0ms	(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify2.4s

Counts

203 → 203

Iterations

Useful iterations: 2 (946.0ms)

Iter	Nodes	Cost
0	303	2968
1	853	2732
2	4043	2134
done	5000	2134

prune710.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 2.4b

regimes311.0ms

Accuracy

0% (3.5b remaining)

Error of 6.2b against oracle of 2.7b and baseline of 6.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	6	5
done	6	5

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.1s	16070×	pre	80	true
968.0ms	2964×	body	160	valid
967.0ms	3640×	body	320	valid
816.0ms	8070×	body	80	nan
152.0ms	482×	body	640	valid
108.0ms	914×	body	80	valid