Details

sample134.0ms

Algorithm

intervals

Results

43.0ms	540×	pre	80	true
30.0ms	149×	body	160	valid
28.0ms	284×	body	80	nan
11.0ms	107×	body	80	valid

simplify99.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* c a) 4)))
0.3b	(- (* b b) (* (* c a) 4))
0.3b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
29.3b	(- (sqrt (- (* b b) (* (* c a) 4))) b)

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

13.0ms	(sqrt (- (* b b) (* (* c a) 4)))
13.0ms	(- (* b b) (* (* c a) 4))
90.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
35.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)

series434.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (- (* b b) (* (* c a) 4)))
67.0ms	(- (* b b) (* (* c a) 4))
139.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
129.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	2005
3	2005
2	1103
1	400
0	161

prune1000.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.3b

localize11.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune59.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* -2 (/ (* a c) b)) a)
0.2b	(/ (* a c) b)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-cbrt-cube` `add-exp-log`
8×	`cbrt-undiv` `div-exp`
6×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `times-frac` `add-cube-cbrt`
5×	`prod-exp` `cbrt-unprod`
2×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 49

Calls

2 calls:

14.0ms	(/ (* -2 (/ (* a c) b)) a)
8.0ms	(/ (* a c) b)

series68.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (* -2 (/ (* a c) b)) a)
33.0ms	(/ (* a c) b)

simplify1.1s

Counts

55 → 55

Iterations

Iter	Nodes
done	2083
3	2083
2	1429
1	278
0	99

prune485.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 8.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* a c) b)
0.4b	(* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b))
0.5b	(* (/ (* a c) b) (/ (* a c) b))
0.6b	(cbrt (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

216×	`add-cbrt-cube` `add-exp-log`
101×	`prod-exp` `cbrt-unprod`
70×	`cbrt-undiv` `div-exp`
30×	`pow1`
19×	`add-sqr-sqrt`
18×	`times-frac`
16×	`*-un-lft-identity` `add-cube-cbrt`
14×	`associate-r`
11×	`frac-times` `associate-*l/`
8×	`associate-l`
7×	`cbrt-div` `pow-plus` `swap-sqr` `associate-*r/` `pow-prod-up`
6×	`div-inv`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`pow2` `associate-/r*` `pow-sqr`
2×	`pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `clear-num` `frac-2neg` `pow1/3` `rem-cbrt-cube` `associate-/l*`

Counts

4 → 193

Calls

4 calls:

8.0ms	(/ (* a c) b)
101.0ms	(* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b))
42.0ms	(* (/ (* a c) b) (/ (* a c) b))
120.0ms	(cbrt (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (* a c) b)
118.0ms	(* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b))
60.0ms	(* (/ (* a c) b) (/ (* a c) b))
49.0ms	(cbrt (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b)))

simplify1.1s

Counts

205 → 205

Iterations

Iter	Nodes
done	2000
2	2000
1	692
0	216

prune2.2s

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 8.2b

regimes730.0ms

Accuracy

45.1% (7.6b remaining)

Error of 16.5b against oracle of 8.9b and baseline of 22.7b

bsearch3.0ms

Steps

Iters	Range		Point
0	2862.7645223887616	2921.618168739223	2892.1913455639924

simplify4.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample5.2s

Algorithm

intervals

Results

1.4s	4500×	body	160	valid
1.2s	8403×	body	80	nan
1.2s	16403×	pre	80	true
989.0ms	3500×	body	80	valid