Details

sample49.0ms

Algorithm

intervals

Results

11.0ms	171×	body	160	valid
9.0ms	517×	pre	80	true
8.0ms	261×	body	80	nan
3.0ms	33×	body	320	valid
2.0ms	52×	body	80	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	75	16
4	87	16
5	95	16
done	95	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
38.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-log-exp`
9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-sub` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 73

Calls

4 calls:

2.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(* (* 3.0 a) c)
34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(* (* 3.0 a) c)
103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.0s

Counts

85 → 85

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	154	1437
1	417	1361
2	1615	1139
done	5001	1138

prune221.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

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

prune33.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b	(* -1.5 (/ (* a c) b))
0.3b	(/ (* 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×	`associate-l` `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 → 78

Calls

3 calls:

8.0ms	(* -1.5 (/ (* a c) b))
3.0ms	(/ (* a c) b)
9.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series70.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(* -1.5 (/ (* a c) b))
19.0ms	(/ (* a c) b)
24.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify995.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (191.0ms)

Iter	Nodes	Cost
0	123	1086
1	377	1045
2	1938	761
done	5000	761

prune161.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 5.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b	(* -1.5 (/ (* a c) b))
0.3b	(/ (* a c) b)
0.3b	(/ 1 (* 3.0 a))
0.3b	(* (* -1.5 (/ (* a c) b)) (/ 1 (* 3.0 a)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-exp-log`
77×	`add-cbrt-cube`
76×	`prod-exp`
38×	`div-exp`
34×	`cbrt-unprod`
20×	`cbrt-undiv`
15×	`add-sqr-sqrt`
14×	`pow1` `associate-r`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`rec-exp` `1-exp`
5×	`pow-prod-down`
4×	`associate-r/` `associate-l` `associate-/r` `div-inv` `associate-/l*` `add-log-exp`
2×	`pow-flip` `frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-*l/` `un-div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

8.0ms	(* -1.5 (/ (* a c) b))
5.0ms	(/ (* a c) b)
4.0ms	(/ 1 (* 3.0 a))
29.0ms	(* (* -1.5 (/ (* a c) b)) (/ 1 (* 3.0 a)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* -1.5 (/ (* a c) b))
18.0ms	(/ (* a c) b)
16.0ms	(/ 1 (* 3.0 a))
20.0ms	(* (* -1.5 (/ (* a c) b)) (/ 1 (* 3.0 a)))

simplify1.3s

Counts

150 → 150

Iterations

Useful iterations: 2 (292.0ms)

Iter	Nodes	Cost
0	184	1978
1	569	1720
2	2079	1272
done	5000	1272

prune168.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 5.5b

regimes320.0ms

Accuracy

8.7% (6.1b remaining)

Error of 11.3b against oracle of 5.2b and baseline of 11.9b

bsearch30.0ms

Steps

Iters	Range		Point
4	0.1123162942048503	0.21462860711519482	0.11411310699712364

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	40
1	26	40
done	26	40

end0.0ms

sample1.4s

Algorithm

intervals

Results

308.0ms	4861×	body	160	valid
306.0ms	16375×	pre	80	true
260.0ms	8375×	body	80	nan
130.0ms	1380×	body	320	valid
60.0ms	1759×	body	80	valid