Details

sample95.0ms

Algorithm

intervals

Results

32.0ms	153×	body	160	valid
14.0ms	506×	pre	80	true
12.0ms	250×	body	80	nan
5.0ms	35×	body	320	valid
4.0ms	68×	body	80	valid

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	83	16
4	112	16
5	120	16
done	120	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
37.7b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite275.0ms

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:

19.0ms	(- (* b b) (* (* 3.0 a) c))
41.0ms	(* (* 3.0 a) c)
147.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
62.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series374.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b b) (* (* 3.0 a) c))
36.0ms	(* (* 3.0 a) c)
165.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
93.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify2.5s

Counts

121 → 121

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	201	2338
1	544	2075
2	3120	1752
done	5001	1750

prune449.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.1b

localize5.0ms

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

prune73.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.1b

localize9.0ms

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))

rewrite78.0ms

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:

27.0ms	(* -1.5 (/ (* a c) b))
21.0ms	(/ (* a c) b)
26.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series97.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* -1.5 (/ (* a c) b))
26.0ms	(/ (* a c) b)
33.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify1.5s

Counts

93 → 93

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	129	1138
1	401	1097
2	2854	869
done	5001	853

prune358.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*` `div-inv`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 73

Calls

2 calls:

26.0ms	(/ (/ (* a c) b) a)
11.0ms	(/ (* a c) b)

series59.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(/ (/ (* a c) b) a)
42.0ms	(/ (* a c) b)

simplify1.1s

Counts

79 → 79

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	121	831
1	310	794
2	1619	722
done	5001	712

prune337.0ms

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 6.0b

regimes770.0ms

Accuracy

12.3% (6.0b remaining)

Error of 11.2b against oracle of 5.1b and baseline of 12.0b

bsearch3.0ms

Steps

Iters	Range		Point
0	0.0031282979026107443	0.0031669466915584974	0.003147622297084621

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	38
1	24	38
done	24	38

end0.0ms

sample4.1s

Algorithm

intervals

Results

843.0ms	4896×	body	160	valid
817.0ms	1320×	body	320	valid
783.0ms	8179×	body	80	nan
714.0ms	16179×	pre	80	true
123.0ms	1784×	body	80	valid