Details

sample147.0ms

Algorithm

intervals

Results

47.0ms	508×	pre	80	true
26.0ms	143×	body	160	valid
21.0ms	252×	body	80	nan
10.0ms	113×	body	80	valid

simplify113.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(- (* b b) (* (* 3.0 a) c))
0.4b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
28.5b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite333.0ms

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:

38.0ms	(* (* 3.0 a) c)
17.0ms	(- (* b b) (* (* 3.0 a) c))
171.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
100.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series365.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (* 3.0 a) c)
50.0ms	(- (* b b) (* (* 3.0 a) c))
164.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
124.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.9s

Counts

121 → 121

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	201	2338
1	495	2065
2	1674	1747
done	5000	1676

prune396.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.8b

localize6.0ms

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

prune51.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (* a c) b)
0.3b	(* -1.5 (/ (* a c) b))
0.4b	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

rewrite94.0ms

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:

20.0ms	(/ (* a c) b)
28.0ms	(* -1.5 (/ (* a c) b))
42.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series106.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ (* a c) b)
53.0ms	(* -1.5 (/ (* a c) b))
30.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify992.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (366.0ms)

Iter	Nodes	Cost
0	129	1138
1	353	1097
2	1740	813
done	5000	813

prune303.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 8.7b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ -1.5 (/ (* 3.0 a) (/ (* a c) b)))
0.3b	(/ (* a c) b)
0.4b	(/ (* 3.0 a) (/ (* a c) b))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
58×	`add-exp-log` `add-cbrt-cube`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
29×	`cbrt-undiv` `div-exp`
22×	`associate-/r*`
13×	`div-inv`
11×	`prod-exp` `cbrt-unprod`
6×	`associate-/r/`
5×	`associate-/l*`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`

Counts

3 → 141

Calls

3 calls:

16.0ms	(/ -1.5 (/ (* 3.0 a) (/ (* a c) b)))
14.0ms	(/ (* a c) b)
31.0ms	(/ (* 3.0 a) (/ (* a c) b))

series120.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ -1.5 (/ (* 3.0 a) (/ (* a c) b)))
36.0ms	(/ (* a c) b)
39.0ms	(/ (* 3.0 a) (/ (* a c) b))

simplify1.4s

Counts

150 → 150

Iterations

Useful iterations: 2 (523.0ms)

Iter	Nodes	Cost
0	229	2237
1	549	2149
2	2326	1475
done	5000	1475

prune363.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 8.7b

regimes900.0ms

Accuracy

46% (7.4b remaining)

Error of 16.3b against oracle of 8.9b and baseline of 22.6b

bsearch35.0ms

Steps

Iters	Range		Point
2	1430.9534847553177	1659.0567802753424	1459.4663966953208

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	38
1	28	38
done	28	38

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	4482×	body	160	valid
739.0ms	16601×	pre	80	true
675.0ms	8601×	body	80	nan
352.0ms	3518×	body	80	valid