Details

sample54.0ms

Algorithm

intervals

Results

12.0ms	168×	body	160	valid
10.0ms	517×	pre	80	true
9.0ms	261×	body	80	nan
3.0ms	34×	body	320	valid
2.0ms	54×	body	80	valid

simplify58.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	105	16
5	113	16
done	113	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
38.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
19×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 183

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
40.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
24.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series320.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms	(- (* b b) (* (* 4.0 a) c))
118.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
80.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.0s

Counts

195 → 195

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	321	4967
1	759	4592
2	2196	4283
done	5000	4264

prune520.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.5b

localize4.0ms

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

prune55.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.3b	(/ (* a c) b)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 77

Calls

2 calls:

14.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
3.0ms	(/ (* a c) b)

series41.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
20.0ms	(/ (* a c) b)

simplify865.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (206.0ms)

Iter	Nodes	Cost
0	171	1200
1	444	1154
2	1838	992
done	5000	992

prune232.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (/ (* -2.0 (* (* a c) (/ 1 b))) 2.0) a)
0.3b	(* (* a c) (/ 1 b))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
47×	`add-cbrt-cube`
42×	`times-frac`
33×	`prod-exp`
29×	`div-exp`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`cbrt-undiv` `cbrt-unprod`
13×	`associate-r`
7×	`pow1` `associate-/l*`
6×	`div-inv`
4×	`rec-exp` `1-exp`
3×	`pow-prod-down` `associate-/r*`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`frac-2neg` `associate-r/` `associate-l` `clear-num` `un-div-inv` `-commutative` `associate-/l/`

Counts

2 → 102

Calls

2 calls:

27.0ms	(/ (/ (* -2.0 (* (* a c) (/ 1 b))) 2.0) a)
12.0ms	(* (* a c) (/ 1 b))

series46.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(/ (/ (* -2.0 (* (* a c) (/ 1 b))) 2.0) a)
24.0ms	(* (* a c) (/ 1 b))

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: 2 (510.0ms)

Iter	Nodes	Cost
0	230	1768
1	669	1459
2	2709	1179
done	5001	1179

prune167.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 5.4b

regimes344.0ms

Accuracy

8.5% (6.2b remaining)

Error of 11.3b against oracle of 5.1b and baseline of 11.9b

bsearch37.0ms

Steps

Iters	Range		Point
4	0.1123162942048503	0.21462860711519482	0.11411310699712364

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	38
1	26	38
done	26	38

end0.0ms

sample1.5s

Algorithm

intervals

Results

340.0ms	4871×	body	160	valid
313.0ms	16451×	pre	80	true
282.0ms	8451×	body	80	nan
147.0ms	1368×	body	320	valid
65.0ms	1761×	body	80	valid