Details

sample114.0ms

Algorithm

intervals

Results

31.0ms	275×	body	80	nan
21.0ms	145×	body	160	valid
17.0ms	531×	pre	80	true
11.0ms	48×	body	320	valid
5.0ms	63×	body	80	valid

simplify107.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	104
5	104
4	96
3	76
2	41
1	21
0	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize28.0ms

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))
36.9b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite577.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-cbrt-cube` `add-exp-log`
13×	`*-un-lft-identity`
9×	`pow1`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-r` `pow-prod-down` `sqrt-prod` `flip--` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `div-sub` `associate-l` `-commutative` `div-inv`

Counts

4 → 75

Calls

4 calls:

13.0ms	(- (* b b) (* (* 3.0 a) c))
27.0ms	(* (* 3.0 a) c)
103.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
431.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series433.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (* b b) (* (* 3.0 a) c))
36.0ms	(* (* 3.0 a) c)
157.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
153.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify2.0s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
2	2483
1	428
0	155

prune588.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.3b

localize5.0ms

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

prune88.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-cbrt-cube` `add-exp-log`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`times-frac` `associate-r`
5×	`pow1`
4×	`associate-/r*`
3×	`associate-l` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r/` `associate-/l`
1×	`pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

3 → 78

Calls

3 calls:

9.0ms	(/ (* a c) b)
16.0ms	(* -1.5 (/ (* a c) b))
24.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series83.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ (* a c) b)
34.0ms	(* -1.5 (/ (* a c) b))
26.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify1.7s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	2789
1	391
0	123

prune640.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-cbrt-cube` `add-exp-log`
42×	`times-frac`
29×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cube-cbrt`
21×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
9×	`associate-/r` `associate-/l`
8×	`div-inv`
7×	`associate-r`
6×	`pow1`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l`
2×	`associate-*r/` `associate-/l/`
1×	`pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

9.0ms	(/ (* a c) b)
18.0ms	(/ (/ (* -1.5 (/ (* a c) b)) 3.0) a)
21.0ms	(/ (* -1.5 (/ (* a c) b)) 3.0)
15.0ms	(* -1.5 (/ (* a c) b))

series149.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (* a c) b)
23.0ms	(/ (/ (* -1.5 (/ (* a c) b)) 3.0) a)
39.0ms	(/ (* -1.5 (/ (* a c) b)) 3.0)
50.0ms	(* -1.5 (/ (* a c) b))

simplify2.1s

Counts

138 → 138

Iterations

Iter	Nodes
done	5001
2	3211
1	528
0	192

prune748.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 5.2b

regimes1.0s

Accuracy

11.2% (6.6b remaining)

Error of 11.7b against oracle of 5.1b and baseline of 12.5b

bsearch4.0ms

Steps

Iters	Range		Point
0	1.1367127926867939e-06	1.150970403537976e-06	1.1438415981123848e-06

simplify6.0ms

Iterations

Iter	Nodes
done	23
1	23
0	19

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	16142×	pre	80	true
820.0ms	8142×	body	80	nan
774.0ms	4773×	body	160	valid
302.0ms	1339×	body	320	valid
164.0ms	1888×	body	80	valid