Details

sample100.0ms

Algorithm

intervals

Results

17.0ms	33×	body	2560	valid
16.0ms	13×	body	640	valid
15.0ms	181×	body	80	valid
11.0ms	27×	body	1280	valid
8.0ms	92×	body	80	nan
3.0ms	4×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify108.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	79	16
4	99	16
5	107	16
done	107	16

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite599.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

144.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
428.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
68.0ms	(- (* b b) (* (* 4.0 a) c))
115.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: 2 (322.0ms)

Iter	Nodes	Cost
0	154	1592
1	405	1496
2	1789	1332
done	5001	1332

prune388.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
0.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

94.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
11.0ms	(- (* b b) (* (* 4.0 a) c))
90.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
51.0ms	(- (* b b) (* (* 4.0 a) c))
92.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify807.0ms

Counts

96 → 96

Iterations

Useful iterations: done (799.0ms)

Iter	Nodes	Cost
0	158	1888
1	396	1782
2	1638	1660
done	5000	1652

prune363.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

77.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
46.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
70.0ms	(- (* b b) (* (* 4.0 a) c))
111.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

174 → 174

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	262	4494
1	653	3983
2	3566	3831
done	5000	3829

prune465.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
493×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
320×	`add-cube-cbrt`
86×	`difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/r*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 423

Calls

4 calls:

85.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
17.0ms	(- (* b b) (* (* 4.0 a) c))
70.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
59.0ms	(- (* b b) (* (* 4.0 a) c))
91.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

435 → 435

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	591	15877
1	2039	13192
done	5001	12421

prune488.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

regimes258.0ms

Accuracy

84.8% (4.3b remaining)

Error of 9.9b against oracle of 5.5b and baseline of 34.0b

bsearch122.0ms

Steps

Iters	Range		Point
7	1.2976235572645919e-73	6.718394677208045e-72	1.2205790981451807e-72
8	-3.0433044982512647e+105	-1.1000082512799256e+103	-1.706986096130974e+105

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	52
1	42	52
done	42	52

end0.0ms

sample2.3s

Algorithm

intervals

Results

512.0ms	1092×	body	2560	valid
474.0ms	3047×	body	80	nan
356.0ms	5893×	body	80	valid
335.0ms	848×	body	1280	valid
89.0ms	463×	body	640	valid
67.0ms	96×	body	5120	valid
39.0ms	105×	body	160	valid
33.0ms	235×	body	320	valid