Details

sample77.0ms

Algorithm

intervals

Results

17.0ms	43×	body	2560	valid
12.0ms	155×	body	80	valid
9.0ms	26×	body	1280	valid
6.0ms	94×	body	80	nan
6.0ms	19×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	12×	body	320	valid
1.0ms	6×	body	160	valid

simplify128.0ms

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize40.0ms

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))
1.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `associate-/r*` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

75.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
12.0ms	(- (* b b) (* (* 4.0 a) c))
50.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
59.0ms	(- (* b b) (* (* 4.0 a) c))
147.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

161 → 161

Iterations

Iter	Nodes
done	5001
2	3078
1	690
0	280

prune947.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

localize6.0ms

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

prune50.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

localize71.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

38.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
58.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
113.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	4453
2	792
1	199
0	81

prune545.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
12.2b	(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`
1×	`difference-of-squares`

Counts

4 → 55

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* b b) (* (* 4.0 a) c))
107.0ms	(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	1114
1	243
0	94

prune519.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.3b

regimes489.0ms

Accuracy

86% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 39.0b

bsearch219.0ms

Steps

Iters	Range		Point
12	2.4919208328047006e-151	1.0529347607547997e-106	6.484072051994264e-107
8	-6.412561728939963e+28	-6.810701174428621e+25	-6.336287344206649e+28

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	26

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	5735×	body	80	valid
654.0ms	1104×	body	2560	valid
505.0ms	957×	body	1280	valid
279.0ms	2942×	body	80	nan
147.0ms	461×	body	640	valid
74.0ms	106×	body	5120	valid
52.0ms	226×	body	320	valid
18.0ms	119×	body	160	valid