Details

sample97.0ms

Algorithm

intervals

Results

32.0ms	188×	body	80	valid
21.0ms	39×	body	2560	valid
14.0ms	31×	body	1280	valid
8.0ms	87×	body	80	nan
5.0ms	13×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify67.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
5	102
4	94
3	75
2	45
1	24
0	14

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) 2) a)
0.4b	(- (* b b) (* (* 4 a) c))
0.4b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite125.0ms

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`
4×	`insert-posit16`
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 → 153

Calls

4 calls:

60.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) 2) a)
7.0ms	(- (* b b) (* (* 4 a) c))
47.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) 2) a)
55.0ms	(- (* b b) (* (* 4 a) c))
116.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
81.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts

165 → 165

Iterations

Iter	Nodes
done	5007
2	2253
1	668
0	279

prune861.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize67.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.4b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite105.0ms

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` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

46.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
40.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
117.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
92.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
88.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5008
3	2360
2	623
1	194
0	82

prune520.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4 a) c))
0.4b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.0b	(/ 1 (sqrt 2))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`add-exp-log` `add-log-exp`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube`
4×	`insert-posit16`
3×	`flip3--` `pow-flip` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-exp` `difference-of-squares`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 91

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4 a) c))
38.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
10.0ms	(/ 1 (sqrt 2))
15.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series277.0ms

Counts

4 → 10

Calls

4 calls:

65.0ms	(- (* b b) (* (* 4 a) c))
113.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.0ms	(/ 1 (sqrt 2))
99.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.8s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
3	2912
2	906
1	328
0	157

prune445.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4 a) c))
0.4b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.0b	(/ 1/2 (sqrt 2))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`add-log-exp`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`insert-posit16`
3×	`flip3--` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv` `distribute-lft-out--`

Counts

4 → 85

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4 a) c))
36.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
4.0ms	(/ 1/2 (sqrt 2))
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series280.0ms

Counts

4 → 10

Calls

4 calls:

56.0ms	(- (* b b) (* (* 4 a) c))
120.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.0ms	(/ 1/2 (sqrt 2))
103.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.5s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
3	3566
2	967
1	340
0	160

prune544.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.3b

regimes358.0ms

Accuracy

83.4% (4.6b remaining)

Error of 10.5b against oracle of 5.8b and baseline of 33.7b

bsearch214.0ms

Steps

Iters	Range		Point
8	1.287554927770862e-68	8.304725640954512e-66	4.5810084990875205e-68
8	-3.370135567630554e+133	-1.481129451033522e+129	-2.1144981103869975e+131

simplify11.0ms

Iterations

Iter	Nodes
done	32
1	32
0	29

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.6s	1064×	body	2560	valid
940.0ms	5890×	body	80	valid
772.0ms	447×	body	640	valid
731.0ms	901×	body	1280	valid
488.0ms	2854×	body	80	nan
104.0ms	95×	body	5120	valid
85.0ms	207×	body	320	valid
37.0ms	133×	body	160	valid