Details

sample210.0ms

Algorithm

intervals

Results

79.0ms	210×	body	80	valid
22.0ms	23×	body	2560	valid
17.0ms	25×	body	1280	valid
10.0ms	84×	body	80	nan
4.0ms	8×	body	640	valid
4.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify49.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	29
5	29
4	27
3	25
2	22
1	14
0	10

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize469.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
20.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite184.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

86.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
62.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
126.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
67.0ms	(- (* b_2 b_2) (* a c))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	4048
2	1029
1	379
0	158

prune508.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.8b	(- (* b_2 b_2) (* a c))
6.5b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
20.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

15.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
8.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
48.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

109 → 109

Iterations

Iter	Nodes
done	5007
3	3339
2	1033
1	401
0	179

prune561.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* c a))) a)
0.8b	(- (* b_2 b_2) (* c a))
6.5b	(- (/ (sqrt (- (* b_2 b_2) (* c a))) a) (/ b_2 a))
20.8b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

13.0ms	(/ (sqrt (- (* b_2 b_2) (* c a))) a)
9.0ms	(- (* b_2 b_2) (* c a))
74.0ms	(- (/ (sqrt (- (* b_2 b_2) (* c a))) a) (/ b_2 a))
15.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (sqrt (- (* b_2 b_2) (* c a))) a)
44.0ms	(- (* b_2 b_2) (* c a))
115.0ms	(- (/ (sqrt (- (* b_2 b_2) (* c a))) a) (/ b_2 a))
85.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify2.6s

Counts

109 → 109

Iterations

Iter	Nodes
done	5006
3	3268
2	1031
1	402
0	180

prune517.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
0.8b	(- (* b_2 b_2) (* a c))
9.5b	(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
20.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

173×	`times-frac`
132×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
82×	`add-cube-cbrt`
43×	`sqrt-prod`
24×	`associate-/r*`
15×	`add-exp-log`
14×	`difference-of-squares`
10×	`sqrt-div`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1` `div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/l*` `distribute-lft-out--`
2×	`rec-exp` `sub-neg` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `frac-sub` `pow-flip` `inv-pow`

Counts

4 → 181

Calls

4 calls:

17.0ms	(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(- (* b_2 b_2) (* a c))
109.0ms	(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
59.0ms	(- (* b_2 b_2) (* a c))
153.0ms	(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

193 → 193

Iterations

Iter	Nodes
done	5004
2	1945
1	728
0	292

prune733.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.5b

regimes358.0ms

Accuracy

81.5% (5.1b remaining)

Error of 10.8b against oracle of 5.7b and baseline of 33.4b

bsearch339.0ms

Steps

Iters	Range		Point
8	5.451909898538592e-70	5.081728108716245e-67	1.546013236023957e-67
7	6.366271362828677e-80	2.0474353944207673e-78	1.6168702840263923e-79
8	1.9015403840268286e-125	4.787339246176752e-121	1.3353078790738604e-121
7	-9.460060253608456e+39	-2.573022393154551e+38	-9.348931433494438e+39

simplify7.0ms

Iterations

Iter	Nodes
done	44
1	44
0	36

end0.0ms

sample3.9s

Algorithm

intervals

Results

842.0ms	1083×	body	2560	valid
830.0ms	5866×	body	80	valid
686.0ms	446×	body	640	valid
607.0ms	910×	body	1280	valid
327.0ms	3005×	body	80	nan
136.0ms	240×	body	320	valid
85.0ms	103×	body	5120	valid
21.0ms	100×	body	160	valid