Details

sample782.0ms

Algorithm

intervals

Results

33.0ms	210×	body	80	valid
24.0ms	23×	body	2560	valid
19.0ms	25×	body	1280	valid
12.0ms	84×	body	80	nan
5.0ms	8×	body	640	valid
4.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	2×	body	160	valid

simplify83.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize40.0ms

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)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
30×	`difference-of-squares`
22×	`sqrt-prod`
18×	`times-frac`
16×	`add-cube-cbrt`
14×	`unswap-sqr`
13×	`distribute-lft-out--`
8×	`associate-l` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1`
4×	`flip3--` `swap-sqr` `*-commutative` `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 → 116

Calls

4 calls:

637.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
386.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
77.0ms	(- (* b_2 b_2) (* a c))
129.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
92.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
44.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1252
1	445
0	187

prune608.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
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)))

rewrite794.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

308.0ms	(/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
371.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
51.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
98.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
66.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
3	4900
2	1273
1	400
0	182

prune640.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 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)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
24×	`difference-of-squares`
19×	`add-cube-cbrt` `sqrt-prod`
18×	`frac-times`
17×	`unswap-sqr`
14×	`associate-l`
13×	`flip3--` `associate-r` `add-exp-log` `flip--`
11×	`times-frac`
10×	`associate-/l*` `distribute-lft-out--`
9×	`associate-/r` `add-cbrt-cube` `associate-r/`
8×	`add-log-exp`
7×	`pow1`
5×	`*-commutative`
4×	`clear-num` `swap-sqr` `prod-exp` `insert-posit16`
3×	`frac-2neg` `un-div-inv`
2×	`sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `div-inv`

Counts

4 → 143

Calls

4 calls:

1.2s	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
356.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
45.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
99.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
54.0ms	(- (* b_2 b_2) (* a c))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

155 → 155

Iterations

Iter	Nodes
done	5003
2	1954
1	616
0	239

prune676.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
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)))

rewrite954.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

378.0ms	(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
446.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
101.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
40.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

131 → 131

Iterations

Iter	Nodes
done	5002
2	1333
1	411
0	183

prune516.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.5b

regimes425.0ms

Accuracy

80.9% (5.3b remaining)

Error of 10.8b against oracle of 5.6b and baseline of 33.1b

bsearch331.0ms

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

simplify23.0ms

Iterations

Iter	Nodes
done	48
3	48
2	45
1	42
0	32

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.2s	5866×	body	80	valid
931.0ms	1083×	body	2560	valid
651.0ms	910×	body	1280	valid
425.0ms	3005×	body	80	nan
276.0ms	446×	body	640	valid
141.0ms	103×	body	5120	valid
79.0ms	240×	body	320	valid
25.0ms	100×	body	160	valid