Details

sample214.0ms

Algorithm

intervals

Results

25.0ms	210×	body	80	valid
19.0ms	23×	body	2560	valid
14.0ms	25×	body	1280	valid
9.0ms	84×	body	80	nan
4.0ms	9×	body	320	valid
3.0ms	8×	body	640	valid
2.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify55.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
5	34
4	32
3	30
2	23
1	15
0	10

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize19.0ms

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)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 122

Calls

4 calls:

88.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
46.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
90.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
51.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.0s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
3	4672
2	1291
1	494
0	199

prune635.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize38.0ms

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)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 121

Calls

4 calls:

41.0ms	(/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
50.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
100.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
48.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
3	4081
2	1236
1	450
0	194

prune625.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.5b

localize40.0ms

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)))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 123

Calls

4 calls:

132.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
60.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
3	4844
2	1510
1	560
0	219

prune631.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.5b

localize25.0ms

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)))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 122

Calls

4 calls:

96.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
93.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
44.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.0s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
3	4672
2	1291
1	494
0	199

prune528.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.5b

regimes415.0ms

Accuracy

81.2% (5.1b remaining)

Error of 10.8b against oracle of 5.6b and baseline of 33.0b

bsearch294.0ms

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

simplify18.0ms

Iterations

Iter	Nodes
done	42
3	42
2	39
1	36
0	30

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.3s	1083×	body	2560	valid
1.3s	5866×	body	80	valid
631.0ms	910×	body	1280	valid
395.0ms	3005×	body	80	nan
191.0ms	446×	body	640	valid
84.0ms	103×	body	5120	valid
80.0ms	240×	body	320	valid
20.0ms	100×	body	160	valid