Details

sample187.0ms

Algorithm

intervals

Results

19.0ms	184×	body	80	valid
15.0ms	26×	body	2560	valid
12.0ms	27×	body	1280	valid
8.0ms	22×	body	640	valid
6.0ms	69×	body	80	nan
3.0ms	4×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
4	44
3	41
2	32
1	18
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 95

Calls

4 calls:

48.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
87.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

107 → 107

Iterations

Iter	Nodes
done	5008
3	3746
2	1049
1	388
0	162

prune489.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.0b

localize63.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 61

Calls

4 calls:

15.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
4	4845
3	1344
2	414
1	148
0	60

prune548.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16`
3×	`cbrt-prod` `flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `pow1/3` `neg-log`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt a)
36.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(cbrt a)
100.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
46.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	2268
2	725
1	267
0	119

prune379.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 4.0b

localize92.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 61

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b_2 b_2) (* a c))
102.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
4	4845
3	1344
2	414
1	148
0	60

prune437.0ms

Pruning

15 alts after pruning (11 fresh and 4 done)

Merged error: 4.0b

regimes629.0ms

Accuracy

81.5% (5.2b remaining)

Error of 10.8b against oracle of 5.6b and baseline of 33.6b

bsearch132.0ms

Steps

Iters	Range		Point
6	4.8498614244770303e+48	2.0602804194761557e+49	2.0410715251838527e+49
10	-2.8993282234165347e-22	-3.09682517328325e-32	-3.136683434005781e-32

simplify8.0ms

Iterations

Iter	Nodes
done	29
1	29
0	25

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.0s	5778×	body	80	valid
672.0ms	1100×	body	2560	valid
590.0ms	474×	body	640	valid
373.0ms	921×	body	1280	valid
235.0ms	2930×	body	80	nan
76.0ms	226×	body	320	valid
55.0ms	98×	body	5120	valid
46.0ms	115×	body	160	valid