Details

sample61.0ms

Algorithm

intervals

Results

34.0ms	281×	body	80	valid
11.0ms	87×	body	80	nan

simplify160.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	169
6	169
5	167
4	155
3	121
2	67
1	36
0	20

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize113.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (fma a (* -4 c) (* b b))) b)
1.0b	(- (- b) (sqrt (fma a (* -4 c) (* b b))))
23.1b	(sqrt (fma a (* -4 c) (* b b)))
23.1b	(sqrt (fma a (* -4 c) (* b b)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 165

Calls

4 calls:

7.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
10.0ms	(- (- b) (sqrt (fma a (* -4 c) (* b b))))
1.0ms	(sqrt (fma a (* -4 c) (* b b)))
3.0ms	(sqrt (fma a (* -4 c) (* b b)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
113.0ms	(- (- b) (sqrt (fma a (* -4 c) (* b b))))
121.0ms	(sqrt (fma a (* -4 c) (* b b)))
123.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify2.5s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
3	3384
2	1054
1	432
0	195

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.4b

localize158.0ms

Local error

Found 4 expressions with local error:

22.8b	(fma (sqrt (sqrt (fma a (* -4 c) (* b b)))) (sqrt (sqrt (fma a (* -4 c) (* b b)))) (- b))
23.1b	(sqrt (fma a (* -4 c) (* b b)))
23.1b	(sqrt (fma a (* -4 c) (* b b)))
23.1b	(sqrt (fma a (* -4 c) (* b b)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (sqrt (sqrt (fma a (* -4 c) (* b b)))) (sqrt (sqrt (fma a (* -4 c) (* b b)))) (- b))
1.0ms	(sqrt (fma a (* -4 c) (* b b)))
1.0ms	(sqrt (fma a (* -4 c) (* b b)))
1.0ms	(sqrt (fma a (* -4 c) (* b b)))

series746.0ms

Counts

4 → 12

Calls

4 calls:

425.0ms	(fma (sqrt (sqrt (fma a (* -4 c) (* b b)))) (sqrt (sqrt (fma a (* -4 c) (* b b)))) (- b))
85.0ms	(sqrt (fma a (* -4 c) (* b b)))
120.0ms	(sqrt (fma a (* -4 c) (* b b)))
115.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify2.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5005
4	2900
3	739
2	235
1	112
0	65

prune633.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.0b

localize188.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

1.0ms	(sqrt (fma a (* -4 c) (* b b)))
1.0ms	(sqrt (fma a (* -4 c) (* b b)))
1.0ms	(sqrt (fma a (* -4 c) (* b b)))
1.0ms	(sqrt (fma a (* -4 c) (* b b)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(sqrt (fma a (* -4 c) (* b b)))
106.0ms	(sqrt (fma a (* -4 c) (* b b)))
121.0ms	(sqrt (fma a (* -4 c) (* b b)))
123.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify3.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
9	1385
8	477
7	278
6	217
5	183
4	146
3	90
2	53
1	38
0	28

prune754.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.0b

localize222.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma a (* -4 c) (* b b)))
23.9b	(cbrt (fma a (* -4 c) (* b b)))
23.9b	(cbrt (fma a (* -4 c) (* b b)))
23.9b	(cbrt (fma a (* -4 c) (* b b)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

2.0ms	(sqrt (fma a (* -4 c) (* b b)))
1.0ms	(cbrt (fma a (* -4 c) (* b b)))
1.0ms	(cbrt (fma a (* -4 c) (* b b)))
1.0ms	(cbrt (fma a (* -4 c) (* b b)))

series896.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (fma a (* -4 c) (* b b)))
291.0ms	(cbrt (fma a (* -4 c) (* b b)))
229.0ms	(cbrt (fma a (* -4 c) (* b b)))
277.0ms	(cbrt (fma a (* -4 c) (* b b)))

simplify2.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	5006
4	3944
3	903
2	287
1	124
0	68

prune830.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 12.0b

regimes385.0ms

Accuracy

87% (1.0b remaining)

Error of 13.4b against oracle of 12.4b and baseline of 20.0b

bsearch172.0ms

Steps

Iters	Range		Point
10	6.2301214455520334e+75	1.5034565205168897e+88	1.3914912380743042e+88

simplify9.0ms

Iterations

Iter	Nodes
done	31
1	31
0	29

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.7s	8737×	body	80	valid
484.0ms	2854×	body	80	nan