Details

sample72.0ms

Algorithm

intervals

Results

32.0ms	281×	body	80	valid
8.0ms	83×	body	80	nan

simplify249.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	20	38
1	39	38
2	79	37
3	142	37
4	171	37
5	181	37
6	185	37
done	185	37

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize139.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 140

Calls

4 calls:

10.0ms	(- (* b b) (* (* 4.0 a) c))
38.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b b) (* (* 4.0 a) c))
129.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.1s

Counts

152 → 152

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	181	6137
1	404	4128
2	1147	3279
3	4842	2634
done	5000	2634

prune817.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

localize159.0ms

Local error

Found 4 expressions with local error:

12.6b	(- (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
19.7b	(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b	(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `flip3--` `sqrt-div` `diff-log` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 84

Calls

4 calls:

29.0ms	(- (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
2.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
3.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
134.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
119.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
90.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts

96 → 96

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	131	2491
1	300	1521
2	878	1464
3	3363	1428
done	5000	1425

prune641.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

localize157.0ms

Local error

Found 4 expressions with local error:

7.8b	(+ (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
19.7b	(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b	(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2`
2×	`sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3--` `flip3-+` `neg-log` `flip--` `flip-+`

Counts

4 → 72

Calls

4 calls:

28.0ms	(+ (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
2.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
2.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(+ (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
107.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
116.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
119.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts

84 → 84

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	106	1400
1	265	967
2	868	909
3	3099	897
done	5000	895

prune683.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

localize159.0ms

Local error

Found 4 expressions with local error:

19.7b	(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b	(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b	(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-div`
1×	`flip3--` `flip--`

Counts

4 → 62

Calls

4 calls:

2.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
7.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
2.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
110.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
128.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts

74 → 74

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	70	1006
1	157	888
2	466	839
3	1745	839
done	5000	835

prune655.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.6b

regimes243.0ms

Accuracy

88.8% (1.4b remaining)

Error of 9.1b against oracle of 7.7b and baseline of 20.0b

bsearch187.0ms

Steps

Iters	Range		Point
4	9.936283634246925e+77	1.8488019868481542e+78	1.822077811116171e+78
7	-2.95797388004145e+163	-3.6321213431321147e+161	-3.688468976067863e+161

simplify20.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	45	131
1	58	131
2	66	131
done	66	131

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	8776×	body	80	valid
726.0ms	3009×	body	80	nan