Details

sample73.0ms

Algorithm

intervals

Results

39.0ms	285×	body	80	valid
10.0ms	85×	body	80	nan

simplify208.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	170
7	170
6	168
5	164
4	157
3	132
2	76
1	39
0	20

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize138.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (fma c (* a -4) (* b b))))
1.6b	(- (sqrt (fma c (* a -4) (* b b))) b)
22.0b	(sqrt (fma c (* a -4) (* b b)))
22.0b	(sqrt (fma c (* a -4) (* b b)))

rewrite56.0ms

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:

20.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
12.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
3.0ms	(sqrt (fma c (* a -4) (* b b)))
16.0ms	(sqrt (fma c (* a -4) (* b b)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
117.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
118.0ms	(sqrt (fma c (* a -4) (* b b)))
119.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify2.4s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
3	3147
2	965
1	427
0	194

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.1b

localize152.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (fma c (* a -4) (* b b))) b)
22.0b	(sqrt (fma c (* a -4) (* b b)))
22.0b	(sqrt (fma c (* a -4) (* b b)))
22.0b	(sqrt (fma c (* a -4) (* b b)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`sqrt-prod`
21×	`add-cube-cbrt`
18×	`prod-diff`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

22.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
3.0ms	(sqrt (fma c (* a -4) (* b b)))
3.0ms	(sqrt (fma c (* a -4) (* b b)))
4.0ms	(sqrt (fma c (* a -4) (* b b)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
91.0ms	(sqrt (fma c (* a -4) (* b b)))
112.0ms	(sqrt (fma c (* a -4) (* b b)))
98.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify3.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
4	2425
3	908
2	311
1	168
0	85

prune991.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.1b

localize256.0ms

Local error

Found 4 expressions with local error:

22.0b	(sqrt (fma c (* a -4) (* b b)))
22.7b	(cbrt (fma c (* a -4) (* b b)))
22.7b	(cbrt (fma c (* a -4) (* b b)))
22.7b	(cbrt (fma c (* a -4) (* b b)))

rewrite9.0ms

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:

3.0ms	(sqrt (fma c (* a -4) (* b b)))
2.0ms	(cbrt (fma c (* a -4) (* b b)))
2.0ms	(cbrt (fma c (* a -4) (* b b)))
2.0ms	(cbrt (fma c (* a -4) (* b b)))

series912.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(sqrt (fma c (* a -4) (* b b)))
248.0ms	(cbrt (fma c (* a -4) (* b b)))
252.0ms	(cbrt (fma c (* a -4) (* b b)))
296.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify2.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	5019
4	3363
3	861
2	279
1	124
0	68

prune893.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.1b

localize210.0ms

Local error

Found 4 expressions with local error:

22.7b	(cbrt (fma c (* a -4) (* b b)))
22.7b	(cbrt (fma c (* a -4) (* b b)))
22.7b	(cbrt (fma c (* a -4) (* b b)))
22.7b	(cbrt (fma c (* a -4) (* b b)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt (fma c (* a -4) (* b b)))
290.0ms	(cbrt (fma c (* a -4) (* b b)))
272.0ms	(cbrt (fma c (* a -4) (* b b)))
253.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify2.2s

Counts

68 → 68

Iterations

Iter	Nodes
done	5014
4	2944
3	789
2	254
1	105
0	53

prune900.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.1b

regimes388.0ms

Accuracy

83.6% (1.2b remaining)

Error of 13.8b against oracle of 12.6b and baseline of 19.7b

bsearch203.0ms

Steps

Iters	Range		Point
10	24130438545.104744	1.5803814198611752e+21	1.5596668453223772e+21

simplify24.0ms

Iterations

Iter	Nodes
done	50
1	50
0	42

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.6s	8738×	body	80	valid
381.0ms	2975×	body	80	nan