Details

sample500.0ms

Algorithm

intervals

Results

420.0ms	69×	body	80	nan
54.0ms	274×	body	80	valid

simplify203.0ms

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize160.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (fma c (* a -4) (* b b))))
1.0b	(- (sqrt (fma c (* a -4) (* b b))) b)
19.8b	(sqrt (fma c (* a -4) (* b b)))
19.8b	(sqrt (fma c (* a -4) (* b b)))

rewrite35.0ms

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

series435.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
114.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
111.0ms	(sqrt (fma c (* a -4) (* b b)))
105.0ms	(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: 10.7b

localize120.0ms

Local error

Found 4 expressions with local error:

19.0b	(fma (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
19.8b	(sqrt (fma c (* a -4) (* b b)))
19.8b	(sqrt (fma c (* a -4) (* b b)))
19.8b	(sqrt (fma c (* a -4) (* b b)))

rewrite4.0ms

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

series698.0ms

Counts

4 → 12

Calls

4 calls:

403.0ms	(fma (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
89.0ms	(sqrt (fma c (* a -4) (* b b)))
93.0ms	(sqrt (fma c (* a -4) (* b b)))
114.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.9s

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
4	2885
3	715
2	243
1	112
0	65

prune620.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.1b

localize170.0ms

Local error

Found 4 expressions with local error:

19.8b	(sqrt (fma c (* a -4) (* b b)))
19.8b	(sqrt (fma c (* a -4) (* b b)))
19.8b	(sqrt (fma c (* a -4) (* b b)))
19.8b	(sqrt (fma c (* a -4) (* b b)))

rewrite8.0ms

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

series403.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(sqrt (fma c (* a -4) (* b b)))
87.0ms	(sqrt (fma c (* a -4) (* b b)))
107.0ms	(sqrt (fma c (* a -4) (* b b)))
93.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify4.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
9	1082
8	418
7	255
6	196
5	169
4	135
3	89
2	53
1	38
0	28

prune661.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.1b

localize158.0ms

Local error

Found 4 expressions with local error:

19.8b	(sqrt (fma c (* a -4) (* b b)))
20.7b	(cbrt (fma c (* a -4) (* b b)))
20.7b	(cbrt (fma c (* a -4) (* b b)))
20.7b	(cbrt (fma c (* a -4) (* b b)))

rewrite71.0ms

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 c (* a -4) (* b b)))
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)))

series791.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(sqrt (fma c (* a -4) (* b b)))
230.0ms	(cbrt (fma c (* a -4) (* b b)))
225.0ms	(cbrt (fma c (* a -4) (* b b)))
235.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify1.7s

Counts

70 → 70

Iterations

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

prune794.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.1b

regimes383.0ms

Accuracy

79.9% (1.5b remaining)

Error of 13.9b against oracle of 12.4b and baseline of 19.7b

bsearch149.0ms

Steps

Iters	Range		Point
6	4.8498614244770303e+48	2.0602804194761557e+49	2.0410715251838527e+49

simplify26.0ms

Iterations

Iter	Nodes
done	48
1	48
0	42

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.0s	8711×	body	80	valid
575.0ms	2933×	body	80	nan