Details

sample138.0ms

Algorithm

intervals

Results

69.0ms	281×	body	80	valid
41.0ms	98×	body	80	nan

simplify183.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize142.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (fma c (* a -4) (* b b))))
1.1b	(- (sqrt (fma c (* a -4) (* b b))) b)
21.9b	(sqrt (fma c (* a -4) (* b b)))
21.9b	(sqrt (fma c (* a -4) (* b b)))

rewrite44.0ms

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:

22.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
12.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
1.0ms	(sqrt (fma c (* a -4) (* b b)))
3.0ms	(sqrt (fma c (* a -4) (* b b)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
124.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
104.0ms	(sqrt (fma c (* a -4) (* b b)))
120.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.1s

Counts

177 → 177

Iterations

Iter	Nodes
done	2004
3	2004
2	965
1	427
0	194

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.3b

localize166.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma c (* a -4) (* b b))) b)
21.9b	(sqrt (fma c (* a -4) (* b b)))
21.9b	(sqrt (fma c (* a -4) (* b b)))
21.9b	(sqrt (fma c (* a -4) (* b b)))

rewrite20.0ms

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:

11.0ms	(- (sqrt (fma c (* a -4) (* b 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)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
132.0ms	(sqrt (fma c (* a -4) (* b b)))
112.0ms	(sqrt (fma c (* a -4) (* b b)))
105.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	2001
4	2001
3	908
2	311
1	168
0	85

prune791.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.3b

localize205.0ms

Local error

Found 4 expressions with local error:

21.9b	(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)))

rewrite4.0ms

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:

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

series769.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt (fma c (* a -4) (* b b)))
195.0ms	(cbrt (fma c (* a -4) (* b b)))
226.0ms	(cbrt (fma c (* a -4) (* b b)))
264.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify931.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	2024
4	2024
3	861
2	279
1	124
0	68

prune830.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.3b

localize153.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma c (* a -4) (* b b)))
21.9b	(sqrt (fma c (* a -4) (* b b)))
21.9b	(sqrt (fma c (* a -4) (* b b)))
21.9b	(sqrt (fma c (* a -4) (* 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 c (* a -4) (* 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)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(sqrt (fma c (* a -4) (* b b)))
109.0ms	(sqrt (fma c (* a -4) (* b b)))
101.0ms	(sqrt (fma c (* a -4) (* b b)))
93.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.7s

Counts

76 → 76

Iterations

Iter	Nodes
done	2000
10	2000
9	1082
8	418
7	255
6	196
5	169
4	135
3	89
2	53
1	38
0	28

prune658.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.3b

regimes227.0ms

Accuracy

90.7% (0.6b remaining)

Error of 13.1b against oracle of 12.5b and baseline of 19.1b

bsearch175.0ms

Steps

Iters	Range		Point
7	6.52945691119865e+99	1.3360629297740576e+102	2.428102982638899e+100

simplify12.0ms

Iterations

Iter	Nodes
done	43
1	43
0	38

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.2s	8758×	body	80	valid
592.0ms	2940×	body	80	nan