Details

sample121.0ms

Algorithm

intervals

Results

73.0ms	281×	body	80	valid
19.0ms	84×	body	80	nan

simplify159.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize136.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (fma c (* a -4) (* b b))) b)
1.7b	(- (- b) (sqrt (fma c (* a -4) (* b b))))
23.4b	(sqrt (fma c (* a -4) (* b b)))
23.4b	(sqrt (fma c (* a -4) (* 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 c (* a -4) (* b b))) b)
10.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
1.0ms	(sqrt (fma c (* a -4) (* b b)))
3.0ms	(sqrt (fma c (* a -4) (* b b)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
85.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
92.0ms	(sqrt (fma c (* a -4) (* b b)))
88.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify714.0ms

Counts

177 → 177

Iterations

Iter	Nodes
done	2000
2	995
1	426
0	194

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.9b

localize148.0ms

Local error

Found 4 expressions with local error:

16.0b	(fma (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
23.4b	(sqrt (fma c (* a -4) (* b b)))
23.4b	(sqrt (fma c (* a -4) (* b b)))
23.4b	(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)))

series784.0ms

Counts

4 → 12

Calls

4 calls:

425.0ms	(fma (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
125.0ms	(sqrt (fma c (* a -4) (* b b)))
103.0ms	(sqrt (fma c (* a -4) (* b b)))
131.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify654.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	2004
3	715
2	243
1	112
0	65

prune577.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.9b

localize178.0ms

Local error

Found 4 expressions with local error:

23.4b	(sqrt (fma c (* a -4) (* b b)))
24.3b	(cbrt (fma c (* a -4) (* b b)))
24.3b	(cbrt (fma c (* a -4) (* b b)))
24.3b	(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)))

series888.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(sqrt (fma c (* a -4) (* b b)))
250.0ms	(cbrt (fma c (* a -4) (* b b)))
259.0ms	(cbrt (fma c (* a -4) (* b b)))
242.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify564.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	2012
3	861
2	279
1	124
0	68

prune691.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.9b

localize215.0ms

Local error

Found 4 expressions with local error:

23.4b	(sqrt (fma c (* a -4) (* b b)))
23.4b	(sqrt (fma c (* a -4) (* b b)))
24.3b	(cbrt (fma c (* a -4) (* b b)))
24.3b	(cbrt (fma c (* a -4) (* b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series713.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt (fma c (* a -4) (* b b)))
104.0ms	(sqrt (fma c (* a -4) (* b b)))
263.0ms	(cbrt (fma c (* a -4) (* b b)))
242.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify653.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	2012
3	861
2	279
1	124
0	68

prune660.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.9b

regimes386.0ms

Accuracy

92.1% (0.6b remaining)

Error of 12.3b against oracle of 11.7b and baseline of 19.0b

bsearch112.0ms

Steps

Iters	Range		Point
7	1.9723660647371773e+81	3.4101289177416236e+83	2.6416821021932446e+83

simplify9.0ms

Iterations

Iter	Nodes
done	36
1	36
0	32

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.0s	8781×	body	80	valid
539.0ms	2986×	body	80	nan