Details

sample109.0ms

Algorithm

intervals

Results

63.0ms	274×	body	80	valid
18.0ms	88×	body	80	nan

simplify231.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	170
7	170
6	168
5	164
4	157
3	132
2	76
1	39
0	20

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize168.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (fma c (* a -4) (* b b))))
1.3b	(- (sqrt (fma c (* a -4) (* b b))) b)
21.0b	(sqrt (fma c (* a -4) (* b b)))
21.0b	(sqrt (fma c (* a -4) (* b b)))

rewrite31.0ms

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:

10.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
14.0ms	(- (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)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
142.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
132.0ms	(sqrt (fma c (* a -4) (* b b)))
131.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify996.0ms

Counts

177 → 177

Iterations

Iter	Nodes
3	2153
2	837
1	417
0	194

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize179.0ms

Local error

Found 4 expressions with local error:

21.0b	(sqrt (fma c (* a -4) (* b b)))
21.8b	(cbrt (fma c (* a -4) (* b b)))
21.8b	(cbrt (fma c (* a -4) (* b b)))
21.8b	(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)))

series853.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(sqrt (fma c (* a -4) (* b b)))
222.0ms	(cbrt (fma c (* a -4) (* b b)))
247.0ms	(cbrt (fma c (* a -4) (* b b)))
267.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify3.8s

Counts

70 → 70

Iterations

Iter	Nodes
5	6476
4	1995
3	662
2	255
1	123
0	68

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.5b

localize156.0ms

Local error

Found 4 expressions with local error:

21.0b	(sqrt (fma c (* a -4) (* b b)))
21.0b	(sqrt (fma c (* a -4) (* b b)))
21.0b	(sqrt (fma c (* a -4) (* b b)))
21.0b	(sqrt (fma c (* a -4) (* b b)))

rewrite11.0ms

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:

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

series448.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt (fma c (* a -4) (* b b)))
91.0ms	(sqrt (fma c (* a -4) (* b b)))
115.0ms	(sqrt (fma c (* a -4) (* b b)))
141.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify5.7s

Counts

76 → 76

Iterations

Iter	Nodes
10	6396
9	1432
8	579
7	291
6	197
5	159
4	132
3	87
2	51
1	36
0	28

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.5b

localize230.0ms

Local error

Found 4 expressions with local error:

21.0b	(sqrt (fma c (* a -4) (* b b)))
21.0b	(sqrt (fma c (* a -4) (* b b)))
21.6b	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))))))
62.2b	(fma (- (sqrt (sqrt (fma c (* a -4) (* b b))))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `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` `fma-udef`

Counts

4 → 54

Calls

4 calls:

1.0ms	(sqrt (fma c (* a -4) (* b b)))
1.0ms	(sqrt (fma c (* a -4) (* b b)))
0.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))))))
0.0ms	(fma (- (sqrt (sqrt (fma c (* a -4) (* b b))))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))

series851.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (fma c (* a -4) (* b b)))
83.0ms	(sqrt (fma c (* a -4) (* b b)))
193.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))))))
462.0ms	(fma (- (sqrt (sqrt (fma c (* a -4) (* b b))))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))

simplify1.8s

Counts

66 → 66

Iterations

Iter	Nodes
4	3382
3	1041
2	397
1	189
0	97

prune1.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 11.5b

regimes320.0ms

Accuracy

90.1% (0.7b remaining)

Error of 13.4b against oracle of 12.7b and baseline of 19.7b

bsearch169.0ms

Steps

Iters	Range		Point
9	1.7155709022758137e+74	7.648947555279674e+80	6.2482814833755615e+78

simplify6.0ms

Iterations

Iter	Nodes
2	38
1	38
0	33

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.8s	8721×	body	80	valid
970.0ms	2901×	body	80	nan