Details

sample126.0ms

Algorithm

intervals

Results

83.0ms	281×	body	80	valid
18.0ms	82×	body	80	nan

simplify166.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	160
7	160
6	159
5	152
4	140
3	108
2	63
1	36
0	20

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize191.0ms

Local error

Found 4 expressions with local error:

1.2b	(fma -4 (* c a) (* b b))
2.7b	(- (sqrt (fma -4 (* c a) (* b b))) b)
22.2b	(sqrt (fma -4 (* c a) (* b b)))
22.2b	(sqrt (fma -4 (* c a) (* b b)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

0.0ms	(fma -4 (* c a) (* b b))
8.0ms	(- (sqrt (fma -4 (* c a) (* b b))) b)
1.0ms	(sqrt (fma -4 (* c a) (* b b)))
4.0ms	(sqrt (fma -4 (* c a) (* b b)))

series827.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma -4 (* c a) (* b b))
98.0ms	(- (sqrt (fma -4 (* c a) (* b b))) b)
537.0ms	(sqrt (fma -4 (* c a) (* b b)))
124.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.3s

Counts

97 → 97

Iterations

Iter	Nodes
4	4427
3	1221
2	379
1	178
0	98

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.8b

localize157.0ms

Local error

Found 4 expressions with local error:

9.8b	(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
22.2b	(sqrt (fma -4 (* c a) (* b b)))
22.2b	(sqrt (fma -4 (* c a) (* b b)))
22.2b	(sqrt (fma -4 (* c a) (* b b)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

10.0ms	(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
1.0ms	(sqrt (fma -4 (* c a) (* b b)))
1.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
130.0ms	(sqrt (fma -4 (* c a) (* b b)))
106.0ms	(sqrt (fma -4 (* c a) (* b b)))
120.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.4s

Counts

98 → 98

Iterations

Iter	Nodes
4	4009
3	1390
2	496
1	207
0	97

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.8b

localize211.0ms

Local error

Found 4 expressions with local error:

22.2b	(sqrt (fma -4 (* c a) (* b b)))
22.9b	(cbrt (fma -4 (* c a) (* b b)))
22.9b	(cbrt (fma -4 (* c a) (* b b)))
22.9b	(cbrt (fma -4 (* c a) (* b b)))

rewrite10.0ms

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 -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
7.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))

series869.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (fma -4 (* c a) (* b b)))
265.0ms	(cbrt (fma -4 (* c a) (* b b)))
227.0ms	(cbrt (fma -4 (* c a) (* b b)))
256.0ms	(cbrt (fma -4 (* c a) (* b b)))

simplify2.9s

Counts

70 → 70

Iterations

Iter	Nodes
5	6393
4	1999
3	677
2	258
1	122
0	68

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.8b

localize237.0ms

Local error

Found 4 expressions with local error:

22.9b	(cbrt (fma -4 (* c a) (* b b)))
22.9b	(cbrt (fma -4 (* c a) (* b b)))
22.9b	(cbrt (fma -4 (* c a) (* b b)))
22.9b	(cbrt (fma -4 (* c a) (* b b)))

rewrite3.0ms

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

series1.0s

Counts

4 → 12

Calls

4 calls:

259.0ms	(cbrt (fma -4 (* c a) (* b b)))
277.0ms	(cbrt (fma -4 (* c a) (* b b)))
269.0ms	(cbrt (fma -4 (* c a) (* b b)))
238.0ms	(cbrt (fma -4 (* c a) (* b b)))

simplify3.1s

Counts

68 → 68

Iterations

Iter	Nodes
5	6746
4	1953
3	622
2	229
1	103
0	53

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.8b

regimes827.0ms

Accuracy

93% (0.5b remaining)

Error of 13.2b against oracle of 12.6b and baseline of 20.0b

bsearch133.0ms

Steps

Iters	Range		Point
6	1.890398075878753e+149	8.723340275486535e+149	3.188391854507535e+149

simplify11.0ms

Iterations

Iter	Nodes
2	41
1	41
0	36

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.8s	8793×	body	80	valid
598.0ms	2880×	body	80	nan