Details

sample124.0ms

Algorithm

intervals

Results

28.0ms	138×	body	160	valid
26.0ms	511×	pre	80	true
24.0ms	255×	body	80	nan
19.0ms	57×	body	320	valid
6.0ms	61×	body	80	valid

simplify169.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma -3 (* c a) (* b b)))
0.1b	(fma -3 (* c a) (* b b))
0.3b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
37.9b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `fma-neg` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 102

Calls

4 calls:

2.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))
38.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
16.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series427.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (fma -3 (* c a) (* b b)))
71.0ms	(fma -3 (* c a) (* b b))
100.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
135.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify1.1s

Counts

114 → 114

Iterations

Iter	Nodes
done	2000
3	2000
2	940
1	347
0	152

prune1.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 40.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma -3 (* c a) (* b b))
0.1b	(fma -3 (* c a) (* b b))
0.3b	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `fma-udef` `associate-/l*`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 57

Calls

4 calls:

0.0ms	(fma -3 (* c a) (* b b))
0.0ms	(fma -3 (* c a) (* b b))
13.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
1.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.5s

Counts

4 → 12

Calls

4 calls:

69.0ms	(fma -3 (* c a) (* b b))
70.0ms	(fma -3 (* c a) (* b b))
612.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
772.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.2s

Counts

69 → 69

Iterations

Iter	Nodes
done	2005
3	2005
2	672
1	231
0	112

prune978.0ms

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 40.3b

localize87.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

1.0ms	(cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.8s

Counts

4 → 12

Calls

4 calls:

616.0ms	(cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))
401.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
367.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
407.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.4s

Counts

59 → 59

Iterations

Iter	Nodes
done	2013
3	2013
2	604
1	216
0	105

prune1.2s

Pruning

39 alts after pruning (39 fresh and 0 done)

Merged error: 40.2b

localize146.0ms

Local error

Found 4 expressions with local error:

43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
43.5b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

1.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
1.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.6s

Counts

4 → 12

Calls

4 calls:

428.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
364.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
413.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
417.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify899.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2002
4	2002
3	638
2	201
1	88
0	48

prune911.0ms

Pruning

42 alts after pruning (42 fresh and 0 done)

Merged error: 40.2b

regimes1.1s

Accuracy

0% (3.1b remaining)

Error of 44.1b against oracle of 40.9b and baseline of 44.1b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.7s	4791×	body	160	valid
974.0ms	8211×	body	80	nan
956.0ms	16211×	pre	80	true
541.0ms	1490×	body	320	valid
261.0ms	1719×	body	80	valid