Details

sample211.0ms

Algorithm

intervals

Results

52.0ms	96×	body	160	valid
46.0ms	111×	body	320	valid
35.0ms	284×	body	80	nan
35.0ms	540×	pre	80	true
8.0ms	16×	body	640	valid
5.0ms	33×	body	80	valid

simplify100.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	113
5	113
4	105
3	81
2	43
1	22
0	12

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (* -3 a) c (* b b)))
0.1b	(fma (* -3 a) c (* b b))
0.2b	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
26.8b	(- (sqrt (fma (* -3 a) c (* b b))) b)

rewrite52.0ms

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:

1.0ms	(sqrt (fma (* -3 a) c (* b b)))
0.0ms	(fma (* -3 a) c (* b b))
31.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
17.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)

series511.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(sqrt (fma (* -3 a) c (* b b)))
88.0ms	(fma (* -3 a) c (* b b))
178.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
121.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)

simplify3.2s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	4962
2	1033
1	347
0	152

prune766.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 48.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* -3 a) c (* b b))
0.1b	(fma (* -3 a) c (* b b))
0.2b	(/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a))
51.2b	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* 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 a) c (* b b))
0.0ms	(fma (* -3 a) c (* b b))
14.0ms	(/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a))
1.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

series1.1s

Counts

4 → 12

Calls

4 calls:

103.0ms	(fma (* -3 a) c (* b b))
101.0ms	(fma (* -3 a) c (* b b))
425.0ms	(/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a))
480.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

simplify2.2s

Counts

69 → 69

Iterations

Iter	Nodes
done	5027
3	2507
2	690
1	232
0	112

prune618.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 48.5b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)))
51.2b	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
51.2b	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
51.2b	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* 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 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)))
0.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

series2.1s

Counts

4 → 12

Calls

4 calls:

691.0ms	(cbrt (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)))
457.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
477.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
473.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

simplify2.1s

Counts

59 → 59

Iterations

Iter	Nodes
done	5006
3	2585
2	611
1	218
0	105

prune802.0ms

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 48.5b

localize119.0ms

Local error

Found 4 expressions with local error:

51.2b	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
51.2b	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
51.2b	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
51.2b	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* 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 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
1.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
1.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
1.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

series1.8s

Counts

4 → 12

Calls

4 calls:

410.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
438.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
481.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
478.0ms	(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

simplify1.8s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
4	2659
3	644
2	192
1	88
0	48

prune602.0ms

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 48.4b

regimes1.0s

Accuracy

0% (2.6b remaining)

Error of 51.8b against oracle of 49.3b and baseline of 51.8b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	23
1	23
0	20

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.0s	16309×	pre	80	true
1.6s	3705×	body	320	valid
1.0s	8309×	body	80	nan
831.0ms	2921×	body	160	valid
229.0ms	486×	body	640	valid
150.0ms	888×	body	80	valid