Details

sample203.0ms

Algorithm

intervals

Results

52.0ms	520×	pre	80	true
48.0ms	117×	body	320	valid
34.0ms	264×	body	80	nan
25.0ms	94×	body	160	valid
10.0ms	18×	body	640	valid
4.0ms	27×	body	80	valid

simplify106.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma -3 (* c a) (* b b)))
0.1b	(fma -3 (* c a) (* b b))
0.2b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
26.0b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite66.0ms

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))
39.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
22.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series493.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (fma -3 (* c a) (* b b)))
95.0ms	(fma -3 (* c a) (* b b))
142.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
145.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify1.3s

Counts

114 → 114

Iterations

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

prune761.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 49.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma -3 (* c a) (* b b))
0.1b	(fma -3 (* c a) (* b b))
0.2b	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
52.4b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite8.0ms

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))
7.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.2s

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma -3 (* c a) (* b b))
61.0ms	(fma -3 (* c a) (* b b))
695.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
390.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.6s

Counts

69 → 69

Iterations

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

prune675.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 49.8b

localize76.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))))
52.4b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
52.4b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
52.4b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

9.0ms	(* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (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))

series2.3s

Counts

4 → 12

Calls

4 calls:

827.0ms	(* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))))
460.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
460.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
508.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	2002
3	2002
2	806
1	280
0	127

prune1.0s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 49.1b

localize126.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))))
52.4b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
52.4b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
52.4b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

16.0ms	(* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (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))
1.0ms	(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))

series2.4s

Counts

4 → 12

Calls

4 calls:

948.0ms	(* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))))
505.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
442.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
457.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	2002
3	2002
2	806
1	280
0	127

prune864.0ms

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 49.1b

regimes828.0ms

Accuracy

0% (3.2b remaining)

Error of 51.9b against oracle of 48.8b and baseline of 51.9b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	24
1	24
0	21

end0.0ms

sample5.8s

Algorithm

intervals

Results

1.4s	3620×	body	320	valid
1.1s	8197×	body	80	nan
979.0ms	16197×	pre	80	true
890.0ms	2952×	body	160	valid
520.0ms	880×	body	80	valid
288.0ms	548×	body	640	valid