Details

sample119.0ms

Algorithm

intervals

Results

35.0ms	151×	body	160	valid
26.0ms	314×	body	80	nan
21.0ms	570×	pre	80	true
12.0ms	48×	body	320	valid
5.0ms	57×	body	80	valid

simplify108.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
5	134
4	125
3	90
2	47
1	25
0	14

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma (* c a) -4 (* b b)))
0.1b	(fma (* c a) -4 (* b b))
0.1b	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
38.1b	(- (sqrt (fma (* c a) -4 (* b b))) b)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

2.0ms	(sqrt (fma (* c a) -4 (* b b)))
0.0ms	(fma (* c a) -4 (* b b))
30.0ms	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
15.0ms	(- (sqrt (fma (* c a) -4 (* b b))) b)

series401.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (fma (* c a) -4 (* b b)))
81.0ms	(fma (* c a) -4 (* b b))
106.0ms	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
126.0ms	(- (sqrt (fma (* c a) -4 (* b b))) b)

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1070
1	337
0	157

prune784.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 40.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
0.1b	(fma (* c a) -4 (* b b))
0.1b	(fma (* c a) -4 (* b b))
43.2b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

9.0ms	(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
1.0ms	(fma (* c a) -4 (* b b))
1.0ms	(fma (* c a) -4 (* b b))
1.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

series1.0s

Counts

4 → 12

Calls

4 calls:

565.0ms	(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
78.0ms	(fma (* c a) -4 (* b b))
53.0ms	(fma (* c a) -4 (* b b))
329.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify1.8s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	2217
2	504
1	190
0	110

prune656.0ms

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 40.5b

localize101.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
43.2b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
43.2b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
43.2b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite4.0ms

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

series1.5s

Counts

4 → 12

Calls

4 calls:

294.0ms	(cbrt a)
418.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
426.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
394.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify1.1s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
3	1207
2	322
1	128
0	71

prune942.0ms

Pruning

41 alts after pruning (41 fresh and 0 done)

Merged error: 40.4b

localize78.0ms

Local error

Found 4 expressions with local error:

1.5b	(pow a 1/3)
43.2b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
43.2b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
43.2b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unpow-prod-down` `fma-udef`
1×	`pow-to-exp` `pow-pow` `unpow1/3` `pow-exp` `sqr-pow`

Counts

4 → 54

Calls

4 calls:

2.0ms	(pow a 1/3)
0.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

series1.5s

Counts

4 → 12

Calls

4 calls:

301.0ms	(pow a 1/3)
450.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
376.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
386.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify1.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	1943
2	506
1	188
0	84

prune581.0ms

Pruning

42 alts after pruning (42 fresh and 0 done)

Merged error: 40.4b

regimes1.3s

Accuracy

0% (3.1b remaining)

Error of 43.3b against oracle of 40.1b and baseline of 43.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	24

end0.0ms

sample6.0s

Algorithm

intervals

Results

1.9s	4829×	body	160	valid
1.7s	8456×	body	80	nan
976.0ms	16456×	pre	80	true
622.0ms	1386×	body	320	valid
293.0ms	1785×	body	80	valid