Details

sample121.0ms

Algorithm

intervals

Results

35.0ms	151×	body	160	valid
23.0ms	259×	body	80	nan
22.0ms	515×	pre	80	true
16.0ms	49×	body	320	valid
5.0ms	56×	body	80	valid

simplify115.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	115
5	115
4	107
3	85
2	47
1	25
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (* c a) -4 (* b b)))
0.1b	(fma (* c a) -4 (* b b))
0.2b	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
35.7b	(- (sqrt (fma (* c a) -4 (* b b))) b)

rewrite30.0ms

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:

1.0ms	(sqrt (fma (* c a) -4 (* b b)))
0.0ms	(fma (* c a) -4 (* b b))
19.0ms	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
8.0ms	(- (sqrt (fma (* c a) -4 (* b b))) b)

series395.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt (fma (* c a) -4 (* b b)))
77.0ms	(fma (* c a) -4 (* b b))
106.0ms	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
117.0ms	(- (sqrt (fma (* c a) -4 (* b b))) b)

simplify1.9s

Counts

126 → 126

Iterations

Iter	Nodes
done	5004
3	2760
2	799
1	335
0	157

prune794.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 39.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* c a) -4 (* b b))
0.1b	(fma (* c a) -4 (* b b))
0.2b	(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
42.5b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite13.0ms

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:

0.0ms	(fma (* c a) -4 (* b b))
0.0ms	(fma (* c a) -4 (* b b))
10.0ms	(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
0.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

series1.2s

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma (* c a) -4 (* b b))
65.0ms	(fma (* c a) -4 (* b b))
621.0ms	(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
454.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify1.9s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	1733
2	446
1	190
0	110

prune703.0ms

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 39.7b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt a)
42.5b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
42.5b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
42.5b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* 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 a)
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))

series1.4s

Counts

4 → 12

Calls

4 calls:

256.0ms	(cbrt a)
384.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
423.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
337.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify2.0s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
4	3105
3	829
2	280
1	128
0	71

prune925.0ms

Pruning

41 alts after pruning (41 fresh and 0 done)

Merged error: 39.7b

localize102.0ms

Local error

Found 4 expressions with local error:

0.7b	(expm1 (log1p (cbrt a)))
42.5b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
42.5b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
42.5b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite2.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 45

Calls

4 calls:

0.0ms	(expm1 (log1p (cbrt a)))
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))
1.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

series1.7s

Counts

4 → 12

Calls

4 calls:

449.0ms	(expm1 (log1p (cbrt a)))
379.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
397.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
452.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify2.2s

Counts

57 → 57

Iterations

Iter	Nodes
done	5001
4	3173
3	846
2	276
1	124
0	70

prune566.0ms

Pruning

43 alts after pruning (42 fresh and 1 done)

Merged error: 39.7b

regimes1.2s

Accuracy

0% (3.1b remaining)

Error of 43.3b against oracle of 40.2b and baseline of 43.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	24
1	24
0	22

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.7s	4837×	body	160	valid
1.2s	8353×	body	80	nan
919.0ms	16353×	pre	80	true
501.0ms	1380×	body	320	valid
203.0ms	1783×	body	80	valid