Details

sample102.0ms

Algorithm

intervals

Results

59.0ms

684×

body

valid

simplify6.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	12	17
1	26	16
2	50	15
3	87	15
4	154	15
5	473	15
6	3709	15
done	5000	15

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
0.4b	(pow (fma a a (* b b)) 2.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

1.0ms	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
4.0ms	(pow (fma a a (* b b)) 2.0)

series318.0ms

Counts

2 → 6

Calls

2 calls:

119.0ms	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
200.0ms	(pow (fma a a (* b b)) 2.0)

simplify2.7s

Counts

35 → 35

Iterations

Useful iterations: 3 (688.0ms)

Iter	Nodes	Cost
0	72	472
1	159	456
2	479	408
3	2051	404
done	5002	404

prune331.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
17.2b	(cbrt (pow (fma a a (* b b)) 2.0))
17.2b	(cbrt (pow (fma a a (* b b)) 2.0))
17.2b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

43.0ms	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
12.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

304.0ms	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
295.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
309.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
317.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.4s

Counts

129 → 129

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	122	2774
1	241	2629
2	990	2385
done	5001	2243

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

7.8b	(cbrt (pow (hypot a b) 2.0))
7.8b	(cbrt (pow (hypot a b) 2.0))
17.2b	(cbrt (pow (fma a a (* b b)) 2.0))
17.2b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

4.0ms	(cbrt (pow (hypot a b) 2.0))
4.0ms	(cbrt (pow (hypot a b) 2.0))
5.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
15.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

354.0ms	(cbrt (pow (hypot a b) 2.0))
349.0ms	(cbrt (pow (hypot a b) 2.0))
312.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
765.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: 3 (419.0ms)

Iter	Nodes	Cost
0	98	1032
1	177	1016
2	397	936
3	1213	924
done	5000	924

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

17.2b	(cbrt (pow (fma a a (* b b)) 2.0))
17.2b	(cbrt (pow (fma a a (* b b)) 2.0))
17.2b	(cbrt (pow (fma a a (* b b)) 2.0))
17.2b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

309.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
303.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
296.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
342.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.3s

Counts

80 → 80

Iterations

Useful iterations: 3 (223.0ms)

Iter	Nodes	Cost
0	58	1188
1	105	1172
2	228	1064
3	656	1052
4	2741	1052
done	5000	1052

prune868.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 0.0b

regimes278.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	12	15
done	12	15

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.7s

20353×

body

valid