Details

sample73.0ms

Algorithm

intervals

Results

43.0ms

626×

body

valid

simplify5.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	12	17
1	26	16
2	50	15
3	86	15
4	151	15
5	303	15
6	932	15
7	3961	15
done	5001	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
0.0b	(fma a a (* b b))
0.3b	(pow (fma a a (* b b)) 2.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

0.0ms	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
0.0ms	(fma a a (* b b))
3.0ms	(pow (fma a a (* b b)) 2.0)

series365.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
48.0ms	(fma a a (* b b))
200.0ms	(pow (fma a a (* b b)) 2.0)

simplify2.8s

Counts

48 → 48

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	79	580
1	148	561
2	367	493
3	1089	488
4	3747	485
done	5000	485

prune229.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
22.6b	(cbrt (pow (fma a a (* b b)) 2.0))
22.6b	(cbrt (pow (fma a a (* b b)) 2.0))
22.6b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite62.0ms

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:

47.0ms	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series931.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
240.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
200.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
242.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify3.1s

Counts

129 → 129

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	122	2774
1	211	2629
2	498	2385
3	1126	2197
4	3057	2186
done	5000	2122

prune763.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

8.6b	(cbrt (pow (hypot a b) 2.0))
8.6b	(cbrt (pow (hypot a b) 2.0))
22.6b	(cbrt (pow (fma a a (* b b)) 2.0))
22.6b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite10.0ms

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:

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

series959.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(cbrt (pow (hypot a b) 2.0))
227.0ms	(cbrt (pow (hypot a b) 2.0))
234.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
230.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.7s

Counts

80 → 80

Iterations

Useful iterations: 3 (205.0ms)

Iter	Nodes	Cost
0	98	1032
1	176	1016
2	344	936
3	806	924
4	2188	924
done	5001	924

prune700.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

7.9b	(sqrt (pow (hypot a b) 2.0))
8.6b	(cbrt (pow (hypot a b) 2.0))
22.6b	(cbrt (pow (fma a a (* b b)) 2.0))
22.6b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
14×	`add-sqr-sqrt`
13×	`unpow-prod-down`
12×	`add-cube-cbrt` `*-un-lft-identity`
7×	`sqrt-prod`
5×	`sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `pow1/3`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (pow (hypot a b) 2.0))
2.0ms	(cbrt (pow (hypot a b) 2.0))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

275.0ms	(sqrt (pow (hypot a b) 2.0))
236.0ms	(cbrt (pow (hypot a b) 2.0))
274.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
254.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.0s

Counts

84 → 84

Iterations

Useful iterations: 3 (283.0ms)

Iter	Nodes	Cost
0	126	1031
1	226	999
2	454	928
3	1079	919
4	2960	919
done	5000	919

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes185.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.7s

20293×

body

valid