Details

sample77.0ms

Algorithm

intervals

Results

45.0ms

659×

body

valid

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	12	17
1	26	16
2	50	15
3	87	15
4	154	15
5	474	15
6	3761	15
done	5000	15

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `unpow-prod-down` `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 a a (* b b))
0.0ms	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
4.0ms	(pow (fma a a (* b b)) 2.0)

series322.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(fma a a (* b b))
115.0ms	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
159.0ms	(pow (fma a a (* b b)) 2.0)

simplify2.2s

Counts

48 → 48

Iterations

Useful iterations: 3 (602.0ms)

Iter	Nodes	Cost
0	79	580
1	168	560
2	544	493
3	2463	488
done	5001	488

prune293.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cbrt (fma a a (* b b))) 2.0)
8.7b	(cbrt (fma a a (* b b)))
8.7b	(cbrt (fma a a (* b b)))
8.7b	(cbrt (fma a a (* b b)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

5.0ms	(pow (cbrt (fma a a (* b b))) 2.0)
1.0ms	(cbrt (fma a a (* b b)))
1.0ms	(cbrt (fma a a (* b b)))
1.0ms	(cbrt (fma a a (* b b)))

series696.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(pow (cbrt (fma a a (* b b))) 2.0)
160.0ms	(cbrt (fma a a (* b b)))
137.0ms	(cbrt (fma a a (* b b)))
157.0ms	(cbrt (fma a a (* b b)))

simplify999.0ms

Counts

74 → 74

Iterations

Useful iterations: 3 (434.0ms)

Iter	Nodes	Cost
0	78	871
1	200	847
2	567	735
3	2002	726
done	5000	726

prune628.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

8.7b	(cbrt (fma a a (* b b)))
8.7b	(cbrt (fma a a (* b b)))
8.7b	(cbrt (fma a a (* b b)))
8.7b	(cbrt (fma a a (* b b)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (fma a a (* b b)))
1.0ms	(cbrt (fma a a (* b b)))
1.0ms	(cbrt (fma a a (* b b)))
2.0ms	(cbrt (fma a a (* b b)))

series629.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (fma a a (* b b)))
152.0ms	(cbrt (fma a a (* b b)))
160.0ms	(cbrt (fma a a (* b b)))
169.0ms	(cbrt (fma a a (* b b)))

simplify1.3s

Counts

64 → 64

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	37	688
1	67	680
2	158	588
3	536	576
4	2144	576
done	5001	576

prune522.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot a b))
8.7b	(cbrt (fma a a (* b b)))
8.7b	(cbrt (fma a a (* b b)))
8.7b	(cbrt (fma a a (* b b)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (hypot a b))
1.0ms	(cbrt (fma a a (* b b)))
1.0ms	(cbrt (fma a a (* b b)))
1.0ms	(cbrt (fma a a (* b b)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (hypot a b))
131.0ms	(cbrt (fma a a (* b b)))
176.0ms	(cbrt (fma a a (* b b)))
112.0ms	(cbrt (fma a a (* b b)))

simplify1.9s

Counts

64 → 64

Iterations

Useful iterations: 3 (246.0ms)

Iter	Nodes	Cost
0	63	634
1	113	625
2	310	547
3	1090	535
4	4714	535
done	5000	535

prune599.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes333.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b 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

sample3.1s

Algorithm

intervals

Results

2.3s

20551×

body

valid