Details

sample55.0ms

Algorithm

intervals

Results

31.0ms

642×

body

valid

simplify4.8s

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`pow1` `pow-unpow` `unpow-prod-down` `add-exp-log`
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:

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)

series282.0ms

Counts

2 → 6

Calls

2 calls:

110.0ms	(fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0))
171.0ms	(pow (fma a a (* b b)) 2.0)

simplify2.3s

Counts

35 → 35

Iterations

Iter	Nodes
done	5001
3	1825
2	454
1	159
0	71

prune297.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (fma a a (* b b)) 2.0)
0.3b	(pow (fma a a (* b b)) 2.0)
12.4b	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
12.4b	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

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

series786.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(pow (fma a a (* b b)) 2.0)
166.0ms	(pow (fma a a (* b b)) 2.0)
226.0ms	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
232.0ms	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

simplify2.3s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
3	2235
2	566
1	186
0	84

prune775.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

12.4b	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
13.0b	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
13.0b	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
13.0b	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

1.0ms	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
1.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
6.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
2.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

221.0ms	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
297.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
297.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
292.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

simplify1.6s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	1693
2	437
1	164
0	80

prune761.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize109.0ms

Local error

Found 4 expressions with local error:

12.4b	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
12.4b	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
13.0b	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
13.0b	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

227.0ms	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
223.0ms	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
316.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
350.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

simplify1.5s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	1693
2	437
1	164
0	80

prune802.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes549.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	19
1	19
0	17

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.3s

20748×

body

valid