Details

sample129.0ms

Algorithm

intervals

Results

99.0ms

620×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3560
3	785
2	201
1	58
0	19

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a a (* b b))
0.0b	(fma (fma 4 a 4) (* a a) (fma (* b b) (fma a -12 4) (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
0.0b	(fma a -12 4)
0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) -1)

rewrite1.0ms

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

Counts

4 → 44

Calls

4 calls:

0.0ms	(fma a a (* b b))
0.0ms	(fma (fma 4 a 4) (* a a) (fma (* b b) (fma a -12 4) (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
0.0ms	(fma a -12 4)
0.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)

series331.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma a a (* b b))
145.0ms	(fma (fma 4 a 4) (* a a) (fma (* b b) (fma a -12 4) (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
49.0ms	(fma a -12 4)
81.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)

simplify1.9s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
3	1436
2	333
1	122
0	73

prune427.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b))))
11.7b	(cbrt (fma a a (* b b)))
11.7b	(cbrt (fma a a (* b b)))
11.7b	(cbrt (fma a a (* b b)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

14.0ms	(* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b 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)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b))))
130.0ms	(cbrt (fma a a (* b b)))
146.0ms	(cbrt (fma a a (* b b)))
127.0ms	(cbrt (fma a a (* b b)))

simplify2.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
4	2938
3	1018
2	413
1	171
0	80

prune734.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma a a (* b b)) (fma a a (* b b)))
0.3b	(* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (cbrt (fma a a (* b b))))
11.7b	(cbrt (fma a a (* b b)))
21.4b	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`cbrt-prod` `pow1`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log`
7×	`associate-l`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `pow1/3` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `pow-prod-down`
2×	`prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow3` `pow-sqr` `pow-prod-up`

Counts

4 → 86

Calls

4 calls:

11.0ms	(* (fma a a (* b b)) (fma a a (* b b)))
20.0ms	(* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (cbrt (fma a a (* b b))))
1.0ms	(cbrt (fma a a (* b b)))
6.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (fma a a (* b b)) (fma a a (* b b)))
46.0ms	(* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (cbrt (fma a a (* b b))))
133.0ms	(cbrt (fma a a (* b b)))
153.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))

simplify2.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5007
3	2367
2	722
1	246
0	120

prune799.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize94.0ms

Local error

Found 4 expressions with local error:

3.0b	(sqrt (cbrt (* (fma a a (* b b)) (fma a a (* b b)))))
11.7b	(cbrt (fma a a (* b b)))
21.4b	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))
21.4b	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

7×	`cbrt-prod` `add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow1/3` `add-exp-log` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1`
1×	`pow1/2`

Counts

4 → 57

Calls

4 calls:

5.0ms	(sqrt (cbrt (* (fma a a (* b b)) (fma a a (* b b)))))
2.0ms	(cbrt (fma a a (* b b)))
6.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))
15.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(sqrt (cbrt (* (fma a a (* b b)) (fma a a (* b b)))))
134.0ms	(cbrt (fma a a (* b b)))
164.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))
164.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))

simplify2.2s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
4	2932
3	945
2	304
1	131
0	76

prune650.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes286.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	21
1	21
0	19

end0.0ms

sample3.5s

Algorithm

intervals

Results

3.1s

20337×

body

valid