Details

sample112.0ms

Algorithm

intervals

Results

74.0ms

626×

body

valid

simplify6.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	19	31
1	55	29
2	178	28
3	545	28
4	1672	28
5	4797	28
done	5000	28

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.1b	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b	(pow (fma a a (* b b)) 2.0)
0.9b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-*r/` `fma-udef`
1×	`pow-to-exp` `flip3--` `pow-pow` `associate-l` `pow-exp` `*-commutative` `flip--` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

1.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
1.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
6.0ms	(pow (fma a a (* b b)) 2.0)
38.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
94.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
182.0ms	(pow (fma a a (* b b)) 2.0)
94.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.6s

Counts

84 → 84

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	160	1452
1	377	1411
2	1145	1221
3	4249	1207
done	5000	1207

prune492.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (* b b) (- 1.0 (* 3.0 a)))
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))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `unpow-prod-down` `add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

33.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
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))

series671.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
183.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
225.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
199.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify3.1s

Counts

96 → 96

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	131	1430
1	303	1413
2	865	1248
3	3061	1230
done	5000	1194

prune584.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize58.0ms

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))

series944.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(cbrt (pow (hypot a b) 2.0))
280.0ms	(cbrt (pow (hypot a b) 2.0))
214.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
233.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.7s

Counts

80 → 80

Iterations

Useful iterations: 3 (167.0ms)

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

prune860.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

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))

series944.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(cbrt (pow (hypot a b) 2.0))
243.0ms	(cbrt (pow (hypot a b) 2.0))
241.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
215.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.6s

Counts

80 → 80

Iterations

Useful iterations: 3 (203.0ms)

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

prune542.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes216.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	17	28
1	20	28
done	20	28

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.6s

20293×

body

valid