Details

sample55.0ms

Algorithm

intervals

Results

36.0ms

691×

body

valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	19	31
1	55	29
2	158	28
3	443	28
4	1206	28
5	3454	28
done	5001	28

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(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)
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite20.0ms

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:

0.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
1.0ms	(pow (fma a a (* b b)) 2.0)
16.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
50.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
115.0ms	(pow (fma a a (* b b)) 2.0)
49.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify666.0ms

Counts

84 → 84

Iterations

Useful iterations: 2 (187.0ms)

Iter	Nodes	Cost
0	160	1452
1	383	1411
2	1445	1221
done	5000	1221

prune478.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
9.4b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
9.4b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity` `prod-diff`
10×	`distribute-rgt-in` `distribute-lft-in`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
12.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms	(sqrt (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	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
51.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
196.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
203.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify595.0ms

Counts

108 → 108

Iterations

Useful iterations: done (589.0ms)

Iter	Nodes	Cost
0	130	2220
1	324	2078
2	1158	1844
done	5001	1836

prune378.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
19.0b	(cbrt (pow (fma a a (* b b)) 2.0))
19.0b	(cbrt (pow (fma a a (* b b)) 2.0))
19.0b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite18.0ms

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:

13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
1.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
1.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series521.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
152.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
158.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
158.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify558.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	131	1430
1	308	1413
2	1086	1248
done	5001	1248

prune419.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

19.0b	(cbrt (pow (fma a a (* b b)) 2.0))
19.0b	(cbrt (pow (fma a a (* b b)) 2.0))
19.0b	(cbrt (pow (fma a a (* b b)) 2.0))
19.0b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite6.0ms

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:

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

series638.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
158.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
159.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
159.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.3s

Counts

80 → 80

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	58	1188
1	104	1172
2	225	1064
3	644	1052
4	2284	1052
done	5000	1052

prune438.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes158.0ms

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	19	57
1	22	57
done	22	57

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

21017×

body

valid