Details

sample50.0ms

Algorithm

intervals

Results

32.0ms

622×

body

valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	19	31
1	55	29
2	158	28
3	443	28
4	1206	28
5	3442	28
done	5000	28

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

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)
1.3b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite17.0ms

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)
13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
59.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
133.0ms	(pow (fma a a (* b b)) 2.0)
55.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify865.0ms

Counts

84 → 84

Iterations

Useful iterations: done (862.0ms)

Iter	Nodes	Cost
0	160	1452
1	383	1411
2	1371	1221
done	5001	1218

prune287.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a a (* b b))
0.0b	(fma 1.0 (fma a a (* b b)) (pow a 3))
0.0b	(fma 4.0 (fma 1.0 (fma a a (* b b)) (pow a 3)) (pow (fma a a (* b b)) 2.0))
0.3b	(pow (fma a a (* b b)) 2.0)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

0.0ms	(fma a a (* b b))
0.0ms	(fma 1.0 (fma a a (* b b)) (pow a 3))
0.0ms	(fma 4.0 (fma 1.0 (fma a a (* b b)) (pow a 3)) (pow (fma a a (* b b)) 2.0))
1.0ms	(pow (fma a a (* b b)) 2.0)

series282.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma a a (* b b))
47.0ms	(fma 1.0 (fma a a (* b b)) (pow a 3))
81.0ms	(fma 4.0 (fma 1.0 (fma a a (* b b)) (pow a 3)) (pow (fma a a (* b b)) 2.0))
118.0ms	(pow (fma a a (* b b)) 2.0)

simplify812.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (212.0ms)

Iter	Nodes	Cost
0	90	889
1	169	849
2	519	744
3	1883	740
done	5000	740

prune241.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
17.9b	(cbrt (pow (fma a a (* b b)) 2.0))
17.9b	(cbrt (pow (fma a a (* b b)) 2.0))
17.9b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

12.0ms	(* (cbrt (pow (fma a a (* b b)) 2.0)) (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))

series653.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
163.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
160.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
167.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.1s

Counts

129 → 129

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	122	2774
1	212	2629
2	519	2385
3	1406	2197
4	3787	2186
done	5000	2186

prune543.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

8.9b	(cbrt (fma a a (* b b)))
12.6b	(cbrt (pow (* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b)))) 2.0))
17.9b	(cbrt (pow (fma a a (* b b)) 2.0))
17.9b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`unpow-prod-down`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqr-pow`

Counts

4 → 62

Calls

4 calls:

0.0ms	(cbrt (fma a a (* b b)))
1.0ms	(cbrt (pow (* (cbrt (fma a a (* b b))) (cbrt (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))

series598.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (fma a a (* b b)))
166.0ms	(cbrt (pow (* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b)))) 2.0))
166.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
161.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.6s

Counts

74 → 74

Iterations

Useful iterations: 3 (156.0ms)

Iter	Nodes	Cost
0	112	1202
1	210	1189
2	456	1077
3	1167	1065
4	3409	1065
done	5001	1065

prune458.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.0b

regimes207.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
done	13	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

20276×

body

valid