Details

sample103.0ms

Algorithm

intervals

Results

68.0ms

655×

body

valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	18	29
1	53	27
2	172	26
3	554	26
4	2113	26
done	5001	26

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
0.0b	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.3b	(pow (fma a a (* b b)) 2.0)
1.2b	(* (* b b) (+ 3.0 a))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

0.0ms	(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
0.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
3.0ms	(pow (fma a a (* b b)) 2.0)
52.0ms	(* (* b b) (+ 3.0 a))

series392.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
80.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
143.0ms	(pow (fma a a (* b b)) 2.0)
50.0ms	(* (* b b) (+ 3.0 a))

simplify3.1s

Counts

77 → 77

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	136	1157
1	366	1105
2	2153	971
done	5004	969

prune466.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (* b b) (+ 3.0 a))
20.6b	(cbrt (pow (fma a a (* b b)) 2.0))
20.6b	(cbrt (pow (fma a a (* b b)) 2.0))
20.6b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

65.0ms	(* (* b b) (+ 3.0 a))
4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
4.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series842.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (* b b) (+ 3.0 a))
271.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
255.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
255.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.0s

Counts

89 → 89

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	109	1189
1	283	1158
2	1737	1035
done	5001	1026

prune483.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

10.5b	(cbrt (fma a a (* b b)))
16.4b	(cbrt (pow (* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b)))) 2.0))
20.6b	(cbrt (pow (fma a a (* b b)) 2.0))
20.6b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite10.0ms

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:

1.0ms	(cbrt (fma a a (* b b)))
3.0ms	(cbrt (pow (* (cbrt (fma a a (* b b))) (cbrt (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))

series812.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(cbrt (fma a a (* b b)))
216.0ms	(cbrt (pow (* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b)))) 2.0))
245.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
214.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.0s

Counts

74 → 74

Iterations

Useful iterations: 3 (436.0ms)

Iter	Nodes	Cost
0	112	1202
1	211	1189
2	465	1077
3	1525	1065
done	5000	1065

prune720.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize91.0ms

Local error

Found 4 expressions with local error:

20.6b	(cbrt (pow (fma a a (* b b)) 2.0))
20.6b	(cbrt (pow (fma a a (* b b)) 2.0))
20.6b	(cbrt (pow (fma a a (* b b)) 2.0))
20.6b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite17.0ms

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:

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

series978.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
211.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
231.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
284.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.5s

Counts

80 → 80

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	58	1188
1	105	1172
2	228	1064
3	656	1052
4	2741	1052
done	5000	1052

prune795.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes229.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	26
1	18	26
done	18	26

end0.0ms

sample3.7s

Algorithm

intervals

Results

3.0s

20583×

body

valid