Details

sample90.0ms

Algorithm

intervals

Results

56.0ms

650×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (369.0ms)

Iter	Nodes	Cost
0	18	29
1	82	27
2	1107	26
done	5000	26

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

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))
0.1b	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.4b	(pow (fma a a (* b b)) 2.0)
0.4b	(* (* b b) (+ 3.0 a))

rewrite54.0ms

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)
49.0ms	(* (* b b) (+ 3.0 a))

series456.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
86.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
172.0ms	(pow (fma a a (* b b)) 2.0)
58.0ms	(* (* b b) (+ 3.0 a))

simplify1.8s

Counts

77 → 77

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	136	1157
1	812	1107
done	5001	969

prune361.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* b b) (+ 3.0 a))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite66.0ms

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:

50.0ms	(* (* 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))
5.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series799.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (* b b) (+ 3.0 a))
247.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
238.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
258.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.9s

Counts

89 → 89

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	109	1189
1	596	1152
done	5000	1026

prune677.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

9.3b	(cbrt (pow (hypot b a) 2.0))
9.3b	(cbrt (pow (hypot b a) 2.0))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))
19.6b	(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 b a) 2.0))
2.0ms	(cbrt (pow (hypot b a) 2.0))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

259.0ms	(cbrt (pow (hypot b a) 2.0))
277.0ms	(cbrt (pow (hypot b a) 2.0))
281.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
273.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify5.6s

Counts

80 → 80

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	103	1032
1	282	1016
2	3383	924
done	5000	924

prune775.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

9.3b	(cbrt (fma a a (* b b)))
14.2b	(cbrt (pow (* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b)))) 2.0))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite9.0ms

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))

series912.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (fma a a (* b b)))
270.0ms	(cbrt (pow (* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b)))) 2.0))
240.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
262.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify4.5s

Counts

74 → 74

Iterations

Useful iterations: 2 (2.7s)

Iter	Nodes	Cost
0	112	1202
1	322	1189
2	4586	1065
done	5000	1065

prune767.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes269.0ms

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 (0.0ms)

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

end0.0ms

sample4.4s

Algorithm

intervals

Results

3.6s

20563×

body

valid