Details

sample76.0ms

Algorithm

intervals

Results

51.0ms

650×

body

valid

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	18	29
1	53	27
2	172	26
3	509	26
4	1497	26
5	3573	26
done	5000	26

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

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))

rewrite63.0ms

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

series397.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
69.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
156.0ms	(pow (fma a a (* b b)) 2.0)
49.0ms	(* (* b b) (+ 3.0 a))

simplify3.8s

Counts

77 → 77

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	136	1157
1	320	1101
2	1101	970
3	4265	962
done	5000	962

prune491.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize64.0ms

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))

rewrite90.0ms

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:

74.0ms	(* (* 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))

series697.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* b b) (+ 3.0 a))
194.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
215.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
230.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.9s

Counts

89 → 89

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	109	1189
1	258	1158
2	850	1035
3	3163	1026
done	5000	1026

prune504.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

12.1b	(sqrt (pow (fma a a (* b b)) 2.0))
12.1b	(sqrt (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))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`cbrt-prod` `unpow-prod-down` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
6×	`rem-sqrt-square` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 76

Calls

4 calls:

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

series879.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(sqrt (pow (fma a a (* b b)) 2.0))
247.0ms	(sqrt (pow (fma a a (* b b)) 2.0))
206.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
218.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.7s

Counts

88 → 88

Iterations

Useful iterations: 3 (148.0ms)

Iter	Nodes	Cost
0	82	1174
1	145	1114
2	284	1030
3	623	1024
4	1616	1024
5	4529	1024
done	5001	1024

prune571.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

localize60.0ms

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))

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))

series662.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (fma a a (* b b)))
183.0ms	(cbrt (pow (* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b)))) 2.0))
176.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
186.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.7s

Counts

74 → 74

Iterations

Useful iterations: 3 (211.0ms)

Iter	Nodes	Cost
0	112	1202
1	210	1189
2	427	1077
3	1007	1065
4	2703	1065
done	5000	1065

prune503.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes215.0ms

Accuracy

0% (0.2b 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

sample2.9s

Algorithm

intervals

Results

2.3s

20563×

body

valid