Details

sample81.0ms

Algorithm

intervals

Results

55.0ms

709×

body

valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (59.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b	(* (* a a) (- 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.4b	(* (* b b) (+ 3.0 a))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`associate-*r/` `prod-diff`
17×	`pow1` `add-exp-log`
16×	`add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-r`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

103.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
48.0ms	(* (* a a) (- 1.0 a))
11.0ms	(pow (+ (* a a) (* b b)) 2.0)
54.0ms	(* (* b b) (+ 3.0 a))

series381.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
65.0ms	(* (* a a) (- 1.0 a))
166.0ms	(pow (+ (* a a) (* b b)) 2.0)
37.0ms	(* (* b b) (+ 3.0 a))

simplify2.5s

Counts

132 → 132

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	271	2229
1	747	1890
2	2835	1671
done	5001	1645

prune584.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* b b) (+ 3.0 a))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite71.0ms

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:

56.0ms	(* (* 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))

series793.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* b b) (+ 3.0 a))
228.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
260.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
241.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify3.1s

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

prune593.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

11.5b	(cbrt (pow (hypot a b) 2.0))
11.5b	(cbrt (pow (hypot a b) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite14.0ms

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:

4.0ms	(cbrt (pow (hypot a b) 2.0))
3.0ms	(cbrt (pow (hypot a 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))

series914.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(cbrt (pow (hypot a b) 2.0))
225.0ms	(cbrt (pow (hypot a b) 2.0))
256.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
194.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.1s

Counts

80 → 80

Iterations

Useful iterations: 3 (179.0ms)

Iter	Nodes	Cost
0	98	1032
1	176	1016
2	344	936
3	806	924
4	2188	924
done	5001	924

prune641.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (pow (sqrt (hypot a b)) 2.0))
11.5b	(cbrt (pow (hypot a b) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

6.0ms	(cbrt (pow (sqrt (hypot a b)) 2.0))
4.0ms	(cbrt (pow (hypot a 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))

series895.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(cbrt (pow (sqrt (hypot a b)) 2.0))
232.0ms	(cbrt (pow (hypot a b) 2.0))
191.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
236.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.1s

Counts

83 → 83

Iterations

Useful iterations: 3 (301.0ms)

Iter	Nodes	Cost
0	142	1107
1	253	1081
2	491	1000
3	1155	988
4	3129	988
done	5000	988

prune791.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes257.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	25	29
done	25	29

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.6s

20340×

body

valid