Details

sample86.0ms

Algorithm

intervals

Results

31.0ms	47×	body	1280	valid
18.0ms	40×	body	640	valid
12.0ms	138×	body	80	valid
7.0ms	24×	body	320	valid
3.0ms	7×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	8
2	15	8
done	15	8

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (cos y)) (* z (sin y)))
0.1b	(* x (cos y))
0.1b	(* z (sin y))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

3 → 54

Calls

3 calls:

10.0ms	(+ (* x (cos y)) (* z (sin y)))
9.0ms	(* x (cos y))
10.0ms	(* z (sin y))

series177.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(+ (* x (cos y)) (* z (sin y)))
39.0ms	(* x (cos y))
52.0ms	(* z (sin y))

simplify2.8s

Counts

63 → 63

Iterations

Useful iterations: 2 (134.0ms)

Iter	Nodes	Cost
0	87	494
1	206	449
2	713	417
3	3984	417
done	5000	417

prune329.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos y))
0.3b	(cbrt (cos y))
0.3b	(cbrt (cos y))
0.3b	(* (cbrt (cos y)) (cbrt (cos y)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

2.0ms	(cbrt (cos y))
2.0ms	(cbrt (cos y))
2.0ms	(cbrt (cos y))
35.0ms	(* (cbrt (cos y)) (cbrt (cos y)))

series760.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (cos y))
157.0ms	(cbrt (cos y))
168.0ms	(cbrt (cos y))
296.0ms	(* (cbrt (cos y)) (cbrt (cos y)))

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	68	726
1	152	651
2	643	551
done	5001	537

prune440.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (pow (cos y) 2) 1/3)
0.2b	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
0.2b	(pow (cos y) 2)
0.3b	(cbrt (cos y))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
14×	`unpow-prod-down`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`prod-exp`
9×	`pow-exp`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`cbrt-prod` `pow-unpow` `associate-r`
5×	`pow-to-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqr-pow`
2×	`pow-pow` `unpow1/3` `unpow2`
1×	`pow1/3` `associate-l` `pow-prod-down` `*-commutative`

Counts

4 → 87

Calls

4 calls:

12.0ms	(pow (pow (cos y) 2) 1/3)
59.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
6.0ms	(pow (cos y) 2)
3.0ms	(cbrt (cos y))

series428.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(pow (pow (cos y) 2) 1/3)
48.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
30.0ms	(pow (cos y) 2)
142.0ms	(cbrt (cos y))

simplify1.4s

Counts

99 → 99

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	132	964
1	364	802
2	1726	712
done	5000	679

prune462.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos y) 2)
0.2b	(pow (cos y) 2)
0.3b	(cbrt (cos y))
0.3b	(* (pow (pow (cos y) 2) 1/6) (pow (pow (cos y) 2) 1/6))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

110×	`unpow-prod-down`
57×	`add-sqr-sqrt`
42×	`pow-exp`
36×	`add-exp-log` `unswap-sqr`
34×	`sqr-pow`
25×	`prod-exp`
22×	`pow-to-exp`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`unpow2`
12×	`swap-sqr` `associate-r` `associate-l`
6×	`pow1` `pow-unpow` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`pow-pow`
1×	`pow2` `pow1/3` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 165

Calls

4 calls:

3.0ms	(pow (cos y) 2)
3.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))
90.0ms	(* (pow (pow (cos y) 2) 1/6) (pow (pow (cos y) 2) 1/6))

series390.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos y) 2)
23.0ms	(pow (cos y) 2)
127.0ms	(cbrt (cos y))
222.0ms	(* (pow (pow (cos y) 2) 1/6) (pow (pow (cos y) 2) 1/6))

simplify1.6s

Counts

177 → 177

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	172	2777
1	407	1948
2	1958	1531
done	5001	1510

prune609.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

regimes261.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	18	17
done	18	17

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	1531×	body	1280	valid
1.2s	1259×	body	640	valid
1.0s	4296×	body	80	valid
196.0ms	584×	body	320	valid
73.0ms	330×	body	160	valid