Details

sample50.0ms

Algorithm

intervals

Results

17.0ms	42×	body	1280	valid
12.0ms	46×	body	640	valid
7.0ms	134×	body	80	valid
4.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

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`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 47

Calls

3 calls:

3.0ms	(+ (* x (cos y)) (* z (sin y)))
3.0ms	(* z (sin y))
4.0ms	(* x (cos y))

series141.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(+ (* x (cos y)) (* z (sin y)))
35.0ms	(* z (sin y))
40.0ms	(* x (cos y))

simplify70.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	183	248
1	698	227
2	2213	227
3	5001	227

prune143.0ms

Filtered

56 candidates to 39 candidates (69.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

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×	`add-cbrt-cube` `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 → 73

Calls

4 calls:

6.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))

series445.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
97.0ms	(cbrt (cos y))
95.0ms	(cbrt (cos y))
95.0ms	(cbrt (cos y))

simplify104.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	122	441
1	481	389
2	3180	357
3	5001	351

prune261.0ms

Filtered

85 candidates to 60 candidates (70.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
22×	`add-sqr-sqrt`
19×	`unpow-prod-down`
18×	`associate-r`
16×	`prod-exp`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-cbrt-cube`
9×	`pow-exp`
7×	`pow1` `cbrt-unprod`
6×	`cbrt-prod` `unswap-sqr`
5×	`pow-to-exp` `sqr-pow`
4×	`associate-l` `add-log-exp`
3×	`pow-unpow` `unpow2`
2×	`unpow1/3` `*-commutative`
1×	`pow-pow` `pow1/3` `pow-prod-down`

Counts

4 → 90

Calls

4 calls:

12.0ms	(* x (pow (pow (cos y) 2) 1/3))
17.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
1.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))

series247.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* x (pow (pow (cos y) 2) 1/3))
40.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
17.0ms	(pow (cos y) 2)
96.0ms	(cbrt (cos y))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	320	572
1	1417	499
2	5002	468

prune296.0ms

Filtered

102 candidates to 62 candidates (60.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-exp-log`
55×	`prod-exp`
27×	`add-cbrt-cube` `cbrt-unprod`
21×	`associate-r`
17×	`unpow-prod-down`
15×	`pow-to-exp` `pow-exp`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`unpow1/3`
8×	`sqrt-prod`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-log-exp`
3×	`pow-unpow` `sqr-pow`
2×	`associate-l` `*-commutative` `unpow2`
1×	`pow-pow` `pow1/3` `pow-prod-down`

Counts

4 → 107

Calls

4 calls:

43.0ms	(* (* (* x (pow (fabs (cos y)) 1/3)) (pow (sqrt (pow (cos y) 2)) 1/3)) (cbrt (cos y)))
21.0ms	(* (* x (pow (fabs (cos y)) 1/3)) (pow (sqrt (pow (cos y) 2)) 1/3))
1.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))

series303.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (* (* x (pow (fabs (cos y)) 1/3)) (pow (sqrt (pow (cos y) 2)) 1/3)) (cbrt (cos y)))
88.0ms	(* (* x (pow (fabs (cos y)) 1/3)) (pow (sqrt (pow (cos y) 2)) 1/3))
22.0ms	(pow (cos y) 2)
94.0ms	(cbrt (cos y))

simplify67.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	463	1168
1	2259	955
2	5001	784

prune312.0ms

Filtered

119 candidates to 61 candidates (51.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes119.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	15
1	23	15

end0.0ms

sample1.5s

Algorithm

intervals

Results

626.0ms	1514×	body	1280	valid
318.0ms	1261×	body	640	valid
227.0ms	4302×	body	80	valid
125.0ms	632×	body	320	valid
34.0ms	291×	body	160	valid