Details

sample52.0ms

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

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	19	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

localize9.0ms

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))

rewrite10.0ms

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×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 48

Calls

3 calls:

3.0ms	(- (* x (cos y)) (* z (sin y)))
3.0ms	(* z (sin y))
3.0ms	(* x (cos y))

series146.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(- (* x (cos y)) (* z (sin y)))
36.0ms	(* z (sin y))
41.0ms	(* x (cos y))

simplify58.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	174	254
1	636	233
2	2041	233
3	5001	233

prune142.0ms

Filtered

57 candidates to 39 candidates (68.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

series454.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
102.0ms	(cbrt (cos y))
97.0ms	(cbrt (cos y))
95.0ms	(cbrt (cos y))

simplify100.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (95.0ms)

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

prune253.0ms

Filtered

85 candidates to 60 candidates (70.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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))

rewrite33.0ms

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))

series249.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* x (pow (pow (cos y) 2) 1/3))
41.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
16.0ms	(pow (cos y) 2)
97.0ms	(cbrt (cos y))

simplify46.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

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

prune291.0ms

Filtered

102 candidates to 62 candidates (60.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow (pow (cos y) 2) 1/6)) (pow (pow (cos y) 2) (/ 1/3 2)))
0.3b	(pow (cos y) 2)
0.3b	(pow (cos y) 2)
0.3b	(cbrt (cos y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-exp-log`
55×	`prod-exp`
46×	`pow-exp`
24×	`pow-to-exp`
17×	`unpow-prod-down`
12×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`add-cbrt-cube`
6×	`pow1` `pow-unpow`
4×	`add-log-exp` `sqr-pow`
3×	`cbrt-prod` `cbrt-unprod` `unpow2`
2×	`pow-pow`
1×	`pow1/3` `associate-l` `*-commutative`

Counts

4 → 100

Calls

4 calls:

26.0ms	(* (* x (pow (pow (cos y) 2) 1/6)) (pow (pow (cos y) 2) (/ 1/3 2)))
1.0ms	(pow (cos y) 2)
1.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))

series223.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (* x (pow (pow (cos y) 2) 1/6)) (pow (pow (cos y) 2) (/ 1/3 2)))
16.0ms	(pow (cos y) 2)
16.0ms	(pow (cos y) 2)
97.0ms	(cbrt (cos y))

simplify51.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	343	707
1	1333	483
2	5002	475

prune272.0ms

Filtered

112 candidates to 54 candidates (48.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes125.0ms

Accuracy

1.3% (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	22	14
1	24	14
2	24	14

end0.0ms

sample1.5s

Algorithm

intervals

Results

634.0ms	1514×	body	1280	valid
324.0ms	1261×	body	640	valid
243.0ms	4302×	body	80	valid
112.0ms	632×	body	320	valid
35.0ms	291×	body	160	valid