Details

sample55.0ms

Algorithm

intervals

Results

24.0ms	52×	body	1280	valid
9.0ms	38×	body	640	valid
7.0ms	132×	body	80	valid
4.0ms	25×	body	320	valid
1.0ms	9×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	4
1	15	4
2	15	4

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x (sin y) (* z (cos y)))
0.1b	(* z (cos y))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

1.0ms	(fma x (sin y) (* z (cos y)))
4.0ms	(* z (cos y))

series112.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(fma x (sin y) (* z (cos y)))
35.0ms	(* z (cos y))

simplify51.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	85	150
1	280	130
2	715	130
3	1541	130
4	5001	130

prune94.0ms

Filtered

36 candidates to 28 candidates (77.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	31	5	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	31	6	37

Merged error: 0.1b

Counts

37 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos y)) (cbrt (cos y)))
0.4b	(cbrt (cos y))
0.4b	(cbrt (cos y))
0.4b	(cbrt (cos y))

rewrite12.0ms

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:

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

series444.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
97.0ms	(cbrt (cos y))
94.0ms	(cbrt (cos y))
95.0ms	(cbrt (cos y))

simplify103.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	128	471
1	500	419
2	3232	387
3	5002	381

prune259.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	91	8	99

Merged error: 0.0b

Counts

99 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (pow (pow (cos y) 2) 1/3))
0.2b	(* (* z (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
0.2b	(pow (cos y) 2)
0.4b	(cbrt (cos y))

rewrite24.0ms

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×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unpow2`
2×	`unpow1/3` `*-commutative`
1×	`pow-pow` `pow1/3` `pow-prod-down`

Counts

4 → 98

Calls

4 calls:

8.0ms	(* z (pow (pow (cos y) 2) 1/3))
9.0ms	(* (* z (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
3.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))

series246.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* z (pow (pow (cos y) 2) 1/3))
41.0ms	(* (* z (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
16.0ms	(pow (cos y) 2)
96.0ms	(cbrt (cos y))

simplify50.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	330	610
1	1447	529
2	5001	498

prune292.0ms

Filtered

110 candidates to 69 candidates (62.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	110	8	118

Merged error: 0.0b

Counts

118 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* z (pow (expm1 (log1p (pow (cos y) 2))) 1/3)) (cbrt (cos y)))
0.2b	(expm1 (log1p (pow (cos y) 2)))
0.2b	(pow (cos y) 2)
0.4b	(cbrt (cos y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

6.0ms	(* (* z (pow (expm1 (log1p (pow (cos y) 2))) 1/3)) (cbrt (cos y)))
1.0ms	(expm1 (log1p (pow (cos y) 2)))
3.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))

series384.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (* z (pow (expm1 (log1p (pow (cos y) 2))) 1/3)) (cbrt (cos y)))
115.0ms	(expm1 (log1p (pow (cos y) 2)))
16.0ms	(pow (cos y) 2)
100.0ms	(cbrt (cos y))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	246	459
1	1091	376
2	5002	342

prune234.0ms

Filtered

81 candidates to 56 candidates (69.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	81	8	89

Merged error: 0.0b

Counts

89 → 8

regimes113.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample1.5s

Algorithm

intervals

Results

588.0ms	1437×	body	1280	valid
330.0ms	1277×	body	640	valid
241.0ms	4344×	body	80	valid
113.0ms	610×	body	320	valid
40.0ms	332×	body	160	valid