Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	42×	body	1280	valid
9.0ms	34×	body	640	valid
8.0ms	134×	body	80	valid
6.0ms	32×	body	320	valid
2.0ms	14×	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))

rewrite6.0ms

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))

series120.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(fma x (sin y) (* z (cos y)))
41.0ms	(* z (cos y))

simplify51.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 1 (4.0ms)

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

prune100.0ms

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

localize12.0ms

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))

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)))
2.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))

series460.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
99.0ms	(cbrt (cos y))
100.0ms	(cbrt (cos y))
98.0ms	(cbrt (cos y))

simplify109.0ms

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

prune291.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	93	6	99

Merged error: 0.1b

Counts

99 → 6

localize16.0ms

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)))
0.3b	(pow (cos y) 2)
0.3b	(cbrt (cos y))

rewrite25.0ms

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))
10.0ms	(* (* z (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
2.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))

series260.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* z (pow (pow (cos y) 2) 1/3))
37.0ms	(* (* z (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
24.0ms	(pow (cos y) 2)
99.0ms	(cbrt (cos y))

simplify53.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (44.0ms)

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

prune337.0ms

Filtered

110 candidates to 69 candidates (62.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	109	7	116

Merged error: 0.1b

Counts

116 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* z (pow (pow (cos y) 2) 1/3)) (log (exp (cbrt (cos y)))))
0.2b	(log (exp (cbrt (cos y))))
0.3b	(pow (cos y) 2)
0.3b	(cbrt (cos y))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`log-pow`
12×	`exp-prod`
11×	`prod-exp` `add-cbrt-cube`
10×	`associate-r`
9×	`pow1` `cbrt-prod` `log-prod`
5×	`pow-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `pow-to-exp` `unpow-prod-down` `pow-unpow` `distribute-lft-in`
1×	`pow-pow` `unpow1/3` `pow1/3` `rem-log-exp` `associate-l` `pow-prod-down` `*-commutative` `unpow2` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

11.0ms	(* (* z (pow (pow (cos y) 2) 1/3)) (log (exp (cbrt (cos y)))))
3.0ms	(log (exp (cbrt (cos y))))
3.0ms	(pow (cos y) 2)
2.0ms	(cbrt (cos y))

series266.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* z (pow (pow (cos y) 2) 1/3)) (log (exp (cbrt (cos y)))))
104.0ms	(log (exp (cbrt (cos y))))
23.0ms	(pow (cos y) 2)
101.0ms	(cbrt (cos y))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	314	683
1	1318	566
2	5001	534

prune351.0ms

Filtered

102 candidates to 69 candidates (67.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	102	7	109

Merged error: 0.1b

Counts

109 → 7

regimes106.0ms

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

sample1.6s

Algorithm

intervals

Results

627.0ms	1500×	body	1280	valid
323.0ms	1270×	body	640	valid
234.0ms	4281×	body	80	valid
129.0ms	643×	body	320	valid
36.0ms	306×	body	160	valid