Details

sample330.0ms

Algorithm

intervals

Results

28.0ms	64×	body	1280	valid
12.0ms	157×	body	80	valid
11.0ms	38×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	14×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

1.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))

series182.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
59.0ms	(/ 1.0 (tan B))

simplify61.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	246	416
1	694	382
2	2127	382
3	5002	377

prune236.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	68	10	78
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	70	10	80

Merged error: 0.0b

Counts

80 → 10

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (cos B) (sin B))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`fma-udef`

Counts

3 → 68

Calls

3 calls:

1.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ (cos B) (sin B))

series140.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
19.0ms	(/ (cos B) (sin B))

simplify62.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	241	480
1	721	438
2	2196	438
3	5001	433

prune202.0ms

Filtered

77 candidates to 60 candidates (77.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	76	11	87

Merged error: 0.0b

Counts

87 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
0.1b	(* x (cos B))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-l`
12×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
3×	`expm1-log1p-u` `prod-exp` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `sub-neg` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv`
1×	`frac-2neg` `associate-*l/` `clear-num`

Counts

3 → 97

Calls

3 calls:

3.0ms	(/ 1.0 (sin B))
8.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
4.0ms	(* x (cos B))

series136.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ 1.0 (sin B))
72.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
41.0ms	(* x (cos B))

simplify58.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	415	714
1	2094	633
2	5002	629

prune227.0ms

Filtered

106 candidates to 75 candidates (70.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	4	5	9
Picked	0	1	1
Done	1	0	1
Total	108	9	117

Merged error: 0.0b

Counts

117 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

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

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 B)) (cbrt (cos B)))
1.0ms	(cbrt (cos B))
1.0ms	(cbrt (cos B))
1.0ms	(cbrt (cos B))

series466.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (cbrt (cos B)) (cbrt (cos B)))
99.0ms	(cbrt (cos B))
99.0ms	(cbrt (cos B))
105.0ms	(cbrt (cos B))

simplify110.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	128	471
1	498	419
2	3230	387
3	5002	381

prune222.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Merged error: 0.0b

Counts

102 → 9

regimes79.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	6
1	14	6

end0.0ms

sample1.9s

Algorithm

intervals

Results

749.0ms	1738×	body	1280	valid
405.0ms	1461×	body	640	valid
313.0ms	4810×	body	80	valid
144.0ms	723×	body	320	valid
47.0ms	345×	body	160	valid