Details

sample142.0ms

Algorithm

intervals

Results

58.0ms	72×	body	1280	valid
27.0ms	52×	body	640	valid
22.0ms	190×	body	80	valid
11.0ms	31×	body	320	valid
3.0ms	12×	body	160	valid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	48	13
1	158	13
2	903	13
3	5001	13

prune5.0ms

Filtered

1 candidates to 0 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: 30.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

2.6b	(* (/ (pow t 3.0) (* l l)) (sin k))
3.9b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
10.8b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.6b	(/ (pow t 3.0) (* l l))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
58×	`prod-exp`
52×	`add-cbrt-cube`
26×	`cbrt-unprod`
24×	`div-exp`
21×	`add-sqr-sqrt`
20×	`pow1`
19×	`*-un-lft-identity`
17×	`times-frac`
16×	`associate-*l/`
14×	`add-cube-cbrt`
13×	`associate-l`
11×	`associate-r`
10×	`frac-times` `unpow-prod-down` `pow-prod-down`
8×	`tan-quot` `cbrt-undiv` `pow-to-exp` `pow-exp`
7×	`associate-/l*`
6×	`associate-*r/`
4×	`flip3-+` `flip-+` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r*`

Counts

4 → 144

Calls

4 calls:

9.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
11.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
22.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
10.0ms	(/ (pow t 3.0) (* l l))

series348.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
78.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
171.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
41.0ms	(/ (pow t 3.0) (* l l))

simplify122.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	857	1728
1	4784	1448
2	5001	1444

prune313.0ms

Filtered

156 candidates to 96 candidates (38.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	147	9	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	9	157

Merged error: 17.7b

Counts

157 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

4.5b	(* (/ (pow t (/ 3.0 2)) l) (sin k))
7.5b	(/ (pow t (/ 3.0 2)) l)
7.5b	(/ (pow t (/ 3.0 2)) l)
10.8b	(* (* (* (/ (pow t (/ 3.0 2)) l) (* (/ (pow t (/ 3.0 2)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-exp-log`
83×	`prod-exp`
66×	`times-frac`
62×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
52×	`add-cube-cbrt`
51×	`add-cbrt-cube`
36×	`div-exp`
35×	`associate-*l/`
34×	`unpow-prod-down`
29×	`frac-times`
27×	`cbrt-unprod`
26×	`associate-l`
20×	`pow1`
14×	`associate-/l*`
12×	`tan-quot` `pow-to-exp` `pow-exp` `sqr-pow`
11×	`associate-*r/` `pow-prod-down`
8×	`cbrt-undiv` `flip3-+` `associate-r` `flip-+`
6×	`associate-/r*`
4×	`add-log-exp` `unswap-sqr`
3×	`div-inv` `distribute-lft-out`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 211

Calls

4 calls:

9.0ms	(* (/ (pow t (/ 3.0 2)) l) (sin k))
5.0ms	(/ (pow t (/ 3.0 2)) l)
5.0ms	(/ (pow t (/ 3.0 2)) l)
30.0ms	(* (* (* (/ (pow t (/ 3.0 2)) l) (* (/ (pow t (/ 3.0 2)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series295.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ (pow t (/ 3.0 2)) l) (sin k))
37.0ms	(/ (pow t (/ 3.0 2)) l)
38.0ms	(/ (pow t (/ 3.0 2)) l)
166.0ms	(* (* (* (/ (pow t (/ 3.0 2)) l) (* (/ (pow t (/ 3.0 2)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1183	2812
1	5001	2503

prune579.0ms

Filtered

223 candidates to 153 candidates (31.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	218	5	223
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	221	11	232

Merged error: 15.9b

Counts

232 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

7.5b	(/ (pow t (/ 3.0 2)) l)
10.1b	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
10.1b	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
10.1b	(* (* (* (/ (pow t (/ 3.0 2)) l) (* (/ (pow t (/ 3.0 2)) l) (sin k))) (tan k)) (sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

128×	`add-exp-log`
79×	`prod-exp`
44×	`add-cbrt-cube`
39×	`*-un-lft-identity`
34×	`associate-*l/`
30×	`div-exp`
29×	`frac-times`
26×	`add-sqr-sqrt`
25×	`cbrt-unprod`
24×	`add-cube-cbrt`
21×	`times-frac`
20×	`pow1` `sqrt-div`
15×	`sqrt-prod`
12×	`tan-quot` `unpow-prod-down`
11×	`associate-*r/`
10×	`pow-to-exp` `flip3-+` `pow-prod-down` `pow-exp` `flip-+`
9×	`distribute-lft-out`
8×	`associate-r`
7×	`associate-/l*`
6×	`cbrt-undiv`
4×	`add-log-exp` `sqr-pow`
3×	`associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-l` `clear-num` `*-commutative` `div-inv`

Counts

4 → 153

Calls

4 calls:

5.0ms	(/ (pow t (/ 3.0 2)) l)
9.0ms	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
10.0ms	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
32.0ms	(* (* (* (/ (pow t (/ 3.0 2)) l) (* (/ (pow t (/ 3.0 2)) l) (sin k))) (tan k)) (sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series189.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (pow t (/ 3.0 2)) l)
7.0ms	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
7.0ms	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
137.0ms	(* (* (* (/ (pow t (/ 3.0 2)) l) (* (/ (pow t (/ 3.0 2)) l) (sin k))) (tan k)) (sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	870	2343
1	3929	2040
2	5002	2006

prune469.0ms

Filtered

165 candidates to 99 candidates (40.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	163	13	176

Merged error: 15.9b

Counts

176 → 13

localize38.0ms

Local error

Found 4 expressions with local error:

10.1b	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
10.1b	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
10.1b	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
10.1b	(* (* (* (/ (pow t (/ 3.0 2)) l) (* (/ (pow t (/ 3.0 2)) l) (sin k))) (tan k)) (sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-exp-log`
79×	`prod-exp`
42×	`add-cbrt-cube`
34×	`associate-*l/`
29×	`frac-times` `*-un-lft-identity`
27×	`div-exp`
25×	`cbrt-unprod`
22×	`sqrt-div`
21×	`pow1`
20×	`sqrt-prod`
12×	`tan-quot` `add-sqr-sqrt` `distribute-lft-out`
11×	`flip3-+` `associate-*r/` `flip-+`
10×	`pow-prod-down`
9×	`pow-to-exp` `add-cube-cbrt` `pow-exp`
8×	`associate-r`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate-l` `*-commutative`

Counts

4 → 125

Calls

4 calls:

10.0ms	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
10.0ms	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
10.0ms	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
31.0ms	(* (* (* (/ (pow t (/ 3.0 2)) l) (* (/ (pow t (/ 3.0 2)) l) (sin k))) (tan k)) (sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
8.0ms	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
7.0ms	(sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
138.0ms	(* (* (* (/ (pow t (/ 3.0 2)) l) (* (/ (pow t (/ 3.0 2)) l) (sin k))) (tan k)) (sqrt (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify89.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	746	2145
1	3403	1854
2	5002	1794

prune482.0ms

Filtered

137 candidates to 76 candidates (44.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	137	13	150

Merged error: 15.9b

Counts

150 → 13

regimes671.0ms

Accuracy

0% (2.5b remaining)

Error of 19.6b against oracle of 17.1b and baseline of 19.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	24
1	30	24

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	2145×	body	1280	valid
914.0ms	1753×	body	640	valid
712.0ms	5973×	body	80	valid
311.0ms	812×	body	320	valid
101.0ms	399×	body	160	valid

Details

sample142.0ms

simplify32.0ms

prune5.0ms

localize21.0ms

rewrite58.0ms

series348.0ms

simplify122.0ms

prune313.0ms

localize26.0ms

rewrite61.0ms

series295.0ms

simplify57.0ms

prune579.0ms

localize30.0ms

rewrite64.0ms

series189.0ms

simplify102.0ms

prune469.0ms

localize38.0ms

rewrite67.0ms

series161.0ms

simplify89.0ms

prune482.0ms

regimes671.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling