Details

sample122.0ms

Algorithm

intervals

Results

47.0ms	69×	body	1280	valid
27.0ms	60×	body	640	valid
19.0ms	193×	body	80	valid
10.0ms	29×	body	320	valid
2.0ms	9×	body	160	valid

simplify33.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 30.0b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.4b	(* (/ (pow t 3.0) (* l l)) (sin k))
13.7b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
14.0b	(/ (pow t 3.0) (* l l))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

91×	`associate-*l/`
50×	`frac-times`
28×	`tan-quot`
26×	`associate-l`
20×	`associate-/r` `-commutative`
18×	`sqr-pow`
14×	`flip3-+` `flip-+`
10×	`frac-2neg` `clear-num` `associate-/l*`
8×	`times-frac`
6×	`associate-*r/`
4×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `div-inv`

Counts

4 → 94

Calls

4 calls:

9.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
7.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
16.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
4.0ms	(/ (pow t 3.0) (* l l))

series1.4s

Counts

4 → 12

Calls

4 calls:

323.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
251.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
642.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
182.0ms	(/ (pow t 3.0) (* l l))

simplify123.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	781	1341
1	4317	1335
2	5002	1335

prune456.0ms

Filtered

106 candidates to 83 candidates (78.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 14.7b

Counts

107 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (/ (* (/ (pow t 3.0) l) (sin k)) l) (tan k))
2.8b	(/ (pow t 3.0) l)
5.1b	(/ (* (/ (pow t 3.0) l) (sin k)) l)
13.7b	(* (* (/ (* (/ (pow t 3.0) l) (sin k)) l) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

97×	`associate-*l/`
82×	`frac-times`
44×	`tan-quot`
37×	`associate-/l*`
36×	`associate-/l/`
22×	`flip3-+` `flip-+`
19×	`frac-2neg` `clear-num`
14×	`associate-l`
13×	`div-inv`
12×	`*-commutative`
10×	`sqr-pow`
6×	`associate-*r/`
4×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in`

Counts

4 → 114

Calls

4 calls:

9.0ms	(* (/ (* (/ (pow t 3.0) l) (sin k)) l) (tan k))
3.0ms	(/ (pow t 3.0) l)
7.0ms	(/ (* (/ (pow t 3.0) l) (sin k)) l)
17.0ms	(* (* (/ (* (/ (pow t 3.0) l) (sin k)) l) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (/ (* (/ (pow t 3.0) l) (sin k)) l) (tan k))
164.0ms	(/ (pow t 3.0) l)
253.0ms	(/ (* (/ (pow t 3.0) l) (sin k)) l)
663.0ms	(* (* (/ (* (/ (pow t 3.0) l) (sin k)) l) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1130	1765
1	5001	1758

prune587.0ms

Filtered

126 candidates to 109 candidates (86.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	126	10	136

Merged error: 14.7b

Counts

136 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (/ (pow t 3.0) l) (sin k))
2.8b	(/ (pow t 3.0) l)
7.7b	(/ (* (* (/ (pow t 3.0) l) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (sin k)) (cos k)))
13.1b	(* (* (/ (pow t 3.0) l) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

39×	`associate-*l/`
27×	`associate-l`
17×	`*-commutative`
16×	`frac-times`
15×	`times-frac`
14×	`div-inv` `associate-/l/`
13×	`associate-/l*`
10×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
8×	`sqr-pow`
4×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-*r/`
3×	`associate-/r*` `associate-/r/`

Counts

4 → 79

Calls

4 calls:

5.0ms	(* (/ (pow t 3.0) l) (sin k))
3.0ms	(/ (pow t 3.0) l)
20.0ms	(/ (* (* (/ (pow t 3.0) l) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (sin k)) (cos k)))
10.0ms	(* (* (/ (pow t 3.0) l) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

211.0ms	(* (/ (pow t 3.0) l) (sin k))
170.0ms	(/ (pow t 3.0) l)
620.0ms	(/ (* (* (/ (pow t 3.0) l) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (sin k)) (cos k)))
456.0ms	(* (* (/ (pow t 3.0) l) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify115.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	735	1046
1	4177	1035
2	5001	1035

prune460.0ms

Filtered

91 candidates to 82 candidates (90.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	89	12	101

Merged error: 12.1b

Counts

101 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ (* (pow t 3) (sin k)) l)
6.2b	(* t (* (pow k 2) (sin k)))
7.7b	(/ (- (+ (* 2.0 (* (pow (/ 1 (pow -1 3.0)) 1.0) (/ (* (pow t 3) (sin k)) l))) (* (pow (/ 1 (pow -1 3.0)) 1.0) (/ (* t (* (pow k 2) (sin k))) l)))) (* (/ l (sin k)) (cos k)))
8.1b	(/ (* t (* (pow k 2) (sin k))) l)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

222×	`associate-*r/`
103×	`associate-/l*`
82×	`associate-/l/` `distribute-neg-frac`
80×	`frac-add`
72×	`associate-r`
53×	`*-commutative`
48×	`associate-l`
40×	`clear-num`
25×	`div-inv`
22×	`frac-2neg`
21×	`sqr-pow`
18×	`un-div-inv`
16×	`distribute-rgt-out`
15×	`times-frac`
11×	`unpow3`
10×	`unpow2`
8×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`neg-mul-1`
3×	`associate-l/` `associate-/r` `associate-/r/`
1×	`neg-sub0` `flip3-+` `div-sub` `distribute-frac-neg` `flip-+`

Counts

4 → 134

Calls

4 calls:

9.0ms	(/ (* (pow t 3) (sin k)) l)
5.0ms	(* t (* (pow k 2) (sin k)))
32.0ms	(/ (- (+ (* 2.0 (* (pow (/ 1 (pow -1 3.0)) 1.0) (/ (* (pow t 3) (sin k)) l))) (* (pow (/ 1 (pow -1 3.0)) 1.0) (/ (* t (* (pow k 2) (sin k))) l)))) (* (/ l (sin k)) (cos k)))
7.0ms	(/ (* t (* (pow k 2) (sin k))) l)

series1.9s

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (* (pow t 3) (sin k)) l)
72.0ms	(* t (* (pow k 2) (sin k)))
1.6s	(/ (- (+ (* 2.0 (* (pow (/ 1 (pow -1 3.0)) 1.0) (/ (* (pow t 3) (sin k)) l))) (* (pow (/ 1 (pow -1 3.0)) 1.0) (/ (* t (* (pow k 2) (sin k))) l)))) (* (/ l (sin k)) (cos k)))
99.0ms	(/ (* t (* (pow k 2) (sin k))) l)

simplify46.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1012	1861
1	5002	1841

prune1.1s

Filtered

146 candidates to 140 candidates (95.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	136	10	146
Fresh	2	7	9
Picked	1	0	1
Done	2	0	2
Total	141	17	158

Merged error: 5.4b

Counts

158 → 17

regimes421.0ms

Accuracy

41% (3.0b remaining)

Error of 9.9b against oracle of 6.8b and baseline of 12.0b

bsearch118.0ms

Steps

Iters	Range		Point
8	3.0426970750548807e+44	3.932746772352918e+48	3.8548763861618076e+48

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	43
1	79	43
2	86	43
3	94	43
4	100	43
5	100	43

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	2070×	body	1280	valid
783.0ms	1700×	body	640	valid
621.0ms	5961×	body	80	valid
273.0ms	832×	body	320	valid
91.0ms	410×	body	160	valid