Details

sample127.0ms

Algorithm

intervals

Results

50.0ms	75×	body	1280	valid
32.0ms	63×	body	640	valid
19.0ms	187×	body	80	valid
6.0ms	19×	body	320	valid
3.0ms	13×	body	160	valid

simplify30.0ms

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: 33.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.6b	(* (/ (pow t 3.0) (* l l)) (sin k))
14.4b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
14.6b	(/ (pow t 3.0) (* l l))

rewrite47.0ms

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))
21.0ms	(* (* (* (/ (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:

320.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
245.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
631.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
179.0ms	(/ (pow t 3.0) (* l l))

simplify112.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (21.0ms)

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

prune449.0ms

Filtered

106 candidates to 83 candidates (78.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	12	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	12	107

Merged error: 16.2b

Counts

107 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (/ (* (/ (pow t 3.0) l) (sin k)) l) (tan k))
4.6b	(/ (* (/ (pow t 3.0) l) (sin k)) l)
5.2b	(/ (pow t 3.0) l)
14.4b	(* (* (/ (* (/ (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))
7.0ms	(/ (* (/ (pow t 3.0) l) (sin k)) l)
3.0ms	(/ (pow t 3.0) 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:

319.0ms	(* (/ (* (/ (pow t 3.0) l) (sin k)) l) (tan k))
250.0ms	(/ (* (/ (pow t 3.0) l) (sin k)) l)
162.0ms	(/ (pow t 3.0) l)
620.0ms	(* (* (/ (* (/ (pow t 3.0) l) (sin k)) l) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1130	1765
1	5001	1758

prune569.0ms

Filtered

126 candidates to 107 candidates (84.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	127	11	138

Merged error: 15.8b

Counts

138 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (/ (pow t 3.0) l) (sin k))
3.8b	(* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l))
5.2b	(/ (pow t 3.0) l)
18.1b	(* (* (/ (pow t 3.0) l) (sin k)) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

108×	`frac-times`
84×	`associate-*l/`
42×	`clear-num`
39×	`associate-*r/`
36×	`frac-2neg`
30×	`flip3-+` `flip-+`
18×	`tan-quot` `associate-/l/` `associate-/l*` `sqr-pow`
6×	`un-div-inv`
5×	`associate-r` `associate-l` `*-commutative` `div-inv`

Counts

4 → 113

Calls

4 calls:

4.0ms	(* (/ (pow t 3.0) l) (sin k))
7.0ms	(* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l))
3.0ms	(/ (pow t 3.0) l)
14.0ms	(* (* (/ (pow t 3.0) l) (sin k)) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l)))

series1.1s

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (/ (pow t 3.0) l) (sin k))
92.0ms	(* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l))
163.0ms	(/ (pow t 3.0) l)
632.0ms	(* (* (/ (pow t 3.0) l) (sin k)) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l)))

simplify132.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	931	1961
1	4880	1929
2	5003	1929

prune597.0ms

Filtered

125 candidates to 107 candidates (85.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	124	12	136

Merged error: 15.7b

Counts

136 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (pow t 3.0) (sin k))
3.8b	(* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l))
5.7b	(* (* (* (pow t 3.0) (sin k)) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l))) (/ 1 l))
18.1b	(* (* (pow t 3.0) (sin k)) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

102×	`associate-*r/`
93×	`frac-times`
41×	`clear-num`
34×	`frac-2neg`
30×	`flip3-+` `flip-+`
27×	`associate-*l/`
18×	`tan-quot` `associate-/l/`
17×	`associate-l`
10×	`associate-r`
9×	`*-commutative`
8×	`un-div-inv`
4×	`div-inv`
3×	`sqr-pow`

Counts

4 → 116

Calls

4 calls:

4.0ms	(* (pow t 3.0) (sin k))
7.0ms	(* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l))
21.0ms	(* (* (* (pow t 3.0) (sin k)) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l))) (/ 1 l))
12.0ms	(* (* (pow t 3.0) (sin k)) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l)))

series1.2s

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (pow t 3.0) (sin k))
91.0ms	(* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l))
480.0ms	(* (* (* (pow t 3.0) (sin k)) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l))) (/ 1 l))
478.0ms	(* (* (pow t 3.0) (sin k)) (* (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0) (/ (tan k) l)))

simplify119.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	829	1837
1	4589	1816
2	5001	1816

prune475.0ms

Filtered

128 candidates to 95 candidates (74.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	128	12	140

Merged error: 13.2b

Counts

140 → 12

regimes314.0ms

Accuracy

70.4% (2.9b remaining)

Error of 16.2b against oracle of 13.3b and baseline of 23.2b

bsearch315.0ms

Steps

Iters	Range		Point
10	1.024914740653053e-171	5.595930565227217e-159	1.3710261062242033e-160
8	-0.023919459482322245	-3.810242810899289e-05	-3.8655696603753476e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	55
1	75	55

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	2089×	body	1280	valid
798.0ms	1722×	body	640	valid
616.0ms	5939×	body	80	valid
280.0ms	849×	body	320	valid
90.0ms	413×	body	160	valid