Details

sample130.0ms

Algorithm

intervals

Results

51.0ms	75×	body	1280	valid
33.0ms	63×	body	640	valid
19.0ms	187×	body	80	valid
6.0ms	19×	body	320	valid
3.0ms	13×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	48	13
1	161	13
2	944	13
3	5002	12

prune11.0ms

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: 32.0b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (pow t 3.0) (sin k))
3.0b	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
8.2b	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
22.6b	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

50×	`frac-times`
42×	`associate-/l/`
31×	`associate-/l*`
27×	`clear-num`
26×	`frac-2neg`
21×	`associate-/r` `-commutative`
11×	`div-inv`
10×	`associate-l` `associate-*l/`
8×	`sqr-pow`
5×	`associate-*r/`
2×	`tan-quot` `associate-/r/`
1×	`associate-r` `un-div-inv`

Counts

4 → 88

Calls

4 calls:

3.0ms	(* (pow t 3.0) (sin k))
6.0ms	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
3.0ms	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
10.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.4s

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (pow t 3.0) (sin k))
321.0ms	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
71.0ms	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
837.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify90.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	640	986
1	3532	970
2	5001	969

prune376.0ms

Filtered

100 candidates to 71 candidates (71.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	90	10	100
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	91	11	102

Merged error: 22.9b

Counts

102 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (tan k) (pow t 3.0))
3.8b	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
7.8b	(/ (* (/ 2.0 (sin k)) l) (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))
17.0b	(* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

22×	`associate-l`
18×	`times-frac` `*-commutative`
14×	`associate-*l/` `div-inv`
11×	`associate-r`
9×	`tan-quot` `clear-num`
8×	`associate-/r/`
7×	`frac-2neg`
6×	`frac-times` `associate-r/` `associate-/r` `sqr-pow`
3×	`associate-/l/` `associate-/l*`
2×	`un-div-inv`

Counts

4 → 60

Calls

4 calls:

3.0ms	(* (tan k) (pow t 3.0))
2.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
10.0ms	(/ (* (/ 2.0 (sin k)) l) (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))
6.0ms	(* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))

series1.1s

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (tan k) (pow t 3.0))
108.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
487.0ms	(/ (* (/ 2.0 (sin k)) l) (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))
335.0ms	(* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))

simplify59.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	523	711
1	2344	699
2	5002	696

prune366.0ms

Filtered

72 candidates to 68 candidates (94.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 21.2b

Counts

83 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (tan k) (pow t 3.0))
3.8b	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
7.7b	(/ (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (* (/ 2.0 (sin k)) l))
17.0b	(* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

22×	`associate-l`
18×	`times-frac` `*-commutative`
14×	`associate-*l/` `div-inv`
11×	`associate-r`
9×	`tan-quot` `clear-num`
8×	`associate-/l/`
7×	`frac-2neg`
6×	`frac-times` `associate-r/` `associate-/l` `sqr-pow`
3×	`associate-/r*` `associate-/r/`
2×	`un-div-inv`

Counts

4 → 60

Calls

4 calls:

3.0ms	(* (tan k) (pow t 3.0))
2.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
10.0ms	(/ (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (* (/ 2.0 (sin k)) l))
6.0ms	(* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))

series1.1s

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (tan k) (pow t 3.0))
120.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
476.0ms	(/ (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (* (/ 2.0 (sin k)) l))
333.0ms	(* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))

simplify64.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	489	638
1	2465	635
2	5001	635

prune370.0ms

Filtered

72 candidates to 66 candidates (91.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	73	9	82

Merged error: 21.2b

Counts

82 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (sin k))
3.8b	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
5.7b	(/ (* 2.0 l) (* (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (sin k)))
17.0b	(* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

39×	`associate-l`
31×	`associate-*l/`
23×	`*-commutative`
16×	`times-frac`
12×	`tan-quot`
11×	`clear-num`
10×	`associate-r`
9×	`frac-times` `associate-*r/`
8×	`frac-2neg` `associate-/r*` `associate-/r/`
7×	`div-inv`
5×	`sqr-pow`
3×	`un-div-inv`
2×	`associate-/l*`

Counts

4 → 68

Calls

4 calls:

9.0ms	(* (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (sin k))
2.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
11.0ms	(/ (* 2.0 l) (* (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (sin k)))
6.0ms	(* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))

series1.2s

Counts

4 → 12

Calls

4 calls:

371.0ms	(* (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (sin k))
109.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
382.0ms	(/ (* 2.0 l) (* (* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (sin k)))
344.0ms	(* (* (tan k) (pow t 3.0)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))

simplify57.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	548	724
1	2266	711
2	5001	707

prune363.0ms

Filtered

80 candidates to 76 candidates (95.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	79	10	89

Merged error: 14.4b

Counts

89 → 10

regimes293.0ms

Accuracy

85.3% (1.9b remaining)

Error of 16.8b against oracle of 14.9b and baseline of 27.8b

bsearch170.0ms

Steps

Iters	Range		Point
4	3.1709609006244933e-124	5.103003588046316e-124	5.023537655901242e-124
6	-5.3956228688621665e-61	-1.0066585507084447e-61	-1.0511429488171726e-61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	44
1	64	44

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	2089×	body	1280	valid
825.0ms	5939×	body	80	valid
816.0ms	1722×	body	640	valid
283.0ms	849×	body	320	valid
93.0ms	413×	body	160	valid