Details

sample29.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	60	25
1	296	23
2	1711	23
3	5001	23

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: 52.1b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
0.1b	(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
41.0b	(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
41.3b	(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

14×	`associate-*l/`
10×	`associate-/l*`
9×	`associate-/r/` `*-commutative`
6×	`associate-l` `associate-/l/`
5×	`div-inv`
4×	`flip3--` `flip--` `fma-udef`
3×	`frac-2neg` `clear-num`
2×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `associate-*r/`
1×	`flip3-+` `associate-/r*` `flip-+`

Counts

4 → 40

Calls

4 calls:

11.0ms	(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
13.0ms	(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
19.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
15.0ms	(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series3.3s

Counts

4 → 12

Calls

4 calls:

261.0ms	(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
494.0ms	(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
738.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.8s	(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify57.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	455	755
1	2102	692
2	5001	656

prune212.0ms

Filtered

52 candidates to 44 candidates (84.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	48	6	54

Merged error: 38.8b

Counts

54 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
9.0b	(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i))
32.9b	(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
43.5b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

97×	`frac-times`
36×	`clear-num`
35×	`frac-2neg`
32×	`associate-*l/`
31×	`flip3-+` `flip-+`
26×	`associate-/r*`
19×	`associate-*r/`
16×	`*-commutative`
11×	`associate-l`
6×	`associate-/r/`
5×	`div-inv`
4×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in`
1×	`associate-r` `un-div-inv`

Counts

4 → 112

Calls

4 calls:

13.0ms	(* (* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
8.0ms	(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i))
4.0ms	(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
3.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

series1.1s

Counts

4 → 12

Calls

4 calls:

721.0ms	(* (* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
110.0ms	(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i))
134.0ms	(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
152.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

simplify119.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	775	2375
1	4269	2218
2	5001	2214

prune435.0ms

Filtered

124 candidates to 99 candidates (79.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	123	7	130

Merged error: 38.8b

Counts

130 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))
0.0b	(* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))
9.0b	(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i))
32.9b	(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

7×	`flip3-+` `flip-+`
6×	`distribute-rgt-in` `frac-times` `distribute-lft-in`
5×	`+-commutative`
4×	`associate-+l+` `frac-2neg` `clear-num` `associate-/r/` `fma-udef`
3×	`associate-l` `associate-*l/`
2×	`associate-+r+` `associate-r/` `-commutative` `div-inv`
1×	`pow2` `neg-sub0` `associate-+l-` `neg-mul-1` `fma-def`

Counts

4 → 39

Calls

4 calls:

4.0ms	(+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))
2.0ms	(* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))
8.0ms	(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i))
4.0ms	(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))
63.0ms	(* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))
107.0ms	(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i))
137.0ms	(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	400	518
1	1619	476
2	5001	467

prune161.0ms

Filtered

51 candidates to 41 candidates (80.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	51	7	58

Merged error: 38.8b

Counts

58 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))) (+ (+ alpha beta) i))
4.6b	(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))) (+ (+ alpha beta) i)))
32.9b	(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
43.5b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

101×	`frac-times`
35×	`frac-2neg` `clear-num`
32×	`flip3-+` `associate-/r*` `flip-+`
28×	`associate-*l/`
27×	`associate-*r/`
20×	`distribute-rgt-in` `distribute-lft-in`
19×	`*-commutative`
12×	`+-commutative` `associate-+l+`
5×	`associate-l` `div-inv`
4×	`associate-/r/`
3×	`associate-r`

Counts

4 → 131

Calls

4 calls:

7.0ms	(* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))) (+ (+ alpha beta) i))
14.0ms	(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))) (+ (+ alpha beta) i)))
4.0ms	(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
3.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

series1.3s

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))) (+ (+ alpha beta) i))
711.0ms	(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))) (+ (+ alpha beta) i)))
135.0ms	(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
294.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

simplify58.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	915	3120
1	5002	3078

prune412.0ms

Filtered

143 candidates to 104 candidates (72.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	140	3	143
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	143	7	150

Merged error: 38.8b

Counts

150 → 7

regimes121.0ms

Accuracy

19.6% (3.1b remaining)

Error of 38.8b against oracle of 35.8b and baseline of 39.6b

bsearch54.0ms

Steps

Iters	Range		Point
7	1.3375767335112228e+103	3.017176833939405e+104	2.966117077546274e+104

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	33
1	40	33

end0.0ms

sample667.0ms

Algorithm

intervals

Results

349.0ms	8000×	body	80	valid
129.0ms	8000×	pre	80	true