Details

sample30.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	26
1	283	26
2	1620	26
3	5003	26

prune3.0ms

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: 52.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.7b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
45.1b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

36×	`flip3-+` `flip-+`
33×	`associate-/l/`
30×	`associate-*r/`
25×	`-commutative` `associate-/l`
24×	`frac-times`
22×	`distribute-rgt-in` `distribute-lft-in`
18×	`associate-/r/`
16×	`associate-+r+` `times-frac`
14×	`+-commutative` `associate-l`
12×	`associate-+l+` `associate-*l/`
4×	`associate-/r*`
3×	`frac-2neg` `clear-num` `div-inv`
1×	`pow2` `flip3--` `flip--`

Counts

4 → 121

Calls

4 calls:

8.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
20.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.1s

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
101.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
743.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
170.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify110.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	910	2136
1	4336	2070
2	5001	2064

prune378.0ms

Filtered

133 candidates to 93 candidates (69.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	128	5	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	5	134

Merged error: 35.6b

Counts

134 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))))
34.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.0b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
35.7b	(/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

108×	`associate-/l/`
70×	`frac-times`
40×	`associate-*r/`
36×	`flip3-+` `flip-+`
34×	`associate-/l*`
33×	`clear-num`
31×	`frac-2neg`
15×	`*-commutative`
14×	`associate-/r/`
10×	`associate-*l/`
7×	`div-inv`
6×	`associate-r` `associate-l`
2×	`un-div-inv`
1×	`flip3--` `flip--`

Counts

4 → 132

Calls

4 calls:

17.0ms	(* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))))
8.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
10.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
32.0ms	(/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

series753.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))))
81.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
112.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
328.0ms	(/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	825	2663
1	5002	2599

prune493.0ms

Filtered

144 candidates to 132 candidates (91.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	137	7	144
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	141	8	149

Merged error: 35.6b

Counts

149 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))
0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
35.0b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
35.7b	(/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

64×	`associate-/l/`
32×	`associate-/r/`
30×	`frac-times`
21×	`flip3-+` `associate-/r*` `flip-+`
20×	`clear-num`
19×	`frac-2neg`
13×	`div-inv`
11×	`associate-/l*`
6×	`associate-r/` `associate-r*`
5×	`associate-*l/`
3×	`associate-l`
1×	`flip3--` `un-div-inv` `*-commutative` `flip--`

Counts

4 → 83

Calls

4 calls:

7.0ms	(/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))
8.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
10.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
34.0ms	(/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

series579.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))
61.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
108.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
328.0ms	(/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	650	1429
1	3543	1346
2	5001	1338

prune341.0ms

Filtered

95 candidates to 87 candidates (91.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	97	6	103

Merged error: 35.6b

Counts

103 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (+ (+ alpha beta) i))
5.9b	(/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (+ (+ alpha beta) i)) (/ (+ (+ alpha beta) (* 2.0 i)) i))
35.0b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
35.7b	(/ (/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (+ (+ alpha beta) i)) (/ (+ (+ alpha beta) (* 2.0 i)) i)) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

84×	`associate-/l/`
36×	`flip3-+` `flip-+`
30×	`frac-times`
24×	`associate-/r/`
21×	`div-inv` `associate-/l*`
15×	`frac-2neg` `associate-l` `associate-*l/` `clear-num`
10×	`times-frac`
6×	`associate-*r/`
5×	`*-commutative`
4×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in`
2×	`associate-/r*`
1×	`flip3--` `flip--`

Counts

4 → 114

Calls

4 calls:

13.0ms	(* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (+ (+ alpha beta) i))
19.0ms	(/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (+ (+ alpha beta) i)) (/ (+ (+ alpha beta) (* 2.0 i)) i))
11.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
31.0ms	(/ (/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (+ (+ alpha beta) i)) (/ (+ (+ alpha beta) (* 2.0 i)) i)) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

series775.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (+ (+ alpha beta) i))
239.0ms	(/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (+ (+ alpha beta) i)) (/ (+ (+ alpha beta) (* 2.0 i)) i))
109.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
332.0ms	(/ (/ (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (+ (+ alpha beta) i)) (/ (+ (+ alpha beta) (* 2.0 i)) i)) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

simplify127.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	857	2112
1	4975	2085
2	5001	2085

prune445.0ms

Filtered

126 candidates to 113 candidates (89.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	126	6	132

Merged error: 35.6b

Counts

132 → 6

regimes97.0ms

Accuracy

43.1% (2.2b remaining)

Error of 38.0b against oracle of 35.8b and baseline of 39.6b

bsearch66.0ms

Steps

Iters	Range		Point
10	1.1695770500521425e+157	2.6251527105369915e+169	1.183331871632842e+157

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	26
1	31	26

end0.0ms

sample709.0ms

Algorithm

intervals

Results

384.0ms	8000×	body	80	valid
127.0ms	8000×	pre	80	true