Details

sample33.0ms

Algorithm

intervals

Results

8.0ms	198×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	21×	body	1280	valid
3.0ms	19×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	6×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	107	14
2	479	14
3	2315	14
4	5002	14

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: 26.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (- beta alpha))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.9b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.4b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

29×	`associate-/l/`
14×	`flip3-+` `flip-+`
12×	`frac-times`
9×	`flip3--` `flip--`
8×	`associate-/r/`
7×	`associate-/l*`
6×	`associate-r/` `associate-l/`
4×	`div-inv`
3×	`fma-def` `frac-2neg` `clear-num` `*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`+-commutative`

Counts

4 → 55

Calls

4 calls:

8.0ms	(* (+ alpha beta) (- beta alpha))
15.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
17.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
9.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ alpha beta) (- beta alpha))
226.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
278.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
75.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify59.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	432	585
1	2277	536
2	5003	526

prune387.0ms

Filtered

67 candidates to 56 candidates (83.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	4	68

Merged error: 6.6b

Counts

68 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))
0.1b	(/ (/ (- beta alpha) (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (- beta alpha) (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta)))
1.9b	(+ (/ (/ (- beta alpha) (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-/r/`
18×	`associate-/l/`
9×	`flip3-+` `flip-+`
7×	`div-inv`
6×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`
5×	`div-sub`
3×	`fma-def`
2×	`flip3--` `flip--`
1×	`+-commutative` `associate-+l-`

Counts

4 → 48

Calls

4 calls:

8.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))
14.0ms	(/ (/ (- beta alpha) (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
8.0ms	(/ (- beta alpha) (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta)))
16.0ms	(+ (/ (/ (- beta alpha) (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series549.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))
226.0ms	(/ (/ (- beta alpha) (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
80.0ms	(/ (- beta alpha) (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta)))
173.0ms	(+ (/ (/ (- beta alpha) (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	383	507
1	1620	462
2	5001	446

prune196.0ms

Filtered

60 candidates to 51 candidates (85.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	60	4	64

Merged error: 6.3b

Counts

64 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta)))
0.1b	(/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ beta (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta)))
1.9b	(- (/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

25×	`associate-/r/`
12×	`associate-/l/`
9×	`associate-/r*`
8×	`flip3-+` `flip-+` `div-inv`
7×	`frac-2neg` `clear-num`
6×	`associate-/l*`
3×	`fma-neg`
1×	`sub-neg` `flip3--` `flip--`

Counts

4 → 46

Calls

4 calls:

7.0ms	(/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta)))
11.0ms	(/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.0ms	(/ beta (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta)))
20.0ms	(- (/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series606.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta)))
179.0ms	(/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
77.0ms	(/ beta (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta)))
272.0ms	(- (/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	330	420
1	1373	382
2	5001	371

prune218.0ms

Filtered

58 candidates to 48 candidates (82.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	53	5	58
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	56	6	62

Merged error: 6.3b

Counts

62 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.5b	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) beta) (+ alpha beta)))
1.9b	(- (/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
6.2b	(/ (/ (fma i 2.0 (+ alpha beta)) beta) (+ alpha beta))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

22×	`associate-/r/`
15×	`associate-/l/`
10×	`clear-num`
9×	`div-inv`
8×	`frac-2neg` `associate-/l*`
6×	`flip3-+` `associate-/r*` `flip-+`
3×	`fma-neg`
2×	`remove-double-div`
1×	`sub-neg` `flip3--` `flip--` `inv-pow`

Counts

4 → 49

Calls

4 calls:

12.0ms	(/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
5.0ms	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) beta) (+ alpha beta)))
16.0ms	(- (/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
4.0ms	(/ (/ (fma i 2.0 (+ alpha beta)) beta) (+ alpha beta))

series663.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
135.0ms	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) beta) (+ alpha beta)))
275.0ms	(- (/ (/ alpha (/ (+ (+ alpha beta) (* 2.0 i)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
75.0ms	(/ (/ (fma i 2.0 (+ alpha beta)) beta) (+ alpha beta))

simplify42.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	348	404
1	1323	375
2	5001	364

prune218.0ms

Filtered

61 candidates to 49 candidates (80.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	61	6	67

Merged error: 6.3b

Counts

67 → 6

regimes158.0ms

Accuracy

16.8% (5.4b remaining)

Error of 11.3b against oracle of 6.0b and baseline of 12.4b

bsearch100.0ms

Steps

Iters	Range		Point
9	1.097544708491371e+78	2.3793858261423075e+86	1.268355596156671e+86

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	49
1	66	49
2	69	49
3	69	49

end0.0ms

sample826.0ms

Algorithm

intervals

Results

247.0ms	6293×	body	80	valid
131.0ms	8000×	pre	80	true
106.0ms	539×	body	1280	valid
92.0ms	584×	body	640	valid
44.0ms	372×	body	320	valid
16.0ms	212×	body	160	valid