Details

Time bar (total: 4.9s)

sample33.0ms

Algorithm
intervals
Results
8.0ms204×body80valid
4.0ms256×pre80true
4.0ms17×body1280valid
3.0ms20×body640valid
1.0ms12×body320valid
0.0ms3×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.6b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite48.0ms

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:
5.0ms
(* (+ 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)))

series840.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (+ alpha beta) (- beta alpha))
432.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
283.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
84.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify59.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0432585
12277536
25003526

prune237.0ms

Filtered
67 candidates to 56 candidates (83.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New61667
Fresh000
Picked101
Done000
Total62668

Merged error: 5.3b

Counts
68 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
0.0b
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.8b
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-/r/
18×associate-/l/
8×flip3-+ flip-+
7×div-inv
6×frac-2neg clear-num associate-/r* associate-/l*
3×flip3-- fma-def flip--
1×+-commutative
Counts
4 → 45
Calls
4 calls:
7.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
13.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
8.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
16.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series700.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
226.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
80.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
278.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify44.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0368471
11578429
25003420

prune178.0ms

Filtered
57 candidates to 47 candidates (82.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New54357
Fresh415
Picked101
Done000
Total59463

Merged error: 5.3b

Counts
63 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
0.0b
(/ (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.2b
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha)))
3.2b
(+ (/ (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
28×associate-/l/
18×associate-/r/
17×div-inv
9×associate-/l*
8×frac-2neg clear-num
6×flip3-+ times-frac associate-/r* flip-+
4×flip3-- flip--
3×fma-def
1×+-commutative
Counts
4 → 53
Calls
4 calls:
3.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
12.0ms
(/ (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
6.0ms
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha)))
15.0ms
(+ (/ (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series676.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
243.0ms
(/ (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
87.0ms
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha)))
280.0ms
(+ (/ (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify58.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0363509
11972451
25001439

prune189.0ms

Filtered
65 candidates to 49 candidates (75.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New63265
Fresh213
Picked011
Done000
Total65469

Merged error: 5.3b

Counts
69 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
0.0b
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.2b
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha)))
12.4b
(fma (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×associate-/r/ div-inv associate-/l/
5×frac-2neg clear-num
3×flip3-+ times-frac associate-/r* flip-+
2×flip3-- flip--
1×fma-udef associate-/l* inv-pow
Counts
4 → 30
Calls
4 calls:
6.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
6.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.0ms
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha)))
1.0ms
(fma (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series461.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
63.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
84.0ms
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha)))
246.0ms
(fma (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ 1 (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify39.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0258217
11310196
25001193

prune121.0ms

Filtered
42 candidates to 32 candidates (76.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New40242
Fresh202
Picked011
Done011
Total42446

Merged error: 5.3b

Counts
46 → 4

regimes79.0ms

Accuracy

14.2% (5.5b remaining)

Error of 11.5b against oracle of 6.0b and baseline of 12.4b

bsearch69.0ms

Steps
ItersRangePoint
8
3.918843472614674e+137
1.0363106199006555e+140
7.328664447613938e+139

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04424
14424

end0.0ms

sample872.0ms

Algorithm
intervals
Results
265.0ms6350×body80valid
140.0ms8000×pre80true
114.0ms518×body1280valid
95.0ms567×body640valid
44.0ms359×body320valid
17.0ms206×body160valid