Details

Time bar (total: 6.6s)

sample33.0ms

Algorithm
intervals
Results
8.0ms198×body80valid
4.0ms256×pre80true
4.0ms21×body1280valid
3.0ms19×body640valid
1.0ms12×body320valid
0.0ms6×body160valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

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: 26.7b

Counts
2 → 1

localize17.0ms

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)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
29×associate-/l/
13×flip3-+ flip-+
12×frac-times
9×flip3-- flip--
7×associate-/l*
6×associate-*r/ associate-*l/ associate-/r/
3×frac-2neg clear-num *-commutative div-inv
2×distribute-rgt-in sub-neg distribute-lft-in
1×+-commutative
Counts
4 → 52
Calls
4 calls:
4.0ms
(* (+ alpha beta) (- beta alpha))
15.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms
(+ (/ (/ (* (+ 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)))

series626.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (+ alpha beta) (- beta alpha))
230.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
272.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
80.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify56.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0416594
12175591
25002589

prune221.0ms

Filtered
64 candidates to 53 candidates (82.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New60464
Fresh000
Picked101
Done000
Total61465

Merged error: 6.6b

Counts
65 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-/r/
21×flip3-+ flip-+
20×frac-times
16×associate-/l/
10×associate-*r/ clear-num
8×frac-2neg
6×associate-*r*
5×associate-/r*
4×associate-*l/ div-inv
3×flip3-- flip--
2×un-div-inv *-commutative
1×+-commutative
Counts
4 → 60
Calls
4 calls:
7.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
11.0ms
(* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
19.0ms
(+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)
15.0ms
(/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))

series780.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
149.0ms
(* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
279.0ms
(+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)
234.0ms
(/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))

simplify71.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0491922
12511914
25001912

prune256.0ms

Filtered
72 candidates to 65 candidates (90.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New69372
Fresh213
Picked101
Done000
Total72476

Merged error: 6.6b

Counts
76 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.2b
(/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
2.0b
(* (+ alpha beta) (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))))
3.6b
(+ (* (+ alpha beta) (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))) 1.0)

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
46×frac-times associate-/r/
37×flip3-+ flip-+
34×associate-*r*
23×associate-*r/
20×associate-/r*
18×associate-/l/
17×clear-num
13×frac-2neg
8×associate-*l/
7×div-inv
6×*-commutative
5×flip3-- un-div-inv flip--
1×+-commutative inv-pow
Counts
4 → 100
Calls
4 calls:
12.0ms
(* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
13.0ms
(/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
18.0ms
(* (+ alpha beta) (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))))
23.0ms
(+ (* (+ alpha beta) (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))) 1.0)

series835.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
164.0ms
(/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
231.0ms
(* (+ alpha beta) (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))))
282.0ms
(+ (* (+ alpha beta) (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))) 1.0)

simplify114.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
06891438
144101426
250021426

prune546.0ms

Filtered
112 candidates to 98 candidates (87.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1102112
Fresh123
Picked011
Done000
Total1115116

Merged error: 6.6b

Counts
116 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i))))
2.0b
(* (+ alpha beta) (/ (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- beta alpha))))
6.3b
(+ (* (+ alpha beta) (/ (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- beta alpha)))) 1.0)
19.4b
(/ (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- beta alpha)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
138×associate-/r/
88×flip3-+ flip-+
84×frac-times
54×times-frac
42×associate-*r/
37×associate-/l*
36×div-inv
31×associate-*r*
24×associate-*l/
22×flip3-- associate-/r* flip-- associate-/l/
13×clear-num
11×frac-2neg
6×*-commutative
4×un-div-inv
1×+-commutative inv-pow
Counts
4 → 165
Calls
4 calls:
11.0ms
(/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i))))
23.0ms
(* (+ alpha beta) (/ (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- beta alpha))))
33.0ms
(+ (* (+ alpha beta) (/ (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- beta alpha)))) 1.0)
17.0ms
(/ (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- beta alpha)))

series841.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i))))
232.0ms
(* (+ alpha beta) (/ (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- beta alpha))))
279.0ms
(+ (* (+ alpha beta) (/ (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- beta alpha)))) 1.0)
169.0ms
(/ (/ 1 (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- beta alpha)))

simplify54.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010113149
150013101

prune707.0ms

Filtered
177 candidates to 151 candidates (85.3%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1770177
Fresh033
Picked011
Done011
Total1775182

Merged error: 6.6b

Counts
182 → 5

regimes120.0ms

Accuracy

13.7% (5.7b remaining)

Error of 11.9b against oracle of 6.2b and baseline of 12.8b

bsearch76.0ms

Steps
ItersRangePoint
9
1.097544708491371e+78
2.3793858261423075e+86
1.268355596156671e+86

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04826
14826

end0.0ms

sample829.0ms

Algorithm
intervals
Results
246.0ms6293×body80valid
132.0ms8000×pre80true
107.0ms539×body1280valid
96.0ms584×body640valid
46.0ms372×body320valid
19.0ms212×body160valid