Details

Time bar (total: 4.8s)

sample52.0ms

Algorithm
intervals
Results
18.0ms202×body80valid
6.0ms256×pre80true
5.0ms20×body640valid
4.0ms12×body1280valid
2.0ms9×body320valid
2.0ms13×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
0497027
1497027

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.9b

Counts
2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
0.1b
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
2.7b
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
3.8b
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))) 1.0)

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
23×add-sqr-sqrt
17×add-cube-cbrt times-frac
15×flip3-+ flip-+
13×add-exp-log add-cbrt-cube
10×associate-/r/
8×frac-times associate-/l*
7×distribute-lft-out
6×pow1 add-log-exp
5×associate-/r*
4×associate-*r/ associate-*r* associate-*l* associate-*l/ associate-/l/
3×cbrt-undiv div-exp
2×frac-2neg div-sub prod-exp clear-num cbrt-unprod div-inv distribute-lft-out-- difference-of-squares
1×+-commutative distribute-rgt-in associate-+l- flip3-- distribute-lft-in pow-prod-down sum-log *-commutative flip-- unswap-sqr
Counts
4 → 114
Calls
4 calls:
8.0ms
(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
20.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
22.0ms
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
30.0ms
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))) 1.0)

series368.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
28.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
219.0ms
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
110.0ms
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))) 1.0)

simplify46.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
052762819

prune298.0ms

Filtered
100 candidates to 126 candidates (-26.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11412126
Fresh101
Picked101
Done000
Total11612128

Merged error: 12.0b

Counts
128 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))
1.4b
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
1.8b
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
3.8b
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
18×flip3-+ flip-+
16×add-exp-log *-un-lft-identity associate-/r/ add-cbrt-cube
14×add-sqr-sqrt
12×frac-times
10×add-cube-cbrt
6×pow1 times-frac associate-*r/ associate-*l/ associate-/l* add-log-exp
4×cbrt-undiv div-exp associate-*r* associate-*l*
3×prod-exp cbrt-unprod
2×frac-2neg clear-num associate-/r* div-inv distribute-lft-out
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log pow-prod-down *-commutative flip-- distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 102
Calls
4 calls:
21.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))
22.0ms
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
20.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
24.0ms
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

series179.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))
38.0ms
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
41.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
69.0ms
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

simplify47.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
051032806

prune349.0ms

Filtered
93 candidates to 114 candidates (-22.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1077114
Fresh7411
Picked101
Done000
Total11511126

Merged error: 5.9b

Counts
126 → 11

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt beta)
1.4b
(* (* (cbrt beta) (/ (cbrt beta) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) (/ (cbrt beta) (+ alpha (+ (* 2.0 i) beta))))
1.8b
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
3.8b
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
30×add-exp-log associate-*r*
27×times-frac
24×add-sqr-sqrt
22×add-cube-cbrt
21×add-cbrt-cube
15×cbrt-prod
11×prod-exp cbrt-unprod
10×associate-/r/
9×pow1
7×cbrt-undiv flip3-+ div-exp flip-+
6×distribute-lft-out add-log-exp
5×frac-times associate-*r/
3×pow-prod-down associate-*l/ associate-/l*
2×div-inv
1×sub-neg flip3-- frac-2neg pow1/3 diff-log associate-*l* clear-num associate-/r* *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 110
Calls
4 calls:
1.0ms
(cbrt beta)
35.0ms
(* (* (cbrt beta) (/ (cbrt beta) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) (/ (cbrt beta) (+ alpha (+ (* 2.0 i) beta))))
20.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
24.0ms
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

series181.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cbrt beta)
44.0ms
(* (* (cbrt beta) (/ (cbrt beta) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) (/ (cbrt beta) (+ alpha (+ (* 2.0 i) beta))))
44.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
67.0ms
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

simplify37.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
053062680

prune342.0ms

Filtered
88 candidates to 122 candidates (-38.6%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1175122
Fresh1910
Picked101
Done000
Total11914133

Merged error: 5.9b

Counts
133 → 14

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt beta)
1.8b
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
2.6b
(* (* (cbrt beta) (* (/ (cbrt beta) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)) (* (cbrt (cbrt beta)) (cbrt (cbrt beta))))) (/ (cbrt (cbrt beta)) (+ alpha (+ (* 2.0 i) beta))))
3.8b
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
65×add-exp-log
49×*-un-lft-identity
42×associate-*r*
39×cbrt-prod times-frac
37×add-cbrt-cube
35×prod-exp cbrt-unprod
31×add-sqr-sqrt
29×add-cube-cbrt
18×pow1
12×cbrt-undiv div-exp
10×pow-prod-down associate-/r/
9×distribute-lft-out
7×flip3-+ flip-+
6×add-log-exp
5×frac-times associate-*r/ associate-*l/
3×associate-/l*
2×div-inv
1×sub-neg flip3-- frac-2neg pow1/3 diff-log associate-*l* clear-num associate-/r* *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 136
Calls
4 calls:
1.0ms
(cbrt beta)
19.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
46.0ms
(* (* (cbrt beta) (* (/ (cbrt beta) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)) (* (cbrt (cbrt beta)) (cbrt (cbrt beta))))) (/ (cbrt (cbrt beta)) (+ alpha (+ (* 2.0 i) beta))))
24.0ms
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

series182.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(cbrt beta)
42.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
44.0ms
(* (* (cbrt beta) (* (/ (cbrt beta) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)) (* (cbrt (cbrt beta)) (cbrt (cbrt beta))))) (/ (cbrt (cbrt beta)) (+ alpha (+ (* 2.0 i) beta))))
71.0ms
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

simplify72.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
050743347

prune280.0ms

Filtered
86 candidates to 148 candidates (-72.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1453148
Fresh11213
Picked101
Done000
Total14715162

Merged error: 5.9b

Counts
162 → 15

regimes489.0ms

Accuracy

-5% (6.7b remaining)

Error of 12.5b against oracle of 5.8b and baseline of 12.2b

bsearch61.0ms

Steps
ItersRangePoint
9
1.1487285604221614e+41
1.7990872848798823e+50
1.4898782167186468e+48
8
583199030713779.1
2.5181932757383506e+18
2.463897326213938e+18

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
076157
176157

end0.0ms

sample1.3s

Algorithm
intervals
Results
392.0ms6367×body80valid
179.0ms8000×pre80true
164.0ms534×body1280valid
135.0ms549×body640valid
59.0ms328×body320valid
27.0ms222×body160valid

Profiling

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