Details

Time bar (total: 4.9s)

sample42.0ms

Algorithm
intervals
Results
11.0ms207×body80valid
5.0ms256×pre80true
3.0ms12×body1280valid
3.0ms15×body640valid
2.0ms14×body320valid
1.0ms8×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0497027
1497027

prune10.0ms

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: 11.7b

Counts
2 → 2

localize14.0ms

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))))
2.2b
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))) 1.0)
2.6b
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))

rewrite75.0ms

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:
7.0ms
(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
18.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
24.0ms
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))) 1.0)
23.0ms
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
22.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
91.0ms
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))) 1.0)
187.0ms
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
052752819

prune288.0ms

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

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New11313126
Fresh101
Picked101
Done000
Total11513128

Merged error: 11.1b

Counts
128 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
1.1b
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
2.2b
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
2.2b
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

rewrite82.0ms

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:
18.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
18.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
18.0ms
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
24.0ms
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

series148.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
34.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
34.0ms
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
57.0ms
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

simplify56.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
051372806

prune299.0ms

Filtered
92 candidates to 114 candidates (-23.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1077114
Fresh8412
Picked101
Done000
Total11611127

Merged error: 5.6b

Counts
127 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
1.1b
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
2.2b
(- (* (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta)))) (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))) (* 1.0 1.0))
2.2b
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-/r/
19×add-exp-log add-cbrt-cube
18×flip3-+ flip-+
12×frac-times
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac associate-/l*
6×cbrt-undiv associate-*r/ div-exp associate-*l/ add-log-exp
4×pow1
3×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod div-inv
1×sub-neg flip3-- diff-log flip-- difference-of-squares
Counts
4 → 100
Calls
4 calls:
19.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
22.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
39.0ms
(- (* (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta)))) (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))) (* 1.0 1.0))
18.0ms
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))

series184.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
36.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
82.0ms
(- (* (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta)))) (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))) (* 1.0 1.0))
32.0ms
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
049922913
149922913

prune548.0ms

Filtered
91 candidates to 112 candidates (-23.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1084112
Fresh3710
Picked101
Done000
Total11211123

Merged error: 5.6b

Counts
123 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
1.1b
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
2.2b
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
2.7b
(- (* (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta)))) (* alpha (/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ (* 2.0 i) alpha)))))) (* 1.0 1.0))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-/r/
19×add-exp-log add-cbrt-cube
18×flip3-+ flip-+
12×frac-times
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac associate-/l*
6×cbrt-undiv associate-*r/ div-exp associate-*l/ add-log-exp
4×pow1
3×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod div-inv
1×sub-neg flip3-- diff-log flip--
Counts
4 → 99
Calls
4 calls:
19.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
19.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
17.0ms
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
43.0ms
(- (* (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta)))) (* alpha (/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ (* 2.0 i) alpha)))))) (* 1.0 1.0))

series185.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
34.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta))))
32.0ms
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
85.0ms
(- (* (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ (* 2.0 i) beta)))) (* alpha (/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ (* 2.0 i) alpha)))))) (* 1.0 1.0))

simplify63.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
050392867

prune500.0ms

Filtered
90 candidates to 111 candidates (-23.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1083111
Fresh01010
Picked101
Done000
Total10913122

Merged error: 5.6b

Counts
122 → 13

regimes431.0ms

Accuracy

14.3% (5.2b remaining)

Error of 10.9b against oracle of 5.7b and baseline of 11.7b

bsearch47.0ms

Steps
ItersRangePoint
9
4.3525177164867255e+233
4.009938817162507e+239
9.726887261988919e+234

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
065147
165147

end0.0ms

sample1.2s

Algorithm
intervals
Results
366.0ms6408×body80valid
164.0ms8000×pre80true
136.0ms487×body1280valid
122.0ms546×body640valid
61.0ms371×body320valid
21.0ms188×body160valid

Profiling

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