Details

Time bar (total: 10.7s)

sample31.0ms

Algorithm
intervals
Results
8.0ms215×body80valid
4.0ms256×pre80true
3.0ms14×body1280valid
2.0ms14×body640valid
1.0ms6×body320valid
1.0ms7×body160valid

simplify50.0ms

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: 21.7b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
50×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-exp-log add-cbrt-cube
15×add-log-exp
14×associate-/r/
12×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* sum-log div-inv
4×pow1 frac-times
3×flip3-- flip--
2×+-commutative frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×associate-+l+
Counts
4 → 126
Calls
4 calls:
8.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
19.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
29.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
13.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series588.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
219.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
268.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
79.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify106.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07322016
141081891
250021891

prune380.0ms

Filtered
138 candidates to 102 candidates (73.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1326138
Fresh000
Picked101
Done000
Total1336139

Merged error: 3.5b

Counts
139 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.3b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.8b
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

rewrite668.0ms

Algorithm
rewrite-expression-head
Rules
5126×times-frac
3533×*-un-lft-identity
2233×add-sqr-sqrt
1787×add-cube-cbrt
650×distribute-lft-out
223×distribute-lft-out-- difference-of-squares
183×div-inv
167×associate-/r/
113×associate-/r*
76×flip3-+ flip-+
41×add-exp-log
32×add-cbrt-cube
28×div-exp
25×associate-/l*
19×cbrt-undiv
6×add-log-exp
5×associate-/l/
4×pow1
3×frac-2neg 1-exp clear-num
1×+-commutative flip3-- div-sub sum-log flip--
Counts
4 → 1734
Calls
4 calls:
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
26.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
57.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
371.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

series726.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
143.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
231.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
275.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

simplify432.0ms

Algorithm
egg-herbie
Counts
1746 → 1746
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500148152

prune3.4s

Filtered
1746 candidates to 760 candidates (43.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New174331746
Fresh325
Picked011
Done000
Total174661752

Merged error: 3.5b

Counts
1752 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.2b
(* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
3.0b
(+ (* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
51×add-sqr-sqrt
50×add-exp-log
43×times-frac
32×add-cube-cbrt add-cbrt-cube
22×associate-*r* associate-*l* prod-exp
12×div-exp cbrt-unprod
11×pow1 frac-times
10×flip3-+ flip-+
8×associate-*r/
7×cbrt-undiv associate-*l/ distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
5×associate-/l*
4×pow-prod-down distribute-lft-out
3×rec-exp 1-exp associate-/r* div-inv
2×*-commutative associate-/l/ unswap-sqr
1×+-commutative flip3-- frac-2neg div-sub clear-num sum-log flip--
Counts
4 → 154
Calls
4 calls:
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
16.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
29.0ms
(* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
24.0ms
(+ (* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

series665.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
80.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
232.0ms
(* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
277.0ms
(+ (* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

simplify115.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
08122047
145541790
250011781

prune431.0ms

Filtered
166 candidates to 115 candidates (69.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1651166
Fresh134
Picked011
Done011
Total1666172

Merged error: 3.5b

Counts
172 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sqrt 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (sqrt 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
5.0b
(+ (* (/ (sqrt 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
116×sqrt-prod
104×times-frac
102×*-un-lft-identity
86×add-sqr-sqrt
68×add-cube-cbrt
48×associate-*l*
47×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp
16×distribute-lft-out
14×prod-exp associate-/r* cbrt-unprod
13×associate-*r*
8×sqrt-div associate-/r/
7×flip3-+ flip-+ associate-/l* unswap-sqr
6×pow1 add-log-exp
5×associate-/l/
4×div-inv
3×frac-times associate-*l/
2×frac-2neg associate-*r/ clear-num
1×+-commutative sqrt-undiv pow-prod-down sum-log *-commutative
Counts
4 → 215
Calls
4 calls:
42.0ms
(* (/ (sqrt 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
23.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
15.0ms
(/ (sqrt 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
32.0ms
(+ (* (/ (sqrt 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series960.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(* (/ (sqrt 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
313.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
127.0ms
(/ (sqrt 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
284.0ms
(+ (* (/ (sqrt 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify138.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
09214539
147374013
250013890

prune624.0ms

Filtered
227 candidates to 142 candidates (62.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2243227
Fresh213
Picked101
Done112
Total2285233

Merged error: 3.5b

Counts
233 → 5

regimes178.0ms

Accuracy

16.8% (5.4b remaining)

Error of 11.2b against oracle of 5.8b and baseline of 12.3b

bsearch73.0ms

Steps
ItersRangePoint
8
2.911341738631546e+214
3.8498885149509344e+217
2.9093475849372547e+217

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04826
14826

end0.0ms

sample790.0ms

Algorithm
intervals
Results
245.0ms6361×body80valid
127.0ms8000×pre80true
102.0ms531×body1280valid
86.0ms560×body640valid
38.0ms345×body320valid
15.0ms203×body160valid