Details

Time bar (total: 23.7s)

sample57.0ms

Algorithm
intervals
Results
19.0ms198×body80valid
8.0ms24×body640valid
8.0ms19×body1280valid
7.0ms256×pre80true
2.0ms9×body320valid
1.0ms6×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.4b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite422.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
93.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
301.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
24.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series574.0ms

Counts
3 → 9
Calls
3 calls:
225.0ms
(/ (/ (* (+ 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)
77.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify94.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250031789

prune333.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.3b

localize17.0ms

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))))
1.4b
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
2.7b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

rewrite1.5s

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:
22.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
157.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
973.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
138.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

series727.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
144.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
269.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
239.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

simplify445.0ms

Algorithm
egg-herbie
Counts
1746 → 1746
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0500148152

prune3.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.4b
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
1.4b
(log (exp (+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)))
2.7b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

rewrite4.6s

Algorithm
rewrite-expression-head
Rules
5111×times-frac
3519×*-un-lft-identity
2217×add-sqr-sqrt
1779×add-cube-cbrt
651×distribute-lft-out
219×distribute-lft-out-- difference-of-squares
182×div-inv
165×associate-/r/
110×associate-/r*
75×flip3-+ flip-+
39×add-exp-log
30×add-cbrt-cube
27×div-exp
20×associate-/l*
18×cbrt-undiv
6×add-log-exp
5×pow1 log-pow
4×log-prod exp-prod
3×1-exp associate-/l/
2×frac-2neg clear-num
1×+-commutative rem-log-exp exp-sum sum-log
Counts
4 → 1711
Calls
4 calls:
152.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
963.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
3.1s
(log (exp (+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)))
146.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

series957.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
284.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
280.0ms
(log (exp (+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)))
238.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

simplify660.0ms

Algorithm
egg-herbie
Counts
1723 → 1723
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500148111

prune3.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ alpha beta))
0.6b
(cbrt (+ alpha beta))
8.2b
(+ (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (sqrt 1))) (/ (/ (cbrt (+ alpha beta)) (sqrt 1)) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i))))))) 1.0)
9.4b
(/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (sqrt 1)))

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
52×cbrt-div
36×add-exp-log flip3-+ associate-*l/ flip-+
32×frac-times
26×associate-/r/
24×add-cbrt-cube
18×sqrt-div
16×associate-*r/ prod-exp cbrt-unprod
10×*-un-lft-identity
8×cbrt-undiv cbrt-prod div-exp associate-/l/
6×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1
2×pow1/3 distribute-lft-out
1×+-commutative frac-2neg times-frac clear-num associate-/r* sum-log div-inv associate-/l*
Counts
4 → 102
Calls
4 calls:
2.0ms
(cbrt (+ alpha beta))
2.0ms
(cbrt (+ alpha beta))
2.1s
(+ (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (sqrt 1))) (/ (/ (cbrt (+ alpha beta)) (sqrt 1)) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i))))))) 1.0)
368.0ms
(/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (sqrt 1)))

series938.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(cbrt (+ alpha beta))
127.0ms
(cbrt (+ alpha beta))
281.0ms
(+ (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (sqrt 1))) (/ (/ (cbrt (+ alpha beta)) (sqrt 1)) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i))))))) 1.0)
396.0ms
(/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (sqrt 1)))

simplify122.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
011382973
144792574
250012545

prune611.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

regimes345.0ms

Accuracy

72.1% (1.8b remaining)

Error of 7.6b against oracle of 5.8b and baseline of 12.2b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05240
15640
25640

end0.0ms

sample1.5s

Algorithm
intervals
Results
635.0ms6378×body80valid
201.0ms609×body640valid
198.0ms8000×pre80true
194.0ms482×body1280valid
84.0ms338×body320valid
37.0ms193×body160valid