Details

Time bar (total: 9.7s)

sample36.0ms

Algorithm
intervals
Results
10.0ms209×body80valid
6.0ms256×pre80true
5.0ms20×body1280valid
1.0ms7×body640valid
1.0ms12×body160valid
1.0ms8×body320valid

simplify51.0ms

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: 23.6b

Counts
2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
3.0b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite70.0ms

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:
21.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
30.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
14.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series569.0ms

Counts
3 → 9
Calls
3 calls:
219.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
271.0ms
(+ (/ (/ (* (+ 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)))

simplify93.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250031789

prune310.0ms

Filtered
120 candidates to 89 candidates (74.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1119120
Fresh000
Picked101
Done000
Total1129121

Merged error: 5.2b

Counts
121 → 9

localize16.0ms

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))))
1.8b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
3.0b
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

rewrite731.0ms

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:
10.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
20.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
62.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
396.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

series709.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
140.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
226.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
270.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

simplify459.0ms

Algorithm
egg-herbie
Counts
1746 → 1746
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0500148152

prune3.0s

Filtered
1746 candidates to 760 candidates (43.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New174151746
Fresh448
Picked011
Done000
Total1745101755

Merged error: 5.2b

Counts
1755 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ alpha beta))
0.6b
(cbrt (+ alpha beta))
0.6b
(cbrt (+ alpha beta))
6.2b
(+ (* (* (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3 distribute-lft-out
1×+-commutative sum-log
Counts
4 → 53
Calls
4 calls:
3.0ms
(cbrt (+ alpha beta))
3.0ms
(cbrt (+ alpha beta))
3.0ms
(cbrt (+ alpha beta))
60.0ms
(+ (* (* (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

series657.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(cbrt (+ alpha beta))
124.0ms
(cbrt (+ alpha beta))
124.0ms
(cbrt (+ alpha beta))
279.0ms
(+ (* (* (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

simplify43.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0273878
1990797
25002787

prune296.0ms

Filtered
65 candidates to 57 candidates (87.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New62365
Fresh178
Picked101
Done011
Total641175

Merged error: 5.2b

Counts
75 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ alpha beta))
0.6b
(cbrt (+ alpha beta))
4.0b
(log (+ (* (* (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0))
6.2b
(+ (* (* (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
5×pow1 add-exp-log
4×cbrt-div flip3-+ add-cbrt-cube flip-+
3×log-prod
2×log-div pow1/3 distribute-lft-out
1×+-commutative rem-log-exp sum-log log-pow
Counts
4 → 53
Calls
4 calls:
3.0ms
(cbrt (+ alpha beta))
3.0ms
(cbrt (+ alpha beta))
61.0ms
(log (+ (* (* (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0))
65.0ms
(+ (* (* (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

series807.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(cbrt (+ alpha beta))
130.0ms
(cbrt (+ alpha beta))
278.0ms
(log (+ (* (* (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0))
276.0ms
(+ (* (* (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

simplify50.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03471632
112081454
250011438

prune297.0ms

Filtered
65 candidates to 57 candidates (87.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New64165
Fresh189
Picked101
Done011
Total661076

Merged error: 3.5b

Counts
76 → 10

regimes249.0ms

Accuracy

60% (3.1b remaining)

Error of 7.4b against oracle of 4.2b and baseline of 12.1b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04637
15037
25037

end0.0ms

sample988.0ms

Algorithm
intervals
Results
313.0ms6389×body80valid
181.0ms8000×pre80true
128.0ms519×body1280valid
107.0ms566×body640valid
50.0ms315×body320valid
20.0ms211×body160valid