Details

Time bar (total: 5.3s)

sample47.0ms

Algorithm
intervals
Results
11.0ms205×body80valid
7.0ms13×body640valid
6.0ms17×body1280valid
5.0ms256×pre80true
2.0ms15×body320valid
1.0msbody160valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 23.0b

Counts
2 → 1

localize12.0ms

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))
2.2b
(+ (/ (/ (* (+ 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)))

rewrite68.0ms

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*
associate-/l/
cbrt-undiv div-exp associate-/r* div-inv
add-log-exp
frac-times
pow1 flip3-- flip--
frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
19.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(+ (/ (/ (* (+ 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)))

series168.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
85.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify90.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06811905
136221789
250011789

prune255.0ms

Filtered
89 candidates to 120 candidates (-34.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10911120
Fresh000
Picked101
Done000
Total11011121

Merged error: 4.9b

Counts
121 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.2b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.4b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×div-inv
cbrt-undiv div-exp associate-/r*
pow1 add-log-exp
associate-*l*
div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
frac-times frac-2neg associate-*l/ clear-num
+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 295
Calls
4 calls:
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
20.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
37.0ms
(* (+ 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)

series205.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
40.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
64.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
86.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify77.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010804781
150014605

prune572.0ms

Filtered
199 candidates to 307 candidates (-54.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New3016307
Fresh4610
Picked101
Done000
Total30612318

Merged error: 4.9b

Counts
318 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

4.4b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.4b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.4b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.3b
(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
49×add-sqr-sqrt *-un-lft-identity
45×times-frac
31×add-cube-cbrt
distribute-lft-out-- difference-of-squares
associate-/r/ add-log-exp
pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
cbrt-div pow1/3 div-inv
+-commutative sum-log
Counts
4 → 101
Calls
4 calls:
8.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
63.0ms
(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series331.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
78.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
78.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
93.0ms
(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify52.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03601874
111941757
250021749

prune435.0ms

Filtered
93 candidates to 113 candidates (-21.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1112113
Fresh2911
Picked101
Done000
Total11411125

Merged error: 4.9b

Counts
125 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

4.4b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.4b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.4b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.3b
(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
49×add-sqr-sqrt *-un-lft-identity
45×times-frac
31×add-cube-cbrt
distribute-lft-out-- difference-of-squares
associate-/r/ add-log-exp
pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
cbrt-div pow1/3 div-inv
+-commutative sum-log
Counts
4 → 101
Calls
4 calls:
8.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
63.0ms
(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series323.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
77.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
78.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
91.0ms
(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify49.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03601874
111941757
250021749

prune448.0ms

Filtered
93 candidates to 113 candidates (-21.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1103113
Fresh3710
Picked101
Done000
Total11410124

Merged error: 4.9b

Counts
124 → 10

regimes546.0ms

Accuracy

76.9% (1.5b remaining)

Error of 7.3b against oracle of 5.8b and baseline of 12.4b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05962
15962

end0.0ms

sample1.2s

Algorithm
intervals
Results
362.0ms6375×body80valid
162.0ms8000×pre80true
155.0ms544×body1280valid
123.0ms551×body640valid
60.0ms353×body320valid
19.0ms177×body160valid

Profiling

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