Details

Time bar (total: 19.7s)

sample48.0ms

Algorithm
intervals
Results
11.0ms200×body80valid
9.0ms16×body1280valid
5.0ms256×pre80true
4.0ms19×body640valid
2.0ms13×body320valid
1.0ms8×body160valid

simplify52.0ms

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.4b

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))
2.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite66.0ms

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))
28.0ms
(+ (/ (/ (* (+ 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)))

series167.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
84.0ms
(+ (/ (/ (* (+ 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)))

simplify95.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
06811905
136221789
250011789

prune260.0ms

Filtered
120 candidates to 89 candidates (25.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New10713120
Fresh000
Picked101
Done000
Total10813121

Merged error: 6.3b

Counts
121 → 13

localize12.0ms

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)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.6b
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
45×add-sqr-sqrt
35×times-frac
26×add-cube-cbrt
21×associate-*r*
20×add-exp-log add-cbrt-cube
8×flip3-+ flip-+
7×associate-/r* associate-/l/ distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv div-exp associate-/r/ associate-/l* add-log-exp
4×frac-times associate-*l* associate-*l/ prod-exp cbrt-unprod distribute-lft-out
3×div-inv
2×frac-2neg associate-*r/ clear-num unswap-sqr
1×+-commutative flip3-- div-sub pow-prod-down sum-log *-commutative flip--
Counts
4 → 129
Calls
4 calls:
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
20.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
17.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
20.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series184.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
66.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
17.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
85.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify93.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
06571569
135541429
250021429

prune227.0ms

Filtered
141 candidates to 100 candidates (29.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1374141
Fresh4812
Picked101
Done000
Total14212154

Merged error: 6.3b

Counts
154 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.6b
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
2.8b
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
48×add-sqr-sqrt
42×associate-*r*
32×times-frac
24×add-cube-cbrt
14×add-exp-log add-cbrt-cube
8×pow1 associate-*l* add-log-exp
7×flip3-+ flip-+ distribute-lft-out distribute-lft-out-- difference-of-squares
4×frac-times unpow-prod-down cube-prod associate-*l/ prod-exp associate-/r/ cbrt-unprod unswap-sqr
2×cbrt-undiv associate-*r/ div-exp pow-prod-down *-commutative div-inv
1×+-commutative sub-neg flip3-- diff-log sum-log sum-cubes flip--
Counts
4 → 121
Calls
4 calls:
16.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
16.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
25.0ms
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
11.0ms
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series3.0s

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
17.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.9s
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
59.0ms
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify75.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05221591
126091452
250011452

prune484.0ms

Filtered
133 candidates to 95 candidates (28.6%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1294133
Fresh11011
Picked101
Done000
Total13114145

Merged error: 6.3b

Counts
145 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log (+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))))
2.0b
(log (+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3)))
2.6b
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
2.8b
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
18×log-prod
15×distribute-lft-out
12×unpow-prod-down cube-prod
9×add-sqr-sqrt exp-sum
8×add-log-exp
7×add-cube-cbrt
6×pow1
5×add-exp-log
4×log-div exp-prod add-cbrt-cube
3×flip3-+ sum-cubes flip-+
2×exp-diff log-pow
1×+-commutative sub-neg flip3-- diff-log rem-log-exp sum-log flip-- rem-exp-log distribute-lft-out-- difference-of-squares
Counts
4 → 74
Calls
4 calls:
24.0ms
(exp (log (+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))))
27.0ms
(log (+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3)))
24.0ms
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
11.0ms
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series12.5s

Counts
4 → 12
Calls
4 calls:
2.9s
(exp (log (+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))))
6.6s
(log (+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3)))
2.9s
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
58.0ms
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify53.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03451834
112621687
250011635

prune291.0ms

Filtered
86 candidates to 55 candidates (36.0%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New84286
Fresh4913
Picked011
Done000
Total8812100

Merged error: 4.4b

Counts
100 → 12

regimes589.0ms

Accuracy

59.1% (3.2b remaining)

Error of 7.3b against oracle of 4.1b and baseline of 11.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05981
15981

end0.0ms

sample1.2s

Algorithm
intervals
Results
376.0ms6414×body80valid
162.0ms8000×pre80true
145.0ms502×body1280valid
129.0ms535×body640valid
62.0ms353×body320valid
23.0ms196×body160valid

Profiling

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