Details

Time bar (total: 5.6s)

sample39.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
5.0ms256×pre80true

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune4.0ms

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: 51.0b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.9b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
43.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 200
Calls
4 calls:
12.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
25.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series398.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
23.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
308.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
54.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify74.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012495670
150015161

prune418.0ms

Filtered
212 candidates to 143 candidates (32.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2075212
Fresh000
Picked011
Done000
Total2076213

Merged error: 33.1b

Counts
213 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
216×times-frac
163×add-sqr-sqrt
151×*-un-lft-identity
99×add-cube-cbrt
32×associate-/r/ difference-of-squares
28×associate-/l*
25×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
11×cbrt-undiv div-exp
10×distribute-lft-out
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
2×associate-*r/ prod-exp cbrt-unprod
1×flip3-- flip--
Counts
4 → 252
Calls
4 calls:
19.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
22.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series134.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
51.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
20.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
27.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify72.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010985877
150015622

prune697.0ms

Filtered
264 candidates to 186 candidates (29.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2613264
Fresh044
Picked011
Done011
Total2619270

Merged error: 33.1b

Counts
270 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.7b
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.7b
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.7b
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×cbrt-div
5×flip3-+ flip-+
4×pow1 add-log-exp
3×times-frac pow1/3 associate-/r*
2×cbrt-undiv associate-*r/ div-exp associate-/r/ associate-/l/
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 64
Calls
4 calls:
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
3.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
5.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series197.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
61.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
61.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
58.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify46.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0369846
11735769
25001754

prune195.0ms

Filtered
76 candidates to 64 candidates (15.8%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New75176
Fresh066
Picked011
Done022
Total751085

Merged error: 33.1b

Counts
85 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.2b
(exp (log (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
309×times-frac
262×add-sqr-sqrt
200×*-un-lft-identity
138×add-cube-cbrt
96×log-prod exp-sum
62×difference-of-squares
34×associate-/r/
31×sqrt-prod distribute-lft-out--
19×associate-/l*
17×flip3-+ flip-+ div-inv
16×add-exp-log add-cbrt-cube
12×associate-/r*
6×cbrt-undiv div-exp
5×pow1 associate-/l/
4×exp-prod add-log-exp
3×frac-2neg clear-num
2×flip3-- associate-*r/ flip--
1×log-div exp-diff prod-exp log-pow cbrt-unprod rem-exp-log
Counts
4 → 293
Calls
4 calls:
24.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
23.0ms
(exp (log (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series152.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
56.0ms
(exp (log (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
16.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
27.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify94.0ms

Algorithm
egg-herbie
Counts
305 → 305
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012657825
150017629

prune1.1s

Filtered
305 candidates to 206 candidates (32.5%)
Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New3050305
Fresh066
Picked011
Done033
Total30510315

Merged error: 33.1b

Counts
315 → 10

regimes373.0ms

Accuracy

26.8% (2.9b remaining)

Error of 37.2b against oracle of 34.3b and baseline of 38.2b

bsearch21.0ms

Steps
ItersRangePoint
7
4.6478881756167835e+153
2.3578722590346403e+155
1.3616623343438624e+154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03329
13329

end0.0ms

sample1.1s

Algorithm
intervals
Results
614.0ms8000×body80valid
170.0ms8000×pre80true

Profiling

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