Details

Time bar (total: 5.2s)

sample39.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
5.0ms256×pre80true

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 53.2b

Counts
2 → 1

localize19.0ms

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))))
33.9b
(/ (/ (* (* 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))
45.7b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite100.0ms

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)))
12.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.0ms
(/ (/ (* (* 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))))

series415.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
24.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
322.0ms
(/ (/ (* (* 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))
56.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify76.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012495670
150015161

prune427.0ms

Filtered
143 candidates to 212 candidates (-48.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2066212
Fresh000
Picked101
Done000
Total2076213

Merged error: 32.2b

Counts
213 → 6

localize19.0ms

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)))
33.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite83.0ms

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:
21.0ms
(/ (/ (* 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)))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series129.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
54.0ms
(/ (/ (+ (* 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)))

simplify74.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010985877
150015622

prune745.0ms

Filtered
186 candidates to 264 candidates (-41.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2595264
Fresh235
Picked101
Done000
Total2628270

Merged error: 32.2b

Counts
270 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
33.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
216×times-frac
163×add-sqr-sqrt
151×*-un-lft-identity
99×add-cube-cbrt
32×difference-of-squares
31×associate-/r/
25×add-exp-log associate-/r* add-cbrt-cube
19×associate-/l*
17×flip3-+ flip-+
16×sqrt-prod div-inv distribute-lft-out--
11×cbrt-undiv div-exp
10×distribute-lft-out
7×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
2×associate-*r/ prod-exp cbrt-unprod
1×flip3-- div-sub flip--
Counts
4 → 253
Calls
4 calls:
20.0ms
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
21.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
14.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series155.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
33.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
19.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
27.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify75.0ms

Algorithm
egg-herbie
Counts
265 → 265
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011615920
150015650

prune906.0ms

Filtered
187 candidates to 265 candidates (-41.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2650265
Fresh077
Picked011
Done000
Total2658273

Merged error: 32.2b

Counts
273 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))
33.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.6b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.6b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
21×times-frac
18×sqrt-prod
11×add-exp-log add-cbrt-cube
7×associate-/l*
6×pow1 flip3-+ sqrt-div associate-/r* flip-+
4×associate-/r/ associate-/l/ add-log-exp
3×cbrt-undiv div-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num div-inv
1×prod-exp cbrt-unprod
Counts
4 → 98
Calls
4 calls:
11.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
4.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series102.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))
19.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
18.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
19.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify55.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04261337
120081249
250011244

prune206.0ms

Filtered
85 candidates to 110 candidates (-29.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1091110
Fresh066
Picked011
Done011
Total1099118

Merged error: 32.2b

Counts
118 → 9

regimes258.0ms

Accuracy

36.9% (2.4b remaining)

Error of 36.8b against oracle of 34.4b and baseline of 38.2b

bsearch24.0ms

Steps
ItersRangePoint
8
1.2816367504786225e+224
2.8730096615755514e+227
1.3017545274946813e+224

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03630
13630

end0.0ms

sample1.1s

Algorithm
intervals
Results
609.0ms8000×body80valid
168.0ms8000×pre80true

Profiling

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