Details

Time bar (total: 4.4s)

sample42.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 85.935212%

Space saved by search: 85.935212%

Guaranteed chance to sample good point: 97.158121%

Results
19.0ms256×body80valid
5.0ms256×pre80true

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 53.7b

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))))
36.0b
(/ (/ (* (* 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))
46.0b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite89.0ms

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:
11.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.0ms
(/ (/ (* (* 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))
22.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series394.0ms

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))))
306.0ms
(/ (/ (* (* 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))
53.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify75.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012495670
150015161

prune426.0ms

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: 33.6b

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)))
35.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
35.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite75.0ms

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)))
20.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
11.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (* 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)))
26.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
16.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify73.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010985877
150015622

prune752.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2577264
Fresh325
Picked101
Done000
Total2619270

Merged error: 33.5b

Counts
270 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
35.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite32.0ms

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
9×associate-/r*
6×pow1 flip3-+ sqrt-div flip-+
4×associate-/r/ associate-/l/ 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:
10.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
21.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
18.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
15.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify59.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04551354
122201254
250011242

prune235.0ms

Filtered
84 candidates to 110 candidates (-31.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1100110
Fresh088
Picked011
Done000
Total1109119

Merged error: 33.5b

Counts
119 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))
35.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 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:
10.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))
5.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series99.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))
19.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
18.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
16.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify58.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04261337
120081249
250021244

prune207.0ms

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

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1100110
Fresh077
Picked011
Done011
Total1109119

Merged error: 33.5b

Counts
119 → 9

regimes245.0ms

Accuracy

38.8% (2.3b remaining)

Error of 36.5b against oracle of 34.1b and baseline of 37.9b

bsearch23.0ms

Steps
ItersRangePoint
6
1.2220734330151961e+216
8.738822657199828e+216
1.2372191283104931e+216

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03537
13537

end0.0ms

sample1.1s

Algorithm
intervals
sampling

Space saved by range analysis: 85.935212%

Space saved by search: 85.935212%

Guaranteed chance to sample good point: 97.158121%

Results
617.0ms8000×body80valid
174.0ms8000×pre80true

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