Details

Time bar (total: 7.6s)

sample149.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 85.935212%

Space saved by search: 85.935212%

Guaranteed chance to sample good point: 99.990845%

Results
20.0ms256×body80valid
5.0ms256×pre80true

simplify41.0ms

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: 54.0b

Counts
2 → 1

localize18.0ms

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))))
37.1b
(/ (/ (* (* 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))
45.9b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite93.0ms

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))
23.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series411.0ms

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))))
320.0ms
(/ (/ (* (* 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))))

simplify78.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012495670
150015161

prune448.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2048212
Fresh000
Picked101
Done000
Total2058213

Merged error: 35.2b

Counts
213 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
36.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
366×times-frac
300×add-sqr-sqrt
235×*-un-lft-identity
155×add-cube-cbrt
96×associate-*r*
70×add-exp-log add-cbrt-cube
62×difference-of-squares
44×associate-/r/
42×associate-*l*
33×cbrt-undiv div-exp
31×sqrt-prod distribute-lft-out--
22×flip3-+ flip-+ div-inv
19×associate-/l*
16×prod-exp cbrt-unprod
12×associate-/r*
9×distribute-lft-out
6×pow1 unswap-sqr
5×associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 364
Calls
4 calls:
21.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
98.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
391.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
27.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
21.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify119.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0168310749
150019903

prune1.4s

Filtered
246 candidates to 376 candidates (-52.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3697376
Fresh437
Picked101
Done000
Total37410384

Merged error: 35.2b

Counts
384 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
36.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
223×times-frac
185×add-sqr-sqrt
147×*-un-lft-identity
117×sqrt-prod
99×add-cube-cbrt associate-*r*
42×associate-*l*
30×associate-/r/ difference-of-squares
27×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
15×div-inv distribute-lft-out--
9×cbrt-undiv div-exp associate-/r* distribute-lft-out
8×unswap-sqr
7×associate-/l*
6×pow1 prod-exp cbrt-unprod associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
2×sqrt-div
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 256
Calls
4 calls:
102.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
410.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (/ (/ (+ (* 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)))
26.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
19.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify89.0ms

Algorithm
egg-herbie
Counts
268 → 268
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013306992
150026588

prune1.1s

Filtered
190 candidates to 268 candidates (-41.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2680268
Fresh099
Picked011
Done000
Total26810278

Merged error: 35.2b

Counts
278 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

36.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
12×associate-/r*
8×flip3-+ associate-/r/ flip-+ associate-/l/ associate-/l*
6×cbrt-undiv div-exp
4×pow1 frac-2neg associate-*r/ clear-num div-inv add-log-exp
2×prod-exp cbrt-unprod
Counts
4 → 112
Calls
4 calls:
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
14.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series87.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
26.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
16.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
16.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify56.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
03541472
119031306
250021306

prune564.0ms

Filtered
100 candidates to 124 candidates (-24.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1240124
Fresh088
Picked011
Done011
Total12410134

Merged error: 35.2b

Counts
134 → 10

regimes269.0ms

Accuracy

31.4% (2.6b remaining)

Error of 36.9b against oracle of 34.3b and baseline of 38.1b

bsearch35.0ms

Steps
ItersRangePoint
6
2.330968681143619e+190
3.064208509337496e+191
2.3834137991297672e+190

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03647
13647

end0.0ms

sample1.2s

Algorithm
intervals
sampling

Space saved by range analysis: 85.935212%

Space saved by search: 85.935212%

Guaranteed chance to sample good point: 99.990845%

Results
637.0ms8000×body80valid
176.0ms8000×pre80true

Profiling

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