Details

Time bar (total: 5.2s)

sample72.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 85.955805%

Space saved by search: 85.955805%

Guaranteed chance to sample good point: 0%

Results
22.0ms256×body80valid
5.0ms256×pre80true

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 53.5b

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

rewrite94.0ms

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)))
11.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.0ms
(/ (/ (* (* 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))))

series405.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
26.0ms
(* (* 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))
58.0ms
(/ (* (* 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 (28.0ms)

IterNodesCost
012495670
150015161

prune456.0ms

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

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2057212
Fresh000
Picked101
Done000
Total2067213

Merged error: 34.6b

Counts
213 → 7

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)))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.2b
(/ (+ (* 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×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:
20.0ms
(/ (/ (* 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)))

series135.0ms

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)))
52.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
21.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
27.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify71.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010985877
150015622

prune675.0ms

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

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2568264
Fresh336
Picked101
Done000
Total26011271

Merged error: 34.5b

Counts
271 → 11

localize25.0ms

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)))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
35.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
62×*-un-lft-identity
42×add-sqr-sqrt add-cube-cbrt
22×add-exp-log add-cbrt-cube
18×associate-/r/
16×associate-/l*
13×associate-/r*
12×flip3-+ flip-+
10×distribute-lft-out
9×cbrt-undiv div-exp div-inv
7×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
2×associate-*r/ prod-exp cbrt-unprod
Counts
4 → 155
Calls
4 calls:
21.0ms
(/ (/ (* 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)))
11.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series105.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
18.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
27.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
27.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify93.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06582642
136112449
250022449

prune622.0ms

Filtered
128 candidates to 167 candidates (-30.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1670167
Fresh01010
Picked011
Done000
Total16711178

Merged error: 34.5b

Counts
178 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.1b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.1b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
265×times-frac
237×add-sqr-sqrt
161×*-un-lft-identity
150×associate-*r*
113×add-cube-cbrt
93×sqrt-prod
48×difference-of-squares
24×distribute-lft-out--
18×add-exp-log add-cbrt-cube
16×associate-/r/
12×flip3-+ flip-+
8×pow1 sqrt-div div-inv unswap-sqr
6×associate-*l*
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod add-log-exp
3×associate-*r/ associate-/r*
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ associate-/l/
1×flip3-- frac-2neg pow-prod-down clear-num *-commutative flip-- associate-/l*
Counts
4 → 239
Calls
4 calls:
53.0ms
(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (/ (sqrt (+ (* beta alpha) (* 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)))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series110.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (/ (sqrt (+ (* 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)))
18.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
19.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify69.0ms

Algorithm
egg-herbie
Counts
251 → 251
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010985360
150024986

prune534.0ms

Filtered
148 candidates to 251 candidates (-69.6%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2510251
Fresh099
Picked011
Done011
Total25111262

Merged error: 34.5b

Counts
262 → 11

regimes271.0ms

Accuracy

35.1% (2.5b remaining)

Error of 37.0b against oracle of 34.5b and baseline of 38.3b

bsearch33.0ms

Steps
ItersRangePoint
7
9.751139691721553e+200
3.285105339797119e+202
9.872752329169805e+200

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03649
13649

end0.0ms

sample1.0s

Algorithm
intervals
sampling

Space saved by range analysis: 85.955805%

Space saved by search: 85.955805%

Guaranteed chance to sample good point: 0%

Results
625.0ms8000×body80valid
179.0ms8000×pre80true

Profiling

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