Details

Time bar (total: 6.7s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 54.7b

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))))
39.0b
(/ (/ (* (* 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))
46.6b
(/ (* (* 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:
16.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(* (* 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))))

series1.1s

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
102.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
720.0ms
(/ (/ (* (* 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))
170.0ms
(/ (* (* 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 (30.0ms)

IterNodesCost
012495670
150015161

prune544.0ms

Filtered
212 candidates to 143 candidates (67.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2057212
Fresh000
Picked101
Done000
Total2067213

Merged error: 36.8b

Counts
213 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.5b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
35.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite78.0ms

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)))

series764.0ms

Counts
4 → 12
Calls
4 calls:
255.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
312.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
83.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
114.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify78.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010985877
150015622

prune742.0ms

Filtered
264 candidates to 186 candidates (70.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2613264
Fresh336
Picked011
Done000
Total2647271

Merged error: 36.7b

Counts
271 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))
35.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.6b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.6b
(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:
10.0ms
(/ (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))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))
83.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
51.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
55.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify53.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04131325
119471225
250021220

prune386.0ms

Filtered
110 candidates to 83 candidates (75.5%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1100110
Fresh055
Picked011
Done011
Total1107117

Merged error: 36.7b

Counts
117 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
8.4b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))
28.2b
(* (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))
35.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
56×add-exp-log
54×times-frac
40×*-un-lft-identity
37×add-cube-cbrt
27×cbrt-prod
24×associate-*r* add-cbrt-cube
21×prod-exp
18×cbrt-div div-exp
15×associate-*l*
14×associate-/r/
12×flip3-+ flip-+
10×cbrt-undiv
9×associate-/r* cbrt-unprod unswap-sqr
6×pow1
5×frac-times associate-*r/
4×rec-exp 1-exp div-inv associate-/l/ associate-/l* add-log-exp
3×associate-*l/
2×frac-2neg clear-num
1×pow1/3 pow-prod-down *-commutative
Counts
4 → 161
Calls
4 calls:
5.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))
34.0ms
(* (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))
17.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series628.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
210.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))
134.0ms
(* (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))
85.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify55.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010353311
150012949

prune665.0ms

Filtered
173 candidates to 138 candidates (79.8%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1721173
Fresh044
Picked011
Done022
Total1728180

Merged error: 36.7b

Counts
180 → 8

regimes150.0ms

Accuracy

27.9% (2.7b remaining)

Error of 36.4b against oracle of 33.7b and baseline of 37.5b

bsearch45.0ms

Steps
ItersRangePoint
7
7.386501921603808e+153
1.459328051334974e+155
1.3297226358063274e+154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03329
13329

end0.0ms

sample685.0ms

Algorithm
intervals
Results
366.0ms8000×body80valid
131.0ms8000×pre80true