Details

Time bar (total: 5.2s)

sample39.0ms

Algorithm
intervals
Results
20.0ms256×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: 52.8b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.8b
(/ (/ (* (* 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))
45.1b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×distribute-lft-out
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 189
Calls
4 calls:
8.0ms
(* i (+ (+ alpha beta) i))
13.0ms
(* (* 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))
22.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series396.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(* i (+ (+ alpha beta) i))
22.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
317.0ms
(/ (/ (* (* 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))
52.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify70.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012085419
150014944

prune424.0ms

Filtered
138 candidates to 201 candidates (-45.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1938201
Fresh000
Picked101
Done000
Total1948202

Merged error: 32.7b

Counts
202 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
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))))
33.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
213×times-frac
175×add-sqr-sqrt
145×*-un-lft-identity
101×associate-*r*
92×add-cube-cbrt
67×add-exp-log add-cbrt-cube
45×associate-*l*
30×cbrt-undiv div-exp difference-of-squares
28×associate-/r/
17×prod-exp cbrt-unprod
16×flip3-+ flip-+
15×sqrt-prod distribute-lft-out--
14×div-inv
12×distribute-lft-out
8×pow1
7×unswap-sqr
6×associate-/r*
5×associate-*r/
4×associate-/l/ associate-/l* add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative
1×distribute-rgt-in frac-times flip3-- distribute-lft-in associate-*l/ flip--
Counts
4 → 260
Calls
4 calls:
8.0ms
(* i (+ (+ alpha beta) i))
94.0ms
(* (/ (/ (* 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
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(* i (+ (+ alpha beta) i))
374.0ms
(* (/ (/ (* 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))))
15.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
30.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify90.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015207165
150016394

prune736.0ms

Filtered
176 candidates to 272 candidates (-54.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2666272
Fresh527
Picked101
Done000
Total2728280

Merged error: 32.6b

Counts
280 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

32.9b
(sqrt (* i (+ (+ alpha beta) i)))
32.9b
(sqrt (* i (+ (+ alpha beta) i)))
33.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.5b
(/ (+ (* beta alpha) (* (sqrt (* i (+ (+ alpha beta) i))) (sqrt (* i (+ (+ alpha beta) i))))) (+ (+ alpha beta) (* 2.0 i)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×times-frac
11×add-exp-log add-cbrt-cube
10×pow1
6×flip3-+ associate-*r/ associate-/r* flip-+
4×sqrt-pow1 sqrt-div associate-/r/ associate-/l/ associate-/l* add-log-exp
3×cbrt-undiv div-exp
2×frac-2neg pow1/2 pow-prod-down clear-num sqrt-prod div-inv
1×prod-exp cbrt-unprod
Counts
4 → 82
Calls
4 calls:
6.0ms
(sqrt (* i (+ (+ alpha beta) i)))
6.0ms
(sqrt (* i (+ (+ alpha beta) i)))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
9.0ms
(/ (+ (* beta alpha) (* (sqrt (* i (+ (+ alpha beta) i))) (sqrt (* i (+ (+ alpha beta) i))))) (+ (+ alpha beta) (* 2.0 i)))

series65.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(sqrt (* i (+ (+ alpha beta) i)))
12.0ms
(sqrt (* i (+ (+ alpha beta) i)))
15.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
27.0ms
(/ (+ (* beta alpha) (* (sqrt (* i (+ (+ alpha beta) i))) (sqrt (* i (+ (+ alpha beta) i))))) (+ (+ alpha beta) (* 2.0 i)))

simplify62.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04441167
12290989
25003974

prune223.0ms

Filtered
79 candidates to 94 candidates (-19.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New94094
Fresh077
Picked011
Done000
Total948102

Merged error: 32.6b

Counts
102 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

33.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
33.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
33.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
15×add-exp-log add-cbrt-cube
12×associate-/r*
10×associate-/l*
8×flip3-+ associate-/r/ flip-+ associate-/l/
5×cbrt-undiv div-exp
4×pow1 frac-2neg clear-num div-inv add-log-exp
2×associate-*r/
1×prod-exp cbrt-unprod
Counts
4 → 118
Calls
4 calls:
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series95.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
26.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
28.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
26.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify55.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
03541678
119031519
250011519

prune531.0ms

Filtered
106 candidates to 130 candidates (-22.6%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1300130
Fresh066
Picked011
Done011
Total1308138

Merged error: 32.6b

Counts
138 → 8

regimes278.0ms

Accuracy

36.1% (2.6b remaining)

Error of 36.7b against oracle of 34.1b and baseline of 38.1b

bsearch26.0ms

Steps
ItersRangePoint
7
5.643043866543123e+197
1.7919956852684628e+199
5.7012749136749404e+197

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03535
13535

end0.0ms

sample1.3s

Algorithm
intervals
Results
832.0ms8000×body80valid
176.0ms8000×pre80true

Profiling

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