Details

Time bar (total: 6.3s)

analyze57.0ms

Algorithm
search

sample38.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
5.0ms256×pre80true

simplify42.0ms

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: 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))))
35.7b
(/ (/ (* (* 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))
44.9b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite91.0ms

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:
9.0ms
(* i (+ (+ alpha beta) i))
12.0ms
(* (* 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))
23.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series399.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(* i (+ (+ alpha beta) 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))
60.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify69.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012085419
150014944

prune430.0ms

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1956201
Fresh000
Picked101
Done000
Total1966202

Merged error: 33.8b

Counts
202 → 6

localize196.0ms

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

rewrite160.0ms

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:
20.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
97.0ms
(* (/ (/ (* 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)))

series545.0ms

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)))
427.0ms
(* (/ (/ (* 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))))
32.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify121.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0168310749
150019903

prune1.2s

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

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3733376
Fresh145
Picked011
Done000
Total3748382

Merged error: 33.8b

Counts
382 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

31.8b
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
32.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log add-cbrt-cube
14×*-un-lft-identity
12×add-sqr-sqrt
10×add-cube-cbrt
8×cbrt-undiv sqrt-div div-exp
7×flip3-+ times-frac associate-/r* flip-+ associate-/l/
6×pow1 sqrt-prod
5×prod-exp cbrt-unprod
4×associate-*r/ associate-/r/ add-log-exp
2×frac-times rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num div-inv distribute-lft-out associate-/l*
1×associate-*l/
Counts
4 → 89
Calls
4 calls:
25.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
5.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series158.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
19.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
18.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
18.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify86.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06501504
136611303
250011301

prune222.0ms

Filtered
78 candidates to 101 candidates (-29.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1010101
Fresh066
Picked011
Done011
Total1018109

Merged error: 33.8b

Counts
109 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
8.4b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))
24.6b
(* (/ 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)))))
32.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite67.0ms

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)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))
32.0ms
(* (/ 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)))))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series151.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
63.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))
30.0ms
(* (/ 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)))))
18.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify53.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010443342
150022953

prune598.0ms

Filtered
139 candidates to 173 candidates (-24.5%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1730173
Fresh055
Picked011
Done022
Total1738181

Merged error: 33.8b

Counts
181 → 8

regimes236.0ms

Accuracy

27% (2.8b remaining)

Error of 36.6b against oracle of 33.7b and baseline of 37.6b

bsearch249.0ms

Steps
ItersRangePoint
8
5.731017712249568e+153
3.3406879451631688e+156
1.3345063179778946e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03329
13329

end0.0ms

analyze46.0ms

Algorithm
search

sample1.0s

Algorithm
intervals
Results
680.0ms8000×body80valid
175.0ms8000×pre80true

Profiling

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