Details

Time bar (total: 11.1s)

sample36.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
6.0ms256×pre80true

simplify40.0ms

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: 51.5b

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))))
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))
43.6b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite101.0ms

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:
13.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
41.0ms
(/ (/ (* (* 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:
61.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
107.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
750.0ms
(/ (/ (* (* 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))
175.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify80.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012495670
150015161

prune596.0ms

Filtered
212 candidates to 143 candidates (67.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2066212
Fresh000
Picked101
Done000
Total2076213

Merged error: 34.5b

Counts
213 → 6

localize18.0ms

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))))
36.0b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.0b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite177.0ms

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:
23.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
106.0ms
(* (/ (/ (* 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))))
13.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series3.0s

Counts
4 → 12
Calls
4 calls:
333.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.4s
(* (/ (/ (* 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))))
122.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
90.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify124.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0168310749
150019903

prune1.1s

Filtered
376 candidates to 246 candidates (65.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New3724376
Fresh325
Picked011
Done000
Total3757382

Merged error: 34.5b

Counts
382 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
0.5b
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.5b
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
36.0b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
141×*-un-lft-identity
117×times-frac
106×add-sqr-sqrt
76×add-cube-cbrt
60×sqrt-prod
39×distribute-lft-out
36×associate-*r*
24×associate-*l*
22×add-exp-log add-cbrt-cube
15×associate-/r*
11×associate-/l*
10×associate-/r/
9×unswap-sqr
8×sqrt-div
7×cbrt-undiv flip3-+ div-exp flip-+
6×pow1
5×div-inv
4×prod-exp cbrt-unprod associate-/l/ add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 218
Calls
4 calls:
37.0ms
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
8.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
14.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
17.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series642.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
175.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
155.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
124.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify114.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
09183163
145882914
250012854

prune741.0ms

Filtered
230 candidates to 157 candidates (68.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2282230
Fresh145
Picked011
Done011
Total2298237

Merged error: 1.5b

Counts
237 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.4b
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
0.5b
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.5b
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
139×*-un-lft-identity
112×times-frac
100×add-sqr-sqrt
70×add-cube-cbrt
60×sqrt-prod
41×distribute-lft-out
38×add-exp-log add-cbrt-cube
36×associate-*r*
24×associate-*l*
16×associate-/r*
15×cbrt-undiv div-exp
10×associate-/r/
9×associate-/l* unswap-sqr
8×sqrt-div prod-exp cbrt-unprod
6×pow1 flip3-+ flip-+
5×div-inv associate-/l/
4×add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/
1×pow-prod-down *-commutative
Counts
4 → 221
Calls
4 calls:
32.0ms
(/ (* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
41.0ms
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
8.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
14.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))

series1.1s

Counts
4 → 12
Calls
4 calls:
529.0ms
(/ (* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
190.0ms
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
180.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
163.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))

simplify59.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
09983600
150013198

prune790.0ms

Filtered
233 candidates to 152 candidates (65.2%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2285233
Fresh055
Picked101
Done022
Total22912241

Merged error: 1.2b

Counts
241 → 12

regimes242.0ms

Accuracy

46.5% (8.8b remaining)

Error of 10.9b against oracle of 2.0b and baseline of 18.5b

bsearch72.0ms

Steps
ItersRangePoint
7
1.2450793825941955e+147
3.154578964166934e+148
1.5248065181528398e+148

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057103
157103

end0.0ms

sample849.0ms

Algorithm
intervals
Results
468.0ms8000×body80valid
176.0ms8000×pre80true

Profiling

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