Details

Time bar (total: 16.8s)

sample37.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
5.0ms256×pre80true

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune4.0ms

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: 54.5b

Counts
2 → 1

localize14.0ms

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))))
36.0b
(/ (/ (* (* 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))
46.7b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite96.0ms

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:
12.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms
(* (* 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))
26.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.0s

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
98.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
693.0ms
(/ (/ (* (* 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))
160.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify71.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012495670
150015161

prune831.0ms

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: 33.6b

Counts
213 → 7

localize22.0ms

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))))
33.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite166.0ms

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:
24.0ms
(/ (/ (+ (* 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)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.7s

Counts
4 → 12
Calls
4 calls:
323.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.2s
(* (/ (/ (* 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))))
85.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
117.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify125.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0168710749
150019903

prune1.5s

Filtered
376 candidates to 246 candidates (65.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3715376
Fresh336
Picked011
Done000
Total3749383

Merged error: 33.6b

Counts
383 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

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)))
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))))
33.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
85×add-exp-log add-cbrt-cube
79×times-frac
63×*-un-lft-identity
61×add-sqr-sqrt
42×associate-*l*
41×add-cube-cbrt
40×cbrt-undiv div-exp
21×prod-exp cbrt-unprod
18×associate-/r/
15×associate-*r*
12×associate-/r*
10×flip3-+ flip-+
9×div-inv distribute-lft-out
7×associate-/l/
6×pow1
5×associate-/l*
4×associate-*r/ add-log-exp difference-of-squares unswap-sqr
3×frac-2neg clear-num
2×frac-times associate-*l/ sqrt-prod distribute-lft-out--
1×flip3-- pow-prod-down *-commutative flip--
Counts
4 → 191
Calls
4 calls:
42.0ms
(/ (* (/ (/ (* 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)))
39.0ms
(* (/ (/ (* 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))))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.0s

Counts
4 → 12
Calls
4 calls:
2.2s
(/ (* (/ (/ (* 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)))
602.0ms
(* (/ (/ (* 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))))
87.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
117.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify72.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011465216
150024213

prune970.0ms

Filtered
203 candidates to 135 candidates (66.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2021203
Fresh167
Picked101
Done011
Total2048212

Merged error: 33.6b

Counts
212 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (/ i 1) 1) (* (/ (/ (+ (+ 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)))
0.1b
(* (/ (/ i 1) 1) (* (/ (/ (+ (+ 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)))))
0.2b
(* (/ (/ (+ (+ 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))))
34.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
554×add-exp-log
326×div-exp
266×add-cbrt-cube
243×times-frac
220×*-un-lft-identity
188×prod-exp
143×add-sqr-sqrt
133×associate-*l*
128×cbrt-undiv
114×add-cube-cbrt
84×cbrt-unprod
70×1-exp
57×distribute-lft-out
16×associate-*r* associate-/r/
12×div-inv
11×pow1 frac-times associate-*r/
9×associate-/r* associate-/l/
8×flip3-+ flip-+
7×associate-*l/
6×unswap-sqr
4×pow-prod-down associate-/l* add-log-exp difference-of-squares
2×frac-2neg clear-num sqrt-prod *-commutative distribute-lft-out--
1×flip3-- flip--
Counts
4 → 401
Calls
4 calls:
55.0ms
(/ (* (/ (/ i 1) 1) (* (/ (/ (+ (+ 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)))
44.0ms
(* (/ (/ i 1) 1) (* (/ (/ (+ (+ 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)))))
49.0ms
(* (/ (/ (+ (+ 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))))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.2s

Counts
4 → 12
Calls
4 calls:
2.1s
(/ (* (/ (/ i 1) 1) (* (/ (/ (+ (+ 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)))
573.0ms
(* (/ (/ i 1) 1) (* (/ (/ (+ (+ 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)))))
366.0ms
(* (/ (/ (+ (+ 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))))
115.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify135.0ms

Algorithm
egg-herbie
Counts
413 → 413
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0216612663
1500310578

prune1.2s

Filtered
413 candidates to 201 candidates (48.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4112413
Fresh246
Picked101
Done011
Total4147421

Merged error: 1.9b

Counts
421 → 7

regimes252.0ms

Accuracy

44.7% (8.9b remaining)

Error of 11.1b against oracle of 2.1b and baseline of 18.3b

bsearch70.0ms

Steps
ItersRangePoint
7
1.9825159127612774e+126
1.8663569521707165e+128
1.821594583047221e+128

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05656
16656
26656

end0.0ms

sample907.0ms

Algorithm
intervals
Results
425.0ms8000×body80valid
161.0ms8000×pre80true

Profiling

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