Details

Time bar (total: 14.6s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify37.0ms

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: 54.8b

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))))
35.5b
(/ (/ (* (* 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))
46.8b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite92.0ms

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:
14.0ms
(* (+ (+ 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))
23.0ms
(/ (* (* 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:
60.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
106.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
766.0ms
(/ (/ (* (* 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))
173.0ms
(/ (* (* 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 (28.0ms)

IterNodesCost
012495670
150015161

prune665.0ms

Filtered
212 candidates to 143 candidates (67.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2039212
Fresh000
Picked101
Done000
Total2049213

Merged error: 34.0b

Counts
213 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
34.0b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite82.0ms

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:
20.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
25.0ms
(/ (/ (+ (* 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)))

series817.0ms

Counts
4 → 12
Calls
4 calls:
264.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
341.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
90.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
121.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify72.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010985877
150015622

prune905.0ms

Filtered
264 candidates to 186 candidates (70.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2586264
Fresh448
Picked101
Done000
Total26310273

Merged error: 33.9b

Counts
273 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
0.5b
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
34.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
4160×times-frac
3009×*-un-lft-identity
1593×add-sqr-sqrt
1529×add-cube-cbrt
810×distribute-lft-out
171×div-inv
147×associate-/r/
101×associate-/r*
67×flip3-+ flip-+
43×add-exp-log
36×associate-/l*
34×add-cbrt-cube
32×difference-of-squares
29×div-exp
20×cbrt-undiv
16×sqrt-prod distribute-lft-out--
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
3×1-exp
1×flip3-- flip--
Counts
4 → 1484
Calls
4 calls:
21.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
13.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
55.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series801.0ms

Counts
4 → 12
Calls
4 calls:
352.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
66.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
262.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
122.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify385.0ms

Algorithm
egg-herbie
Counts
1496 → 1496
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500242613

prune3.8s

Filtered
1496 candidates to 679 candidates (45.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New149151496
Fresh729
Picked011
Done000
Total149881506

Merged error: 2.0b

Counts
1506 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
0.2b
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
0.5b
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))

rewrite276.0ms

Algorithm
rewrite-expression-head
Rules
4175×times-frac
3109×*-un-lft-identity
1550×add-sqr-sqrt
1534×add-cube-cbrt
877×distribute-lft-out
169×div-inv
142×associate-/r/
119×associate-/r*
65×flip3-+ flip-+
43×add-exp-log
34×add-cbrt-cube
29×div-exp
25×associate-/l*
20×cbrt-undiv
8×difference-of-squares
7×associate-/l/
4×pow1 frac-2neg clear-num sqrt-prod distribute-lft-out-- add-log-exp
3×1-exp
1×flip3-- flip--
Counts
4 → 1494
Calls
4 calls:
21.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
20.0ms
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
12.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
49.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))

series697.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
177.0ms
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
74.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
258.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))

simplify615.0ms

Algorithm
egg-herbie
Counts
1506 → 1506
Iterations

Useful iterations: 1 (72.0ms)

IterNodesCost
0476542023
1500140932

prune2.9s

Filtered
1506 candidates to 529 candidates (35.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New150241506
Fresh156
Picked101
Done011
Total1504101514

Merged error: 1.7b

Counts
1514 → 10

regimes215.0ms

Accuracy

45.8% (8.7b remaining)

Error of 10.6b against oracle of 1.9b and baseline of 17.9b

bsearch30.0ms

Steps
ItersRangePoint
3
4.643101948939184e+144
5.979143538489926e+144
5.227620144367633e+144

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06162
16962
26962

end0.0ms

sample653.0ms

Algorithm
intervals
Results
343.0ms8000×body80valid
127.0ms8000×pre80true