Details

Time bar (total: 8.4s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify38.0ms

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: 53.0b

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))))
34.7b
(/ (/ (* (* 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))
45.4b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite93.0ms

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:
15.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.0ms
(/ (/ (* (* 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:
59.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
104.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
765.0ms
(/ (/ (* (* 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))
172.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify75.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012495670
150015161

prune569.0ms

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: 32.5b

Counts
213 → 9

localize17.0ms

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)))
32.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite81.0ms

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)))
21.0ms
(/ (/ (+ (* 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)))
16.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series935.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
473.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
89.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
124.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify79.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010985877
150015622

prune761.0ms

Filtered
264 candidates to 186 candidates (70.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2577264
Fresh268
Picked101
Done000
Total26013273

Merged error: 32.4b

Counts
273 → 13

localize20.0ms

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
(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
32.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.3b
(/ (+ (+ alpha beta) (* 2.0 i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
867×times-frac
548×add-sqr-sqrt
466×*-un-lft-identity
344×add-cube-cbrt
102×difference-of-squares
67×associate-/r/
63×associate-/l*
51×sqrt-prod distribute-lft-out--
39×add-exp-log
37×div-inv
31×flip3-+ flip-+
29×add-cbrt-cube
22×div-exp
16×associate-/r*
14×cbrt-undiv
10×distribute-lft-out
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
2×rec-exp 1-exp associate-*r/ prod-exp cbrt-unprod
1×flip3-- flip--
Counts
4 → 503
Calls
4 calls:
24.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
28.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (+ (* 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)))
10.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series794.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
321.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
86.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
141.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify173.0ms

Algorithm
egg-herbie
Counts
515 → 515
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0216314769
1500114225

prune1.2s

Filtered
515 candidates to 282 candidates (54.8%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New5150515
Fresh01212
Picked011
Done000
Total51513528

Merged error: 32.4b

Counts
528 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
32.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
70×*-un-lft-identity
45×sqrt-prod
44×add-sqr-sqrt add-cube-cbrt
18×add-exp-log associate-/r/ add-cbrt-cube
17×associate-/l*
13×associate-/r* distribute-lft-out
12×flip3-+ flip-+
9×div-inv
7×associate-/l/
6×cbrt-undiv div-exp
4×pow1 frac-2neg associate-*r/ clear-num add-log-exp
2×prod-exp cbrt-unprod
1×sqrt-div
Counts
4 → 160
Calls
4 calls:
20.0ms
(/ (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
14.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
272.0ms
(/ (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
87.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
88.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
123.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify93.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06272816
129322659
250032650

prune596.0ms

Filtered
172 candidates to 128 candidates (74.4%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1702172
Fresh2911
Picked011
Done011
Total17213185

Merged error: 32.4b

Counts
185 → 13

regimes201.0ms

Accuracy

27.8% (2.8b remaining)

Error of 36.6b against oracle of 33.9b and baseline of 37.7b

bsearch73.0ms

Steps
ItersRangePoint
10
2.7149368622143967e+187
7.480150946057167e+197
1.2148514849628163e+188

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03630
13630

end0.0ms

sample661.0ms

Algorithm
intervals
Results
352.0ms8000×body80valid
128.0ms8000×pre80true