Details

Time bar (total: 14.0s)

sample33.0ms

Algorithm
intervals
Results
14.0ms256×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: 54.5b

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))))
39.1b
(/ (/ (* (* 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))
46.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite100.0ms

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))))
40.0ms
(/ (/ (* (* 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))
24.0ms
(/ (* (* 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:
55.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
109.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
747.0ms
(/ (/ (* (* 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))))

simplify81.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012495670
150015161

prune551.0ms

Filtered
212 candidates to 143 candidates (67.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New2093212
Fresh000
Picked101
Done000
Total2103213

Merged error: 35.4b

Counts
213 → 3

localize23.0ms

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))))
34.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite171.0ms

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:
25.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
99.0ms
(* (/ (/ (* 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
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series2.9s

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)))
2.4s
(* (/ (/ (* 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))))
114.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
89.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify129.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0168310749
150019903

prune1.0s

Filtered
376 candidates to 246 candidates (65.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New3724376
Fresh022
Picked101
Done000
Total3736379

Merged error: 35.4b

Counts
379 → 6

localize22.0ms

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))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
34.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite736.0ms

Algorithm
rewrite-expression-head
Rules
2499×times-frac
1610×add-sqr-sqrt
1254×*-un-lft-identity
938×add-cube-cbrt
921×sqrt-prod
900×associate-*r*
298×difference-of-squares
149×distribute-lft-out--
92×associate-/r/
89×add-exp-log add-cbrt-cube
76×sqrt-div
49×div-inv
46×cbrt-undiv div-exp
45×flip3-+ flip-+
42×associate-*l*
21×prod-exp cbrt-unprod
16×unswap-sqr
9×distribute-lft-out
8×pow1
4×add-log-exp
3×associate-*r/ associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times flip3-- frac-2neg pow-prod-down associate-*l/ clear-num *-commutative flip-- associate-/l*
Counts
4 → 1057
Calls
4 calls:
581.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series2.5s

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))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
63.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
58.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify405.0ms

Algorithm
egg-herbie
Counts
1069 → 1069
Iterations

Useful iterations: 1 (83.0ms)

IterNodesCost
0484940898
1500240088

prune2.2s

Filtered
1069 candidates to 409 candidates (38.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New106811069
Fresh055
Picked101
Done000
Total106961075

Merged error: 35.4b

Counts
1075 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))))
34.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
40×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
27×times-frac
19×pow1
18×add-exp-log add-cbrt-cube
14×swap-sqr associate-/r/
12×associate-*r* associate-*l*
10×flip3-+ flip-+
9×associate-/r*
8×sqrt-pow1 pow1/2
7×div-inv
6×associate-/l/
5×cbrt-undiv associate-*r/ div-exp pow-prod-up associate-/l*
4×sqrt-div add-log-exp unswap-sqr
3×frac-2neg pow-prod-down prod-exp clear-num pow-sqr cbrt-unprod
1×pow2 frac-times pow-plus sqrt-unprod associate-*l/ rem-square-sqrt *-commutative
Counts
4 → 151
Calls
4 calls:
28.0ms
(* (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
18.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))))
113.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
84.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
96.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify99.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
05231893
133231675
250011639

prune505.0ms

Filtered
163 candidates to 115 candidates (70.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1630163
Fresh055
Picked011
Done000
Total1636169

Merged error: 35.4b

Counts
169 → 6

regimes113.0ms

Accuracy

28% (2.7b remaining)

Error of 36.2b against oracle of 33.6b and baseline of 37.3b

bsearch64.0ms

Steps
ItersRangePoint
8
3.7441419316489915e+151
1.541204506312033e+154
1.3382376899184736e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03539
13539

end0.0ms

sample782.0ms

Algorithm
intervals
Results
431.0ms8000×body80valid
164.0ms8000×pre80true