Details

Time bar (total: 6.6s)

analyze121.0ms

Algorithm
search

sample37.0ms

Algorithm
intervals
Results
12.0ms209×body80valid
5.0ms256×pre80true
3.0ms16×body640valid
3.0ms10×body1280valid
2.0ms13×body320valid
1.0ms8×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 23.9b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2.0 i))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.5b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
48×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×associate-/r/
12×flip3-+ flip-+
11×distribute-lft-out add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
4×pow1 frac-times sum-log
3×flip3-- flip--
2×+-commutative frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×associate-+l+
Counts
4 → 124
Calls
4 calls:
7.0ms
(+ (+ alpha beta) (* 2.0 i))
18.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
27.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
13.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series169.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (+ alpha beta) (* 2.0 i))
64.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
82.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify100.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07011981
139801865
250021865

prune280.0ms

Filtered
101 candidates to 136 candidates (-34.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New12511136
Fresh000
Picked101
Done000
Total12611137

Merged error: 5.8b

Counts
137 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))
0.1b
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
0.1b
(/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.5b
(+ (/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
1580×times-frac
1545×*-un-lft-identity
747×add-sqr-sqrt
537×add-cube-cbrt
399×distribute-lft-out
117×associate-/l*
105×distribute-lft-out-- difference-of-squares
60×associate-/r/
35×associate-/r*
33×div-inv
26×flip3-- flip--
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×add-log-exp
5×associate-/l/
4×pow1 flip3-+ flip-+
3×frac-2neg clear-num
1×+-commutative sum-log
Counts
4 → 776
Calls
4 calls:
10.0ms
(/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))
18.0ms
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
38.0ms
(/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
132.0ms
(+ (/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series186.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))
17.0ms
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
65.0ms
(/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
88.0ms
(+ (/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify188.0ms

Algorithm
egg-herbie
Counts
788 → 788
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0180116134
1500115862

prune1.4s

Filtered
362 candidates to 788 candidates (-117.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New7853788
Fresh5510
Picked101
Done000
Total7918799

Merged error: 5.8b

Counts
799 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
0.1b
(* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.7b
(+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
450×*-un-lft-identity
427×times-frac
267×add-sqr-sqrt
165×add-cube-cbrt
109×associate-*l*
105×distribute-lft-out
52×add-exp-log
36×distribute-lft-out-- difference-of-squares
32×add-cbrt-cube
30×associate-/r*
24×associate-/r/
23×div-exp
18×associate-*r*
13×cbrt-undiv div-inv
12×prod-exp
9×flip3-- flip-- unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
4×rec-exp flip3-+ 1-exp flip-+
2×frac-2neg clear-num associate-/l/
1×+-commutative frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ sum-log un-div-inv *-commutative inv-pow
Counts
4 → 366
Calls
4 calls:
9.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
55.0ms
(* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
30.0ms
(+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series182.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
17.0ms
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
65.0ms
(* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
89.0ms
(+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify78.0ms

Algorithm
egg-herbie
Counts
378 → 378
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012535308
150014931

prune539.0ms

Filtered
205 candidates to 378 candidates (-84.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3753378
Fresh257
Picked011
Done000
Total3779386

Merged error: 5.8b

Counts
386 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b
(exp (log (+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
2.5b
(log (+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
4.7b
(+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
215×*-un-lft-identity
211×times-frac
144×add-sqr-sqrt
109×associate-*l*
82×add-cube-cbrt
49×distribute-lft-out
44×add-exp-log
25×add-cbrt-cube
18×div-exp associate-*r*
16×distribute-lft-out-- difference-of-squares
12×prod-exp
11×associate-/r/
9×cbrt-undiv unswap-sqr
8×pow1
6×log-prod cbrt-unprod div-inv add-log-exp
4×log-div exp-prod flip3-- flip3-+ flip-- flip-+
3×rec-exp 1-exp exp-sum
2×exp-diff log-pow
1×+-commutative frac-times associate-*r/ rem-log-exp pow-prod-down associate-*l/ sum-log un-div-inv *-commutative rem-exp-log
Counts
4 → 209
Calls
4 calls:
54.0ms
(* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
28.0ms
(exp (log (+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
28.0ms
(log (+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
27.0ms
(+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series329.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
84.0ms
(exp (log (+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
96.0ms
(log (+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
84.0ms
(+ (* (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify132.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010783715
148193363
250023363

prune375.0ms

Filtered
130 candidates to 221 candidates (-70.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2174221
Fresh167
Picked101
Done101
Total22010230

Merged error: 3.7b

Counts
230 → 10

regimes338.0ms

Accuracy

-19.1% (9.1b remaining)

Error of 13.5b against oracle of 4.3b and baseline of 12.0b

bsearch149.0ms

Steps
ItersRangePoint
6
4.628922042532027e+136
2.737833548212726e+137
2.7017646629254024e+137

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05634
15634

end0.0ms

analyze124.0ms

Algorithm
search

sample1.1s

Algorithm
intervals
Results
356.0ms6395×body80valid
178.0ms8000×pre80true
144.0ms518×body1280valid
126.0ms548×body640valid
59.0ms327×body320valid
24.0ms212×body160valid

Profiling

Loading profile data...