Details

Time bar (total: 5.6s)

sample36.0ms

Algorithm
intervals
Results
9.0ms203×body80valid
5.0ms256×pre80true
4.0ms18×body1280valid
3.0ms19×body640valid
1.0ms8×body320valid
1.0ms8×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

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: 23.3b

Counts
2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
19.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
32.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
14.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series584.0ms

Counts
3 → 9
Calls
3 calls:
227.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
276.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
81.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify92.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06811905
136221789
250011789

prune303.0ms

Filtered
120 candidates to 89 candidates (74.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1128120
Fresh000
Picked101
Done000
Total1138121

Merged error: 6.5b

Counts
121 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.0b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 295
Calls
4 calls:
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
19.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
41.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series737.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
160.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
225.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
276.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify70.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
010804781
150014605

prune656.0ms

Filtered
307 candidates to 198 candidates (64.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3007307
Fresh527
Picked101
Done000
Total3069315

Merged error: 6.5b

Counts
315 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.2b
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.0b
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
51×add-sqr-sqrt
50×add-exp-log
43×times-frac
39×associate-*r*
32×add-cube-cbrt add-cbrt-cube
22×prod-exp
12×div-exp cbrt-unprod
11×pow1 frac-times associate-*l/
10×flip3-+ flip-+
7×cbrt-undiv distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
5×associate-*l* associate-/l*
4×associate-*r/ pow-prod-down distribute-lft-out
3×rec-exp 1-exp associate-/r* div-inv
2×*-commutative associate-/l/ unswap-sqr
1×+-commutative flip3-- frac-2neg div-sub clear-num sum-log un-div-inv flip--
Counts
4 → 155
Calls
4 calls:
12.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
16.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
26.0ms
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series655.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
80.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
225.0ms
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
274.0ms
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify122.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
08552016
148211785
250021784

prune355.0ms

Filtered
167 candidates to 113 candidates (67.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1652167
Fresh178
Picked101
Done000
Total1679176

Merged error: 6.5b

Counts
176 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.2b
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.0b
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
4.0b
(log (exp (+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
39×associate-*r*
38×*-un-lft-identity
35×add-sqr-sqrt
30×add-cbrt-cube
28×times-frac
24×add-cube-cbrt
22×prod-exp
12×pow1 cbrt-unprod
11×frac-times div-exp associate-*l/
9×flip3-+ flip-+
6×cbrt-undiv add-log-exp
5×associate-*l*
4×log-prod associate-*r/ pow-prod-down associate-/r/ log-pow distribute-lft-out
3×rec-exp exp-prod 1-exp distribute-lft-out-- difference-of-squares
2×*-commutative div-inv unswap-sqr
1×+-commutative rem-log-exp exp-sum sum-log un-div-inv
Counts
4 → 131
Calls
4 calls:
17.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
26.0ms
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
27.0ms
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
24.0ms
(log (exp (+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

series864.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
230.0ms
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
277.0ms
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
275.0ms
(log (exp (+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify121.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
08131985
146061720
250021691

prune338.0ms

Filtered
143 candidates to 97 candidates (67.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1430143
Fresh088
Picked011
Done000
Total1439152

Merged error: 6.5b

Counts
152 → 9

regimes190.0ms

bsearch4.0ms

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