Details

Time bar (total: 15.7s)

analyze126.0ms (0.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14

sample41.0ms (0.3%)

Algorithm
1×intervals
Results
14.0ms206×body80valid
5.0ms256×pre80true
4.0ms15×body1280valid
4.0ms19×body640valid
2.0ms12×body320valid
0.0ms4×body160valid

simplify43.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
0544629

prune11.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 19.4b

Counts
2 → 2

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
2.1b
(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
2.7b
(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
19.1b
(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

rewrite77.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
26×*-un-lft-identity
22×associate-*r*
21×add-sqr-sqrt flip3-+ flip-+
20×add-exp-log add-cbrt-cube
16×associate-/r/
14×frac-times
11×add-cube-cbrt
10×times-frac
8×pow1 associate-*l* associate-*l/
7×associate-*r/
6×prod-exp cbrt-unprod add-log-exp
5×distribute-lft-out associate-/l*
4×cbrt-undiv div-exp
3×distribute-lft-out-- difference-of-squares
2×pow-prod-down *-commutative div-inv associate-/l/ unswap-sqr
1×+-commutative distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub clear-num associate-/r* sum-log flip--
Counts
4 → 120
Calls

4 calls:

21.0ms
(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
20.0ms
(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
19.0ms
(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
13.0ms
(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))

series214.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

84.0ms
(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
65.0ms
(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
42.0ms
(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
22.0ms
(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))

simplify47.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
055223306

prune319.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1257132
Fresh101
Picked101
Done000
Total1277134

Merged error: 6.4b

Counts
134 → 7

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite269.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Rules
159×*-un-lft-identity
86×times-frac
80×add-sqr-sqrt
51×distribute-lft-out
46×add-cube-cbrt
31×associate-*r*
22×associate-*l*
20×add-exp-log add-cbrt-cube
11×distribute-lft-out-- difference-of-squares
9×associate-/r* associate-/l*
8×associate-/r/
6×pow1 cbrt-undiv flip3-+ div-exp flip-+ add-log-exp
4×prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
2×frac-2neg clear-num
1×+-commutative frac-times flip3-- div-sub associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative flip--
Counts
4 → 180
Calls

4 calls:

213.0ms
(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)
29.0ms
(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
11.0ms
(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
8.0ms
(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))

series160.0ms (1%)

Counts
4 → 12
Calls

4 calls:

68.0ms
(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
61.0ms
(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)
18.0ms
(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
13.0ms
(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))

simplify62.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
052234158

prune415.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1884192
Fresh156
Picked101
Done000
Total1909199

Merged error: 6.4b

Counts
199 → 9

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
0.2b
(/ (/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
0.4b
(/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
5.9b
(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite371.0ms (2.4%)

Algorithm
1×rewrite-expression-head
Rules
1770×*-un-lft-identity
1499×times-frac
930×sqrt-prod
889×add-sqr-sqrt
560×distribute-lft-out
544×add-cube-cbrt
374×associate-*r*
145×distribute-lft-out-- difference-of-squares
51×associate-/l*
42×associate-/r/
40×sqrt-div
32×add-exp-log add-cbrt-cube
22×flip3-+ associate-*l* flip-+
21×div-inv
16×associate-/r*
14×unswap-sqr
13×cbrt-undiv div-exp
6×pow1 prod-exp cbrt-unprod add-log-exp
3×div-sub associate-/l/
2×frac-2neg clear-num
1×+-commutative frac-times flip3-- associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative flip--
Counts
4 → 955
Calls

4 calls:

170.0ms
(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
49.0ms
(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
29.0ms
(/ (/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
17.0ms
(/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))

series821.0ms (5.2%)

Counts
4 → 12
Calls

4 calls:

484.0ms
(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
210.0ms
(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
86.0ms
(/ (/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
40.0ms
(/ (- beta alpha) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))

simplify263.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
967 → 967
Iterations

Useful iterations: 0 (101.0ms)

IterNodesCost
0498531248
1498531248

prune7.3s (46.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New9634967
Fresh268
Picked101
Done000
Total96610976

Merged error: 6.4b

Counts
976 → 10

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- beta alpha) (fabs (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) (sqrt (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
0.6b
(cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
0.6b
(cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
4.9b
(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (/ (/ (- beta alpha) (fabs (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) (sqrt (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite222.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Rules
389×times-frac
356×*-un-lft-identity
246×add-sqr-sqrt
174×add-cube-cbrt
160×sqrt-prod
110×cbrt-prod
66×distribute-lft-out
36×distribute-lft-out-- difference-of-squares
19×associate-/l*
13×div-inv
11×associate-/r*
9×add-exp-log add-cbrt-cube
6×cbrt-div add-log-exp
4×pow1 flip3-+ flip-+
3×cbrt-undiv div-exp
2×pow1/3 sqrt-div div-sub associate-/r/
1×+-commutative frac-2neg clear-num sum-log associate-/l/
Counts
4 → 298
Calls

4 calls:

168.0ms
(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (/ (/ (- beta alpha) (fabs (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) (sqrt (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
18.0ms
(/ (/ (- beta alpha) (fabs (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) (sqrt (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
6.0ms
(cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
6.0ms
(cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))

series342.0ms (2.2%)

Counts
4 → 12
Calls

4 calls:

173.0ms
(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (/ (/ (- beta alpha) (fabs (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) (sqrt (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
88.0ms
(/ (/ (- beta alpha) (fabs (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) (sqrt (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
41.0ms
(cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
40.0ms
(cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))

simplify142.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
310 → 310
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
0497314582
1497314582

prune2.8s (17.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New3091310
Fresh099
Picked011
Done000
Total30911320

Merged error: 6.4b

Counts
320 → 11

regimes413.0ms (2.6%)

Accuracy

Total 6.9b remaining (55%)

Threshold costs 0b (0%)

bsearch62.0ms (0.4%)

Steps
ItersRangePoint
7
1.1808985618698955e+142
3.5721815501977174e+143
4.275223394131328e+142
8
1.6258736136937523e+99
2.847735445401322e+102
7.479662422107554e+100

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
090133
190133

end0.0ms (0%)

sample1.1s (7.1%)

Algorithm
1×intervals
Results
377.0ms6410×body80valid
173.0ms8000×pre80true
158.0ms515×body1280valid
125.0ms522×body640valid
64.0ms365×body320valid
22.0ms188×body160valid

Profiling

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