Details

Time bar (total: 2.5min)

analyze2.7s (1.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%99.9%0.1%8
0%99.9%0.1%9
0%99.9%0.1%10
0%99.5%0.5%11
0%99.1%0.9%12
0.4%97.3%2.3%13
0.7%95.8%3.5%14

sample508.0ms (0.3%)

Algorithm
1×intervals
Results
130.0ms26×body5120invalid
115.0ms42×body2560invalid
91.0ms114×body1280valid
51.0ms35×body2560valid
33.0ms31×body1280invalid
32.0ms58×body640valid
7.0ms18×body320valid
7.0ms3×body5120valid
6.0ms16×body320invalid
5.0ms9×body640invalid
4.0ms31×body80invalid
3.0ms19×body80valid
2.0ms9×body160valid
1.0ms3×body160invalid

simplify47.0ms (0%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0484221
1484221

prune16.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 39.3b

Counts
2 → 1

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
1.3b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
16.5b
(/ (pow t 3.0) (* l l))
25.9b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (pow (/ k t) 2.0))

rewrite55.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
228×add-exp-log
139×prod-exp
52×add-cbrt-cube
51×div-exp
32×pow-exp
28×add-sqr-sqrt
26×times-frac cbrt-unprod
23×pow-to-exp unpow-prod-down associate-*r*
21×add-cube-cbrt *-un-lft-identity
13×associate-*l*
11×pow1
10×associate-*l/
8×cbrt-undiv
7×associate-/l*
5×sqr-pow
4×tan-quot pow-prod-down add-log-exp unswap-sqr
3×*-commutative div-inv
2×frac-times associate-*r/
1×frac-2neg clear-num associate-/r*
Counts
4 → 170
Calls

4 calls:

19.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (pow (/ k t) 2.0))
11.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
6.0ms
(/ (pow t 3.0) (* l l))

series297.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

121.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (pow (/ k t) 2.0))
78.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
57.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
40.0ms
(/ (pow t 3.0) (* l l))

simplify45.0ms (0%)

Algorithm
1×egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
050102797

prune500.0ms (0.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New16913182
Fresh000
Picked101
Done000
Total17013183

Merged error: 16.1b

Counts
183 → 13

localize30.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
4.1b
(/ (pow (sin k) 2) (* (* l l) (cos k)))
6.2b
(* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))
15.9b
(* (/ (pow (sin k) 2) (* (* l l) (cos k))) (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))) 1.0))

rewrite303.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
5529×add-exp-log
4068×pow-exp
3291×prod-exp
2517×div-exp
1470×pow-to-exp
159×unpow-prod-down
100×add-sqr-sqrt
53×times-frac
39×unswap-sqr
36×associate-*r*
35×add-cube-cbrt *-un-lft-identity sqr-pow
33×associate-*l*
29×add-cbrt-cube
11×cbrt-unprod
8×associate-/l*
6×cbrt-undiv
5×pow1 div-inv
4×unpow2 add-log-exp
3×pow-unpow
2×*-commutative
1×pow-pow frac-2neg pow-prod-down associate-*l/ clear-num associate-/r*
Counts
4 → 1364
Calls

4 calls:

43.0ms
(* (/ (pow (sin k) 2) (* (* l l) (cos k))) (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))) 1.0))
25.0ms
(* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))
9.0ms
(/ (pow (sin k) 2) (* (* l l) (cos k)))
2.0ms
(pow (sin k) 2)

series179.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

95.0ms
(* (/ (pow (sin k) 2) (* (* l l) (cos k))) (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))) 1.0))
60.0ms
(* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))
18.0ms
(/ (pow (sin k) 2) (* (* l l) (cos k)))
5.0ms
(pow (sin k) 2)

simplify263.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1376 → 1376
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
0564643659

prune10.5s (7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1366101376
Fresh5712
Picked101
Done000
Total1372171389

Merged error: 14.5b

Counts
1389 → 17

localize29.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
4.1b
(/ (pow (sin k) 2) (* l l))
6.2b
(* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))
15.9b
(* (/ (/ (pow (sin k) 2) (* l l)) (cos k)) (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))) 1.0))

rewrite255.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
4658×add-exp-log
3223×pow-exp
2676×div-exp
2157×prod-exp
1135×pow-to-exp
173×unpow-prod-down
153×add-sqr-sqrt
132×times-frac
61×associate-*l*
54×add-cube-cbrt *-un-lft-identity unswap-sqr
45×sqr-pow
36×associate-*r*
25×add-cbrt-cube
9×unpow2
8×div-inv associate-/l*
7×cbrt-undiv cbrt-unprod
5×pow1
4×add-log-exp
3×pow-unpow
2×*-commutative
1×pow-pow frac-2neg pow-prod-down associate-*l/ clear-num associate-/r*
Counts
4 → 1175
Calls

4 calls:

46.0ms
(* (/ (/ (pow (sin k) 2) (* l l)) (cos k)) (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))) 1.0))
23.0ms
(* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))
6.0ms
(/ (pow (sin k) 2) (* l l))
3.0ms
(pow (sin k) 2)

series172.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

96.0ms
(* (/ (/ (pow (sin k) 2) (* l l)) (cos k)) (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))) 1.0))
62.0ms
(* (pow (pow (/ -1 k) 2.0) 1.0) (pow (pow (/ -1 t) 1.0) 1.0))
11.0ms
(/ (pow (sin k) 2) (* l l))
4.0ms
(pow (sin k) 2)

simplify224.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1187 → 1187
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0567337583

prune8.8s (5.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New118071187
Fresh51116
Picked101
Done000
Total1186181204

Merged error: 10.1b

Counts
1204 → 18

localize31.0ms (0%)

Local error

Found 4 expressions with local error:

2.2b
(/ (pow (sin k) 2) l)
3.9b
(* (/ (/ 1 l) 1) (* (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 t) 1.0) 1.0) (pow (pow (/ -1 k) 2.0) 1.0))) 1.0) (/ (/ (pow (sin k) 2) l) (cos k))))
6.2b
(* (pow (pow (/ -1 t) 1.0) 1.0) (pow (pow (/ -1 k) 2.0) 1.0))
7.0b
(* (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 t) 1.0) 1.0) (pow (pow (/ -1 k) 2.0) 1.0))) 1.0) (/ (/ (pow (sin k) 2) l) (cos k)))

rewrite1.7s (1.2%)

Algorithm
1×rewrite-expression-head
Rules
34133×add-exp-log
22197×div-exp
19463×pow-exp
16275×prod-exp
6665×pow-to-exp
3426×1-exp
1142×rec-exp
310×times-frac
263×add-sqr-sqrt
194×unpow-prod-down
152×add-cube-cbrt *-un-lft-identity
110×associate-*r*
79×associate-*l*
71×add-cbrt-cube
54×unswap-sqr
52×sqr-pow
25×cbrt-undiv cbrt-unprod
16×unpow2
12×div-inv
8×associate-/l*
6×pow1
4×associate-*r/ add-log-exp
3×associate-/r* *-commutative
2×pow-prod-down
1×frac-times frac-2neg associate-*l/ clear-num
Counts
4 → 6083
Calls

4 calls:

125.0ms
(* (/ (/ 1 l) 1) (* (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 t) 1.0) 1.0) (pow (pow (/ -1 k) 2.0) 1.0))) 1.0) (/ (/ (pow (sin k) 2) l) (cos k))))
59.0ms
(* (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 t) 1.0) 1.0) (pow (pow (/ -1 k) 2.0) 1.0))) 1.0) (/ (/ (pow (sin k) 2) l) (cos k)))
28.0ms
(* (pow (pow (/ -1 t) 1.0) 1.0) (pow (pow (/ -1 k) 2.0) 1.0))
5.0ms
(/ (pow (sin k) 2) l)

series267.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

112.0ms
(* (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 t) 1.0) 1.0) (pow (pow (/ -1 k) 2.0) 1.0))) 1.0) (/ (/ (pow (sin k) 2) l) (cos k)))
83.0ms
(* (/ (/ 1 l) 1) (* (pow (/ (pow -1 3.0) (* (pow (pow (/ -1 t) 1.0) 1.0) (pow (pow (/ -1 k) 2.0) 1.0))) 1.0) (/ (/ (pow (sin k) 2) l) (cos k))))
62.0ms
(* (pow (pow (/ -1 t) 1.0) 1.0) (pow (pow (/ -1 k) 2.0) 1.0))
9.0ms
(/ (pow (sin k) 2) l)

simplify1.2s (0.8%)

Algorithm
1×egg-herbie
Counts
6095 → 6095
Iterations

Useful iterations: 0 (168.0ms)

IterNodesCost
05023203607

prune1.9min (77.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New608696095
Fresh9817
Picked101
Done000
Total6096176113

Merged error: 8.1b

Counts
6113 → 17

regimes622.0ms (0.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03649
13649

end0.0ms (0%)

sample5.6s (3.7%)

Algorithm
1×intervals
Results
1.3s509×body2560invalid
1.2s281×body5120invalid
1.1s1346×body1280valid
492.0ms350×body2560valid
422.0ms768×body640valid
278.0ms347×body1280invalid
235.0ms70×body5120valid
96.0ms194×body640invalid
93.0ms248×body320valid
52.0ms135×body320invalid
48.0ms341×body80invalid
42.0ms257×body80valid
24.0ms93×body160valid
21.0ms84×body160invalid

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