Details

Time bar (total: 37.5s)

analyze1.9s (5.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%81.1%18.9%7
0%68.6%31.4%8
0%59.2%40.8%9
0%59.2%40.8%10
0%59.2%40.8%11
0.4%49.5%50.1%12
0.8%44.4%54.8%13
1.4%39.9%58.7%14

sample156.0ms (0.4%)

Algorithm
1×intervals
Results
48.0ms256×body80valid
43.0ms311×body80nan
30.0ms170×body80invalid

simplify23.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0540135

prune11.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 29.3b

Counts
2 → 1

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.9b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.3b
(pow (/ d l) (/ 1.0 2.0))
12.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.5b
(pow (/ d h) (/ 1.0 2.0))

rewrite51.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×distribute-rgt-in frac-times flip3-- distribute-lft-in flip--
Counts
4 → 174
Calls

4 calls:

16.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
6.0ms
(pow (/ d h) (/ 1.0 2.0))

series557.0ms (1.5%)

Counts
4 → 12
Calls

4 calls:

288.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
241.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
14.0ms
(pow (/ d h) (/ 1.0 2.0))
13.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify52.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
054413690

prune811.0ms (2.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New16719186
Fresh000
Picked101
Done000
Total16819187

Merged error: 13.1b

Counts
187 → 19

localize46.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2.0 d))
7.9b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.3b
(pow (/ d l) (/ 1.0 2.0))
12.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite81.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
738×add-exp-log
487×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
28×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* pow-prod-down *-commutative
1×distribute-rgt-in frac-times flip3-- pow-pow frac-2neg distribute-lft-in clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 258
Calls

4 calls:

35.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series552.0ms (1.5%)

Counts
4 → 12
Calls

4 calls:

289.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
243.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))

simplify88.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
050148545

prune1.5s (3.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New2637270
Fresh31518
Picked101
Done000
Total26722289

Merged error: 12.3b

Counts
289 → 22

localize64.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.6b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.0b
(/ (* M D) (* 2.0 d))
7.9b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite344.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
6965×add-exp-log
5245×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
232×rec-exp 1-exp
55×add-cbrt-cube
37×times-frac
32×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×cbrt-unprod
22×unpow-prod-down
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv cbrt-prod
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* *-commutative
1×distribute-rgt-in frac-times flip3-- pow-pow frac-2neg distribute-lft-in clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1227
Calls

4 calls:

86.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
7.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))

series645.0ms (1.7%)

Counts
4 → 12
Calls

4 calls:

352.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
246.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
40.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))

simplify381.0ms (1%)

Algorithm
1×egg-herbie
Counts
1239 → 1239
Iterations

Useful iterations: 0 (98.0ms)

IterNodesCost
0499659876
1499659876

prune9.5s (25.4%)

Pruning

26 alts after pruning (25 fresh and 1 done)

PrunedKeptTotal
New123361239
Fresh21921
Picked011
Done000
Total1235261261

Merged error: 11.0b

Counts
1261 → 26

localize60.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2.0 d))
5.7b
(* h (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)))
6.6b
(/ (* h (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0))) (* 2.0 l))
7.9b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* h (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0))) (* 2.0 l))))

rewrite339.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
6936×add-exp-log
5237×prod-exp
2607×pow-exp
1610×div-exp
787×pow-to-exp
232×rec-exp 1-exp
60×add-cbrt-cube
29×cbrt-unprod
11×pow1
10×cbrt-undiv
8×add-sqr-sqrt *-un-lft-identity
6×add-cube-cbrt associate-*r*
4×associate-*l* pow-prod-down add-log-exp
2×sub-neg frac-2neg times-frac associate-*r/ clear-num associate-/r* *-commutative div-inv associate-/l*
1×distribute-rgt-in flip3-- distribute-lft-in flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 1180
Calls

4 calls:

90.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* h (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0))) (* 2.0 l))))
11.0ms
(/ (* h (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0))) (* 2.0 l))
8.0ms
(* h (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)))
6.0ms
(/ (* M D) (* 2.0 d))

series675.0ms (1.8%)

Counts
4 → 12
Calls

4 calls:

369.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* h (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0))) (* 2.0 l))))
198.0ms
(/ (* h (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0))) (* 2.0 l))
101.0ms
(* h (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)))
6.0ms
(/ (* M D) (* 2.0 d))

simplify359.0ms (1%)

Algorithm
1×egg-herbie
Counts
1192 → 1192
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
0502659189

prune12.9s (34.5%)

Pruning

27 alts after pruning (26 fresh and 1 done)

PrunedKeptTotal
New118751192
Fresh32124
Picked101
Done011
Total1191271218

Merged error: 10.7b

Counts
1218 → 27

regimes1.6s (4.4%)

Accuracy

Total 4.0b remaining (27.9%)

Threshold costs 0b (0%)

bsearch251.0ms (0.7%)

Steps
ItersRangePoint
8
3.9036749666279574e-08
0.0021857205059727662
5.468046365784226e-08
6
-1.5630454568252133e+119
-9.999860355383097e+117
-2.5203757008157784e+118

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0160141
1160141

end0.0ms (0%)

sample4.4s (11.7%)

Algorithm
1×intervals
Results
1.4s8000×body80valid
1.3s8617×body80nan
877.0ms4888×body80invalid

Profiling

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