Details

Time bar (total: 2.7s)

analyze5.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50.1%13
49.9%0%50.1%14

sample20.0ms (0.8%)

Algorithm
1×intervals
Results
14.0ms256×body80valid
0.0ms1×body80nan

simplify197.0ms (7.3%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (195.0ms)

IterNodesCost
0198720
1198720

prune9.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.0b

Counts
2 → 2

localize19.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 2.0 (* 6.0 (* v v))))
0.0b
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.1b
(* 6.0 (* v v))
1.0b
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite39.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
19×pow1
16×associate-*r/
15×prod-exp cbrt-unprod
14×sqrt-div
13×flip3-- flip--
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow-prod-down
8×frac-times associate-/r/
7×associate-*r*
6×sqrt-prod
4×cbrt-undiv div-exp associate-*l* associate-*l/ add-log-exp
3×times-frac associate-/l*
2×*-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r* div-inv unswap-sqr
Counts
4 → 99
Calls

4 calls:

14.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
13.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms
(* 6.0 (* v v))
3.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))

series43.0ms (1.6%)

Counts
4 → 12
Calls

4 calls:

18.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
13.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
8.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
3.0ms
(* 6.0 (* v v))

simplify49.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
057442165

prune287.0ms (10.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1092111
Fresh101
Picked101
Done000
Total1112113

Merged error: 0b

Counts
113 → 2

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(/ 4.0 (* 3.0 (* PI (- 1.0 (* v v)))))
0.0b
(/ (/ 4.0 (* 3.0 (* PI (- 1.0 (* v v))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.0b
(* PI (- 1.0 (* v v)))
0.1b
(* 6.0 (* v v))

rewrite43.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Rules
78×times-frac
47×add-sqr-sqrt
43×add-cube-cbrt *-un-lft-identity
34×add-exp-log associate-*r/ add-cbrt-cube
30×sqrt-prod
18×associate-/r/
12×associate-/l*
11×pow1
10×cbrt-undiv flip3-- div-exp prod-exp flip-- cbrt-unprod
9×div-inv
7×associate-/r*
6×associate-*l*
5×associate-*r*
4×pow-prod-down add-log-exp
2×sub-neg frac-2neg sqrt-div clear-num *-commutative unswap-sqr
1×distribute-rgt-in distribute-lft-in associate-/l/ difference-of-squares
Counts
4 → 157
Calls

4 calls:

17.0ms
(/ (/ 4.0 (* 3.0 (* PI (- 1.0 (* v v))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
8.0ms
(/ 4.0 (* 3.0 (* PI (- 1.0 (* v v)))))
6.0ms
(* 6.0 (* v v))
6.0ms
(* PI (- 1.0 (* v v)))

series34.0ms (1.2%)

Counts
4 → 12
Calls

4 calls:

18.0ms
(/ (/ 4.0 (* 3.0 (* PI (- 1.0 (* v v))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms
(* PI (- 1.0 (* v v)))
6.0ms
(/ 4.0 (* 3.0 (* PI (- 1.0 (* v v)))))
3.0ms
(* 6.0 (* v v))

simplify63.0ms (2.3%)

Algorithm
1×egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
056753652

prune446.0ms (16.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1690169
Fresh011
Picked011
Done000
Total1692171

Merged error: 0b

Counts
171 → 2

localize25.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.1b
(* 6.0 (* (pow v 4) 6.0))
0.1b
(* (pow v 4) 6.0)
0.1b
(* 6.0 (* v v))
1.0b
(* (/ 4.0 (* 3.0 (* PI (* (sqrt (- (* 2.0 2.0) (* 6.0 (* (pow v 4) 6.0)))) (- (* 1.0 1.0) (pow v 4)))))) (* (+ 1.0 (* v v)) (sqrt (+ 2.0 (* 6.0 (* v v))))))

rewrite57.0ms (2.1%)

Algorithm
1×rewrite-expression-head
Rules
69×add-exp-log
61×add-cbrt-cube
40×prod-exp
34×cbrt-unprod
30×associate-*r/
28×associate-*l*
20×frac-times
18×sqrt-div
17×add-sqr-sqrt
16×pow1
12×flip3-+ flip-+
11×add-cube-cbrt *-un-lft-identity
8×cbrt-undiv div-exp associate-/r/
7×pow-prod-down associate-*l/
6×flip3-- associate-*r* flip--
4×unpow-prod-down *-commutative add-log-exp unswap-sqr
3×times-frac
2×pow-to-exp pow-exp sqr-pow
1×div-inv
Counts
4 → 126
Calls

4 calls:

31.0ms
(* (/ 4.0 (* 3.0 (* PI (* (sqrt (- (* 2.0 2.0) (* 6.0 (* (pow v 4) 6.0)))) (- (* 1.0 1.0) (pow v 4)))))) (* (+ 1.0 (* v v)) (sqrt (+ 2.0 (* 6.0 (* v v))))))
8.0ms
(* (pow v 4) 6.0)
6.0ms
(* 6.0 (* (pow v 4) 6.0))
6.0ms
(* 6.0 (* v v))

series34.0ms (1.2%)

Counts
4 → 12
Calls

4 calls:

23.0ms
(* (/ 4.0 (* 3.0 (* PI (* (sqrt (- (* 2.0 2.0) (* 6.0 (* (pow v 4) 6.0)))) (- (* 1.0 1.0) (pow v 4)))))) (* (+ 1.0 (* v v)) (sqrt (+ 2.0 (* 6.0 (* v v))))))
4.0ms
(* 6.0 (* (pow v 4) 6.0))
4.0ms
(* (pow v 4) 6.0)
3.0ms
(* 6.0 (* v v))

simplify82.0ms (3%)

Algorithm
1×egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049653387
149653387

prune655.0ms (24.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1380138
Fresh000
Picked011
Done011
Total1382140

Merged error: 0b

Counts
140 → 2

regimes58.0ms (2.1%)

Accuracy

Total 0.0b remaining (53.4%)

Threshold costs 0.0b (53.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05520
15520

end0.0ms (0%)

sample534.0ms (19.7%)

Algorithm
1×intervals
Results
432.0ms8000×body80valid
0.0ms1×body80nan

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