Details

Time bar (total: 8.5s)

sample30.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
9.0ms272×body80nan

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01620
13220
28820
323320
445420
567420
685020
786220
done86220

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 3.0 PI) (- 1.0 (* v v)))
0.0b
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.2b
(* 6.0 (* v v))
1.0b
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log add-cbrt-cube
23×pow1
18×associate-*r/ prod-exp cbrt-unprod
13×flip3-- flip--
12×add-sqr-sqrt sqrt-div pow-prod-down
11×associate-*r*
10×add-cube-cbrt *-un-lft-identity
8×frac-times associate-/r/
5×associate-*l*
4×cbrt-undiv div-exp associate-*l/ add-log-exp
3×times-frac sqrt-prod *-commutative associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in
1×frac-2neg clear-num associate-/r* div-inv difference-of-squares unswap-sqr
Counts
4 → 109
Calls
4 calls:
10.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
33.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms
(* 6.0 (* v v))
28.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series834.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
277.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
31.0ms
(* 6.0 (* v v))
419.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify1.2s

Counts
121 → 121
Iterations

Useful iterations: 2 (457.0ms)

IterNodesCost
03072810
18852584
237922215
done50002215

prune286.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.0b
(* (* 3.0 PI) (- 1.0 (* v v)))
0.0b
(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
0.2b
(* 6.0 (* v v))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
44×add-sqr-sqrt
42×add-cube-cbrt *-un-lft-identity
37×add-exp-log add-cbrt-cube
30×sqrt-prod
18×associate-*r/ associate-/r/
14×pow1
12×prod-exp cbrt-unprod associate-/l*
10×cbrt-undiv flip3-- div-exp flip--
9×div-inv
7×associate-/r*
6×pow-prod-down
5×associate-*r*
4×associate-*l* add-log-exp
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in sqrt-div clear-num *-commutative
1×associate-/l/ difference-of-squares unswap-sqr
Counts
4 → 159
Calls
4 calls:
16.0ms
(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
14.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
8.0ms
(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
6.0ms
(* 6.0 (* v v))

series666.0ms

Counts
4 → 12
Calls
4 calls:
434.0ms
(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
110.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
98.0ms
(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
24.0ms
(* 6.0 (* v v))

simplify1.2s

Counts
171 → 171
Iterations

Useful iterations: 2 (543.0ms)

IterNodesCost
03554403
19334077
235563732
done50003732

prune545.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 4.0 (/ (* (- (pow 1.0 3) (pow v 6)) (* 3.0 PI)) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v))))))
0.0b
(+ (* (* v v) (* v v)) (* 1.0 (* v v)))
0.1b
(* (* v v) (* v v))
0.2b
(* 6.0 (* v v))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
120×pow1
39×times-frac
36×pow-prod-up
35×add-exp-log add-cbrt-cube
26×pow-prod-down
24×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
22×pow-sqr
18×pow-plus
14×prod-exp cbrt-unprod
13×pow2
9×associate-/r* associate-/r/
7×cbrt-undiv div-exp
6×add-log-exp
5×flip3-+ flip-+ div-inv
4×associate-*l*
3×associate-/l*
2×associate-*r* *-commutative unswap-sqr
1×+-commutative distribute-rgt-out frac-2neg swap-sqr clear-num sum-log
Counts
4 → 152
Calls
4 calls:
82.0ms
(/ 4.0 (/ (* (- (pow 1.0 3) (pow v 6)) (* 3.0 PI)) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v))))))
13.0ms
(+ (* (* v v) (* v v)) (* 1.0 (* v v)))
14.0ms
(* (* v v) (* v v))
7.0ms
(* 6.0 (* v v))

series282.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ 4.0 (/ (* (- (pow 1.0 3) (pow v 6)) (* 3.0 PI)) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v))))))
80.0ms
(+ (* (* v v) (* v v)) (* 1.0 (* v v)))
33.0ms
(* (* v v) (* v v))
25.0ms
(* 6.0 (* v v))

simplify956.0ms

Counts
164 → 164
Iterations

Useful iterations: 2 (330.0ms)

IterNodesCost
02703981
17473089
230772735
done50002735

prune423.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02640
13240
done3240

end0.0ms

sample748.0ms

Algorithm
intervals
Results
293.0ms8000×body80valid
270.0ms8079×body80nan