Details

Time bar (total: 3.0m)

sample125.0ms

Algorithm
intervals
Results
54.0ms256×body80valid
47.0ms283×body80nan

simplify210.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
210.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4/3 (- PI (* (* v v) PI)))
0.2b
(* (* v v) PI)
0.1b
(* (* v -6) v)
0.0b
(- PI (* (* v v) PI))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
16×add-sqr-sqrt add-cbrt-cube add-exp-log
15×add-cube-cbrt
14×pow1
12×times-frac
6×associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
5×distribute-rgt-out--
4×associate-/r* insert-posit16
3×associate-/l*
2×flip3-- associate-*l* associate-/r/ *-commutative flip--
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp div-inv unswap-sqr
Counts
4 → 87
Calls
4 calls:
Slowest
28.0ms
(* (* v v) PI)
25.0ms
(* (* v -6) v)
13.0ms
(/ 4/3 (- PI (* (* v v) PI)))
5.0ms
(- PI (* (* v v) PI))

series253.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(/ 4/3 (- PI (* (* v v) PI)))
73.0ms
(- PI (* (* v v) PI))
48.0ms
(* (* v v) PI)
39.0ms
(* (* v -6) v)

simplify5.1s

Counts
66 → 99
Calls
66 calls:
Slowest
618.0ms
(* (* (* (* v -6) (* v -6)) (* v -6)) (* (* v v) v))
391.0ms
(+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI))))
320.0ms
(/ (* (* 4/3 4/3) 4/3) (* (* (- PI (* (* v v) PI)) (- PI (* (* v v) PI))) (- PI (* (* v v) PI))))
312.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))
307.0ms
(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))

prune953.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4/3 PI)
0.1b
(* (* v -6) v)
0.0b
(/ (/ 4/3 PI) (- 1 (* v v)))
0.0b
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v -6) v))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
1324×times-frac
661×add-sqr-sqrt *-un-lft-identity
556×add-cube-cbrt
216×sqrt-prod
210×difference-of-squares
87×associate-/l*
51×div-inv
25×add-cbrt-cube add-exp-log
18×associate-/r/
14×associate-/r*
10×cbrt-undiv div-exp
9×pow1
8×flip3-- flip--
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sqrt-div associate-/l/
1×flip3-+ associate-*l* *-commutative flip-+
Counts
4 → 671
Calls
4 calls:
Slowest
23.0ms
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v -6) v))))
16.0ms
(* (* v -6) v)
10.0ms
(/ (/ 4/3 PI) (- 1 (* v v)))
7.0ms
(/ 4/3 PI)

series1.0s

Counts
4 → 10
Calls
4 calls:
Slowest
850.0ms
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v -6) v))))
151.0ms
(/ (/ 4/3 PI) (- 1 (* v v)))
40.0ms
(* (* v -6) v)
0.0ms
(/ 4/3 PI)

simplify2.7m

Counts
1131 → 681
Calls
1131 calls:
Slowest
745.0ms
(/ (/ (/ (* (cbrt 4/3) (cbrt 4/3)) (* (cbrt PI) (cbrt PI))) (+ 1 v)) 1)
648.0ms
(* (* (* (* v -6) (* v -6)) (* v -6)) (* (* v v) v))
593.0ms
(/ (* (* (/ 4/3 PI) (/ 4/3 PI)) (/ 4/3 PI)) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v))))
526.0ms
(/ (/ (/ (* (cbrt 4/3) (cbrt 4/3)) (* (cbrt PI) (cbrt PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v))))))
514.0ms
(/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v -6) v)))))

prune7.2s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.4s8000×body80valid
1.1s8121×body80nan