Details

Time bar (total: 2.9m)

sample71.0ms

Algorithm
intervals
Results
30.0ms256×body80valid
28.0ms257×body80nan

simplify215.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
215.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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))

rewrite50.0ms

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
19.0ms
(* (* v v) PI)
13.0ms
(* (* v -6) v)
12.0ms
(/ 4/3 (- PI (* (* v v) PI)))
4.0ms
(- PI (* (* v v) PI))

series258.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(/ 4/3 (- PI (* (* v v) PI)))
71.0ms
(- PI (* (* v v) PI))
50.0ms
(* (* v v) PI)
44.0ms
(* (* v -6) v)

simplify5.1s

Counts
66 → 99
Calls
66 calls:
Slowest
553.0ms
(* (* (* (* v -6) (* v -6)) (* v -6)) (* (* v v) v))
362.0ms
(+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI))))
352.0ms
(/ (* (* 4/3 4/3) 4/3) (* (* (- PI (* (* v v) PI)) (- PI (* (* v v) PI))) (- PI (* (* v v) PI))))
275.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))
265.0ms
(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))

prune960.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize45.0ms

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))))

rewrite95.0ms

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
37.0ms
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v -6) v))))
16.0ms
(/ (/ 4/3 PI) (- 1 (* v v)))
13.0ms
(* (* v -6) v)
3.0ms
(/ 4/3 PI)

series619.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
475.0ms
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v -6) v))))
109.0ms
(/ (/ 4/3 PI) (- 1 (* v v)))
36.0ms
(* (* v -6) v)
0.0ms
(/ 4/3 PI)

simplify2.6m

Counts
1131 → 681
Calls
1131 calls:
Slowest
659.0ms
(/ (/ (/ 1 (* (cbrt PI) (cbrt PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v))))))
587.0ms
(/ (* (* (/ 4/3 PI) (/ 4/3 PI)) (/ 4/3 PI)) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v))))
579.0ms
(* (* (* (* v -6) (* v -6)) (* v -6)) (* (* v v) v))
569.0ms
(/ (/ (/ (* (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
(/ (/ (cbrt (/ 4/3 PI)) (- 1 v)) (sqrt (+ 2 (* (* v -6) v))))

prune7.3s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s7762×body80nan
1.1s8000×body80valid