Details

Time bar (total: 30.3s)

sample95.0ms

Algorithm
intervals
Results
41.0ms256×body80valid
34.0ms230×body80nan

simplify250.0ms

Calls
1 calls:
Slowest
250.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize40.0ms

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))

rewrite45.0ms

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
Calls
4 calls:
Slowest
14.0ms
(* (* v v) PI)
13.0ms
(* (* v -6) v)
10.0ms
(/ 4/3 (- PI (* (* v v) PI)))
7.0ms
(- PI (* (* v v) PI))

series283.0ms

Calls
4 calls:
Slowest
116.0ms
(/ 4/3 (- PI (* (* v v) PI)))
80.0ms
(- PI (* (* v v) PI))
53.0ms
(* (* v v) PI)
34.0ms
(* (* v -6) v)

simplify5.4s

Calls
66 calls:
Slowest
640.0ms
(* (* (* (* v -6) (* v -6)) (* v -6)) (* (* v v) v))
404.0ms
(+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI))))
367.0ms
(/ (* (* 4/3 4/3) 4/3) (* (* (- PI (* (* v v) PI)) (- PI (* (* v v) PI))) (- PI (* (* v v) PI))))
335.0ms
(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))
313.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))

prune938.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
100×times-frac
72×*-un-lft-identity
54×add-sqr-sqrt
53×add-cube-cbrt
39×cbrt-prod
34×associate-/r*
28×add-exp-log
21×add-cbrt-cube
19×distribute-rgt-out--
14×pow1
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×associate-*r* pow-prod-down
5×associate-/l*
4×insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*l* *-commutative associate-/l/
1×flip3-- div-sub associate-/r/ flip-- unswap-sqr
Calls
4 calls:
Slowest
27.0ms
(* (* v -6) v)
22.0ms
(* (* v v) PI)
21.0ms
(/ (- PI (* (* v v) PI)) (cbrt 4/3))
20.0ms
(/ (* (cbrt 4/3) (cbrt 4/3)) (/ (- PI (* (* v v) PI)) (cbrt 4/3)))

series439.0ms

Calls
4 calls:
Slowest
189.0ms
(/ (- PI (* (* v v) PI)) (cbrt 4/3))
167.0ms
(/ (* (cbrt 4/3) (cbrt 4/3)) (/ (- PI (* (* v v) PI)) (cbrt 4/3)))
48.0ms
(* (* v -6) v)
35.0ms
(* (* v v) PI)

simplify18.1s

Calls
185 calls:
Slowest
731.0ms
(/ (* (* (* (cbrt 4/3) (cbrt 4/3)) (* (cbrt 4/3) (cbrt 4/3))) (* (cbrt 4/3) (cbrt 4/3))) (* (* (/ (- PI (* (* v v) PI)) (cbrt 4/3)) (/ (- PI (* (* v v) PI)) (cbrt 4/3))) (/ (- PI (* (* v v) PI)) (cbrt 4/3))))
622.0ms
(* (* (* (* v -6) (* v -6)) (* v -6)) (* (* v v) v))
321.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))
316.0ms
(/ (* 4/3 4/3) (/ (* (* (- PI (* (* v v) PI)) (- PI (* (* v v) PI))) (- PI (* (* v v) PI))) 4/3))
300.0ms
(- (+ (log (cbrt 4/3)) (log (cbrt 4/3))) (log (/ (- PI (* (* v v) PI)) (cbrt 4/3))))

prune1.8s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s8163×body80nan
1.1s8000×body80valid