Details

Time bar (total: 50.4s)

sample66.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
24.0ms251×body80nan

simplify209.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
209.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize24.0ms

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
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* (* v -6) v))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
134×*-un-lft-identity
110×add-sqr-sqrt
109×add-cube-cbrt
57×sqrt-prod
25×distribute-rgt-out--
21×add-cbrt-cube add-exp-log associate-/l*
18×associate-/r/
14×pow1
10×associate-/r*
9×div-inv
8×flip3-- flip--
6×associate-*r* pow-prod-down prod-exp cbrt-unprod
4×cbrt-undiv div-exp insert-posit16 add-log-exp
2×clear-num frac-2neg sqrt-div associate-*l* *-commutative
1×flip3-+ flip-+ unswap-sqr associate-/l/
Counts
4 → 223
Calls
4 calls:
Slowest
17.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* (* v -6) v))))
17.0ms
(* (* v -6) v)
17.0ms
(* (* v v) PI)
10.0ms
(/ 4/3 (- PI (* (* v v) PI)))

series599.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
429.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* (* v -6) v))))
91.0ms
(/ 4/3 (- PI (* (* v v) PI)))
47.0ms
(* (* v v) PI)
31.0ms
(* (* v -6) v)

simplify39.5s

Counts
308 → 235
Calls
308 calls:
Slowest
766.0ms
(/ (+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI)))) (sqrt (cbrt (+ 2 (* (* v -6) v)))))
626.0ms
(* (* (* (* v -6) (* v -6)) (* v -6)) (* (* v v) v))
547.0ms
(/ (/ 4/3 (- (* PI PI) (* (* (* v v) PI) (* (* v v) PI)))) (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v))))))
494.0ms
(- (+ (* 4/3 (/ (sqrt -1/6) (* (pow v 7) PI))) (+ (* 4/3 (/ (sqrt -1/6) (* (pow v 3) PI))) (* 4/3 (/ (sqrt -1/6) (* (pow v 5) PI))))) (+ (* 1/1944 (/ 1 (* (pow v 7) (* PI (pow (sqrt -1/6) 3))))) (+ (* 4/81 (/ 1 (* (pow v 7) (* PI (sqrt -1/6))))) (* 1/27 (/ 1 (* (pow v 5) (* PI (sqrt -1/6))))))))
493.0ms
(/ (/ (* (cbrt 4/3) (cbrt 4/3)) (* (cbrt (- PI (* (* v v) PI))) (cbrt (- PI (* (* v v) PI))))) (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v))))))

prune2.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* v v) PI)
0.1b
(* (* v -6) v)
0.0b
(sqrt (+ 2 (* (* v -6) v)))
0.0b
(- PI (* (* v v) PI))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1
14×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
8×*-un-lft-identity
7×add-cube-cbrt
6×associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
4×insert-posit16
3×sqrt-prod
2×sqrt-div associate-*l* *-commutative
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- distribute-rgt-out-- pow1/2 diff-log flip-+ flip-- unswap-sqr
Counts
4 → 69
Calls
4 calls:
Slowest
32.0ms
(* (* v v) PI)
27.0ms
(* (* v -6) v)
5.0ms
(sqrt (+ 2 (* (* v -6) v)))
4.0ms
(- PI (* (* v v) PI))

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
75.0ms
(sqrt (+ 2 (* (* v -6) v)))
70.0ms
(- PI (* (* v v) PI))
42.0ms
(* (* v -6) v)
28.0ms
(* (* v v) PI)

simplify3.5s

Counts
39 → 81
Calls
39 calls:
Slowest
611.0ms
(* (* (* (* v -6) (* v -6)) (* v -6)) (* (* v v) v))
340.0ms
(sqrt (- (* 2 2) (* (* (* v -6) v) (* (* v -6) v))))
335.0ms
(- (* 1/2 (/ 1 (* (pow v 3) (pow (sqrt -6) 3)))) (+ (/ 1 (* v (sqrt -6))) (* v (sqrt -6))))
304.0ms
(- (sqrt 2) (+ (* 9/2 (/ (pow v 4) (pow (sqrt 2) 3))) (* 3 (/ (pow v 2) (sqrt 2)))))
300.0ms
(- (+ (/ 1 (* v (sqrt -6))) (* v (sqrt -6))) (* 1/2 (/ 1 (* (pow v 3) (pow (sqrt -6) 3)))))

prune725.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.4s7984×body80nan
1.3s8000×body80valid