Details

Time bar (total: 6.2m)

sample95.0ms

Algorithm
intervals
Results
40.0ms284×body80nan
37.0ms256×body80valid

simplify218.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
217.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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))))

rewrite108.0ms

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
35.0ms
(* (* v -6) v)
32.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* (* v -6) v))))
26.0ms
(* (* v v) PI)
7.0ms
(/ 4/3 (- PI (* (* v v) PI)))

series652.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
461.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* (* v -6) v))))
117.0ms
(/ 4/3 (- PI (* (* v v) PI)))
42.0ms
(* (* v -6) v)
32.0ms
(* (* v v) PI)

simplify39.2s

Counts
308 → 235
Calls
308 calls:
Slowest
724.0ms
(/ (/ 4/3 (- (* PI PI) (* (* (* v v) PI) (* (* v v) PI)))) (sqrt (* (cbrt (+ 2 (* (* v -6) v))) (cbrt (+ 2 (* (* v -6) v))))))
616.0ms
(* (* (* (* v -6) (* v -6)) (* v -6)) (* (* v v) v))
531.0ms
(/ (/ 4/3 (- (* PI PI) (* (* (* v v) PI) (* (* v v) PI)))) (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v))))))
529.0ms
(- (+ (* 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))))))))
512.0ms
(/ (/ (* (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))))))

prune2.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4/3 (- PI (* (* v v) PI)))
1.0b
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (* v v) PI)))))
0.2b
(* (* v v) PI)
0.1b
(* (* v -6) v)

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
1071×times-frac
545×*-un-lft-identity
470×add-sqr-sqrt
469×add-cube-cbrt
216×sqrt-prod
117×associate-/r*
76×distribute-rgt-out--
55×associate-/r/
37×add-exp-log
30×div-inv
25×flip3-- add-cbrt-cube flip--
16×div-exp
15×pow1
7×cbrt-undiv
6×associate-*r* pow-prod-down prod-exp cbrt-unprod associate-/l*
4×insert-posit16 add-log-exp
3×rec-exp 1-exp
2×clear-num frac-2neg associate-*l* *-commutative
1×pow-flip inv-pow unswap-sqr
Counts
4 → 554
Calls
4 calls:
Slowest
27.0ms
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (* v v) PI)))))
17.0ms
(* (* v v) PI)
15.0ms
(* (* v -6) v)
7.0ms
(/ 4/3 (- PI (* (* v v) PI)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
472.0ms
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (* v v) PI)))))
97.0ms
(/ 4/3 (- PI (* (* v v) PI)))
44.0ms
(* (* v -6) v)
41.0ms
(* (* v v) PI)

simplify3.3m

Counts
868 → 566
Calls
868 calls:
Slowest
881.0ms
(/ (sqrt (sqrt (+ 2 (* (* v -6) v)))) (/ 1 (- PI (* (* v v) PI))))
842.0ms
(/ (cbrt 1) (/ (sqrt (cbrt (+ 2 (* (* v -6) v)))) (/ 4/3 (- PI (* (* v v) PI)))))
803.0ms
(/ (cbrt 1) (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (* v v) PI)))))
753.0ms
(/ 1 (/ (sqrt (sqrt (+ 2 (* (* v -6) v)))) (/ (cbrt 4/3) (- PI (* (* v v) PI)))))
727.0ms
(/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v))))) (/ (sqrt 4/3) (sqrt (- PI (* (* v v) PI))))))

prune6.1s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

28.8b
(sqrt (* (* v v) PI))
28.8b
(sqrt (* (* v v) PI))
1.0b
(/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))
1.0b
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
1071×times-frac
543×add-sqr-sqrt
467×*-un-lft-identity add-cube-cbrt
218×sqrt-prod
117×associate-/r*
76×difference-of-squares
55×associate-/r/
30×div-inv
27×add-exp-log
25×flip3-- flip--
17×pow1
16×div-exp
15×add-cbrt-cube
7×cbrt-undiv
6×sqrt-pow1 pow-prod-down associate-/l*
4×insert-posit16 add-log-exp
3×rec-exp 1-exp
2×clear-num frac-2neg pow1/2
1×pow-flip inv-pow
Counts
4 → 541
Calls
4 calls:
Slowest
17.0ms
(sqrt (* (* v v) PI))
16.0ms
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))))
14.0ms
(sqrt (* (* v v) PI))
7.0ms
(/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))

series618.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
391.0ms
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))))
104.0ms
(/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))
78.0ms
(sqrt (* (* v v) PI))
45.0ms
(sqrt (* (* v v) PI))

simplify2.0m

Counts
858 → 553
Calls
858 calls:
Slowest
585.0ms
(/ (cbrt 1) (/ (cbrt (sqrt (+ 2 (* (* v -6) v)))) (/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))))
423.0ms
(/ (sqrt (+ 2 (* (* v -6) v))) (/ (sqrt 4/3) (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI))))))
420.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v))))) (/ (* (cbrt 4/3) (cbrt 4/3)) (* (cbrt (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI))))) (cbrt (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))))))
392.0ms
(/ (cbrt 1) (/ (cbrt (sqrt (+ 2 (* (* v -6) v)))) (/ (cbrt 4/3) (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))))
380.0ms
(/ 1 (/ (sqrt 1) (/ (* (cbrt 4/3) (cbrt 4/3)) (+ (sqrt PI) (sqrt (* (* v v) PI))))))

prune4.4s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample1.9s

Algorithm
intervals
Results
753.0ms8000×body80valid
690.0ms8138×body80nan