Details

Time bar (total: 7.3m)

sample108.0ms

Algorithm
intervals
Results
44.0ms284×body80nan
41.0ms256×body80valid

simplify244.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
244.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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
22.0ms
(* (* v -6) v)
19.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* (* v -6) v))))
18.0ms
(* (* v v) PI)
6.0ms
(/ 4/3 (- PI (* (* v v) PI)))

series674.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
485.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* (* v -6) v))))
117.0ms
(/ 4/3 (- PI (* (* v v) PI)))
41.0ms
(* (* v -6) v)
31.0ms
(* (* v v) PI)

simplify39.0s

Counts
308 → 235
Calls
308 calls:
Slowest
603.0ms
(/ (/ 4/3 (- (* PI PI) (* (* (* v v) PI) (* (* v v) PI)))) (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v))))))
593.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (sqrt (+ 2 (* (* v -6) v)))))
565.0ms
(* (* (* (* v -6) (* v -6)) (* v -6)) (* (* v v) v))
466.0ms
(- (+ (* 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))))))) (+ (* 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))))))
440.0ms
(/ (/ (* (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))))))

prune2.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize54.0ms

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)

rewrite132.0ms

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
35.0ms
(* (* v v) PI)
30.0ms
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (* v v) PI)))))
27.0ms
(* (* v -6) v)
13.0ms
(/ 4/3 (- PI (* (* v v) PI)))

series714.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
505.0ms
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (* v v) PI)))))
113.0ms
(/ 4/3 (- PI (* (* v v) PI)))
49.0ms
(* (* v v) PI)
47.0ms
(* (* v -6) v)

simplify3.2m

Counts
868 → 566
Calls
868 calls:
Slowest
903.0ms
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ (cbrt 4/3) (- 1 (* v v)))))
874.0ms
(/ (sqrt 1) (/ (sqrt (+ 2 (* (* v -6) v))) (+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI))))))
640.0ms
(/ (sqrt 1) (/ (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v))))) (/ (* (cbrt 4/3) (cbrt 4/3)) PI)))
626.0ms
(/ (cbrt 1) (/ (cbrt (sqrt (+ 2 (* (* v -6) v)))) (/ 1 (- PI (* (* v v) PI)))))
582.0ms
(/ (sqrt 1) (/ (sqrt (cbrt (+ 2 (* (* v -6) v)))) (+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI))))))

prune6.4s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize33.0ms

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)))))))

rewrite82.0ms

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
30.0ms
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))))
16.0ms
(sqrt (* (* v v) PI))
10.0ms
(sqrt (* (* v v) PI))
8.0ms
(/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))

series768.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
499.0ms
(/ 1 (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))))
122.0ms
(/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))
74.0ms
(sqrt (* (* v v) PI))
73.0ms
(sqrt (* (* v v) PI))

simplify3.1m

Counts
858 → 553
Calls
858 calls:
Slowest
814.0ms
(/ 1 (/ (sqrt (sqrt (+ 2 (* (* v -6) v)))) (/ (* (cbrt 4/3) (cbrt 4/3)) (sqrt (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI))))))))
767.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI))))))) (cbrt (/ (sqrt (+ 2 (* (* v -6) v))) (/ 4/3 (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))))))
611.0ms
(/ (sqrt 1) (/ (sqrt (sqrt (+ 2 (* (* v -6) v)))) (/ 1 (* (cbrt (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI))))) (cbrt (- PI (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI)))))))))
606.0ms
(/ (sqrt 1) (/ (sqrt 1) (/ 4/3 (- (* PI PI) (* (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI))) (* (sqrt (* (* v v) PI)) (sqrt (* (* v v) PI))))))))
595.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ 1 (/ (* (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)))))))))

prune4.9s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.1s8000×body80valid
754.0ms8138×body80nan