Details

Time bar (total: 39.9s)Debug log

sample65.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
24.0ms245×body80nan

simplify147.0ms

Calls
1 calls:
Slowest
147.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4/3 PI)
0.2b
(* (* v v) -6)
0.0b
(/ (/ 4/3 PI) (- 1 (* v v)))
0.0b
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
107×add-cube-cbrt
107×*-un-lft-identity
107×add-sqr-sqrt
57×sqrt-prod
35×div-inv
22×associate-/l*
18×associate-/r/
11×add-exp-log
11×add-cbrt-cube
9×associate-/r*
8×flip--
8×flip3--
4×add-log-exp
4×div-exp
4×cbrt-undiv
4×pow1
3×frac-2neg
3×clear-num
2×associate-/l/
2×sqrt-div
1×flip-+
1×*-commutative
1×associate-*l*
1×flip3-+
Calls
4 calls:
Slowest
6.0ms
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))
3.0ms
(* (* v v) -6)
3.0ms
(/ (/ 4/3 PI) (- 1 (* v v)))
0.0ms
(/ 4/3 PI)

series280.0ms

Calls
4 calls:
Slowest
198.0ms
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))
71.0ms
(/ (/ 4/3 PI) (- 1 (* v v)))
11.0ms
(* (* v v) -6)
0.0ms
(/ 4/3 PI)

simplify18.8s

Calls
289 calls:
Slowest
601.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))
502.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))
340.0ms
(sqrt (+ (* 2 2) (- (* (* (* v v) -6) (* (* v v) -6)) (* 2 (* (* v v) -6)))))
325.0ms
(/ (* (* (/ 4/3 PI) (/ 4/3 PI)) (/ 4/3 PI)) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v))))
320.0ms
(/ (/ (/ 4/3 PI) (- (pow 1 3) (pow (* v v) 3))) (sqrt (sqrt (+ 2 (* (* v v) -6)))))

prune2.1s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
45×add-cube-cbrt
45×*-un-lft-identity
45×add-sqr-sqrt
42×associate-*r*
39×sqrt-prod
30×associate-/r/
17×div-inv
16×add-exp-log
13×flip--
13×flip3--
11×add-cbrt-cube
6×associate-/l*
6×associate-/r*
6×pow1
5×associate-*l*
4×add-log-exp
4×div-exp
4×sqrt-div
3×prod-exp
2×flip-+
2×cbrt-unprod
2×*-commutative
2×flip3-+
2×frac-2neg
2×clear-num
2×rec-exp
2×cbrt-undiv
1×associate-/l/
1×associate-*r/
1×associate-*l/
1×pow-prod-down
1×frac-times
Calls
4 calls:
Slowest
15.0ms
(* (/ 4/3 PI) (/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))
6.0ms
(/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))
2.0ms
(* (* v v) -6)
0.0ms
(/ 4/3 PI)

series300.0ms

Calls
4 calls:
Slowest
210.0ms
(* (/ 4/3 PI) (/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))
76.0ms
(/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))
14.0ms
(* (* v v) -6)
0.0ms
(/ 4/3 PI)

simplify13.3s

Calls
151 calls:
Slowest
484.0ms
(/ (/ 1 (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))
409.0ms
(- (+ (/ (sqrt -1/6) (pow v 7)) (+ (/ (sqrt -1/6) (pow v 5)) (/ (sqrt -1/6) (pow v 3)))) (+ (* 1/36 (/ 1 (* (pow v 5) (sqrt -1/6)))) (+ (* 1/27 (/ 1 (* (pow v 7) (sqrt -1/6)))) (* 1/2592 (/ 1 (* (pow v 7) (pow (sqrt -1/6) 3)))))))
402.0ms
(/ (/ 1 (- (pow 1 3) (pow (* v v) 3))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))
387.0ms
(sqrt (+ (* 2 2) (- (* (* (* v v) -6) (* (* v v) -6)) (* 2 (* (* v v) -6)))))
369.0ms
(/ (* (* (/ 1 (- 1 (* v v))) (/ 1 (- 1 (* v v)))) (/ 1 (- 1 (* v v)))) (* (* (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 2 (* (* v v) -6)))))

prune1.8s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.7s8000×body80valid
1.1s7885×body80nan