Details

Time bar (total: 49.7s)

sample88.0ms

Algorithm
intervals
Results
36.0ms256×body80valid
34.0ms251×body80nan

simplify245.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
245.0ms
(/ 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: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4/3 (- PI (* v (* PI v))))
0.3b
(* PI v)
0.1b
(* v (* PI v))
0.0b
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
98×add-sqr-sqrt
96×*-un-lft-identity add-cube-cbrt
48×sqrt-prod
18×add-cbrt-cube add-exp-log associate-/l*
16×associate-/r/
11×pow1
9×associate-/r* div-inv
8×flip3-- flip--
6×associate-*l*
4×expm1-log1p-u cbrt-undiv div-exp associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg *-commutative
1×unswap-sqr associate-/l/
Counts
4 → 203
Calls
4 calls:
Slowest
31.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
17.0ms
(* v (* PI v))
6.0ms
(/ 4/3 (- PI (* v (* PI v))))
5.0ms
(* PI v)

series687.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
521.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
107.0ms
(/ 4/3 (- PI (* v (* PI v))))
33.0ms
(* v (* PI v))
26.0ms
(* PI v)

simplify35.2s

Counts
259 → 215
Calls
259 calls:
Slowest
684.0ms
(/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3)))
644.0ms
(/ (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v))))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))
514.0ms
(/ (* (cbrt 4/3) (cbrt 4/3)) (* (cbrt (- PI (* v (* PI v)))) (cbrt (- PI (* v (* PI v))))))
514.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
500.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))

prune2.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(* PI v)
0.1b
(* v (* PI v))
0.0b
(sqrt (fma (* v -6) v 2))
0.0b
(* (sqrt (fma (* v -6) v 2)) (- PI (* v (* PI v))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×pow1
13×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
12×associate-*l*
7×associate-*r* sqrt-prod
6×prod-diff
5×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative unswap-sqr
2×sub-neg associate-*r/
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 95
Calls
4 calls:
Slowest
26.0ms
(* v (* PI v))
23.0ms
(* (sqrt (fma (* v -6) v 2)) (- PI (* v (* PI v))))
11.0ms
(* PI v)
2.0ms
(sqrt (fma (* v -6) v 2))

series379.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
231.0ms
(* (sqrt (fma (* v -6) v 2)) (- PI (* v (* PI v))))
87.0ms
(sqrt (fma (* v -6) v 2))
34.0ms
(* v (* PI v))
27.0ms
(* PI v)

simplify7.1s

Counts
61 → 107
Calls
61 calls:
Slowest
566.0ms
(- (sqrt 2) (+ (* 9/2 (/ (pow v 4) (pow (sqrt 2) 3))) (* 3 (/ (pow v 2) (sqrt 2)))))
518.0ms
(+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))
351.0ms
(- (+ (/ 1 (* v (sqrt -6))) (* v (sqrt -6))) (* 1/2 (/ 1 (* (pow v 3) (pow (sqrt -6) 3)))))
317.0ms
(* (* (* v v) v) (* (* (* PI v) (* PI v)) (* PI v)))
310.0ms
(* (sqrt (fma (* v -6) v 2)) (fma (- (* PI v)) v (* (* PI v) v)))

prune924.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s8000×body80valid
1.1s7984×body80nan