Details

Time bar (total: 25.9s)

sample74.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
28.0ms263×body80nan

simplify242.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
242.0ms
(/ 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: 0b

localize32.0ms

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
(- PI (* v (* PI v)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube add-exp-log
11×pow1
9×times-frac
6×associate-*l* add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg prod-diff associate-/l*
2×flip3-- associate-/r/ *-commutative flip--
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp div-inv unswap-sqr
Counts
4 → 95
Calls
4 calls:
Slowest
25.0ms
(* v (* PI v))
11.0ms
(- PI (* v (* PI v)))
7.0ms
(/ 4/3 (- PI (* v (* PI v))))
5.0ms
(* PI v)

series245.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(/ 4/3 (- PI (* v (* PI v))))
57.0ms
(- PI (* v (* PI v)))
29.0ms
(* PI v)
27.0ms
(* v (* PI v))

simplify5.3s

Counts
65 → 107
Calls
65 calls:
Slowest
517.0ms
(+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))
350.0ms
(/ (* (* 4/3 4/3) 4/3) (* (* (- PI (* v (* PI v))) (- PI (* v (* PI v)))) (- PI (* v (* PI v)))))
347.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))
328.0ms
(* (* (* PI PI) PI) (* (* v v) v))
318.0ms
(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))

prune991.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

2.5b
(log (exp (* v (* PI v))))
1.0b
(/ 4/3 (- PI (log (exp (* v (* PI v))))))
0.3b
(* PI v)
0.1b
(* v (* PI v))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
29×add-sqr-sqrt
19×add-cube-cbrt
18×times-frac
16×pow1
13×add-cbrt-cube add-exp-log
8×distribute-lft-out--
7×log-pow
6×associate-/r* associate-*l*
5×add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u difference-of-squares
3×log-prod associate-/l*
2×associate-/r/ *-commutative
1×cbrt-undiv exp-prod clear-num frac-2neg flip3-- exp-to-pow div-exp rem-log-exp div-inv flip-- unswap-sqr
Counts
4 → 103
Calls
4 calls:
Slowest
25.0ms
(* v (* PI v))
9.0ms
(/ 4/3 (- PI (log (exp (* v (* PI v))))))
5.0ms
(* PI v)
4.0ms
(log (exp (* v (* PI v))))

series209.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
83.0ms
(/ 4/3 (- PI (log (exp (* v (* PI v))))))
56.0ms
(log (exp (* v (* PI v))))
49.0ms
(* v (* PI v))
21.0ms
(* PI v)

simplify14.4s

Counts
82 → 115
Calls
82 calls:
Slowest
677.0ms
(- PI (log (exp (* v (* PI v)))))
394.0ms
(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))
378.0ms
(/ 4/3 (cbrt (- PI (log (exp (* v (* PI v)))))))
368.0ms
(/ (cbrt 4/3) (sqrt (- PI (log (exp (* v (* PI v)))))))
365.0ms
(/ (* (cbrt 4/3) (cbrt 4/3)) (* (cbrt (- PI (log (exp (* v (* PI v)))))) (cbrt (- PI (log (exp (* v (* PI v))))))))

prune1.4s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.2s8000×body80valid
1.2s8130×body80nan