Details

Time bar (total: 19.5s)

sample54.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
20.0ms257×body80nan

simplify232.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
231.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

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)))

rewrite64.0ms

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
27.0ms
(* v (* PI v))
14.0ms
(/ 4/3 (- PI (* v (* PI v))))
11.0ms
(- PI (* v (* PI v)))
11.0ms
(* PI v)

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(/ 4/3 (- PI (* v (* PI v))))
70.0ms
(- PI (* v (* PI v)))
34.0ms
(* v (* PI v))
26.0ms
(* PI v)

simplify4.7s

Counts
65 → 107
Calls
65 calls:
Slowest
405.0ms
(+ (* PI PI) (+ (* (* v (* PI v)) (* 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))))))
308.0ms
(/ (* (* 4/3 4/3) 4/3) (* (* (- PI (* v (* PI v))) (- PI (* v (* PI v)))) (- PI (* v (* PI v)))))
302.0ms
(/ (exp PI) (exp (* v (* PI v))))
282.0ms
(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))

prune960.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (- PI (* v (* PI v))))
1.0b
(sqrt (- PI (* v (* PI v))))
1.0b
(/ 4/3 (sqrt (- PI (* v (* PI v)))))
0.3b
(* PI v)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
8×pow1 add-cbrt-cube add-exp-log
6×associate-/r* sqrt-div
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- associate-*r* associate-*l* flip-- associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv clear-num frac-2neg div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 101
Calls
4 calls:
Slowest
13.0ms
(/ 4/3 (sqrt (- PI (* v (* PI v)))))
11.0ms
(sqrt (- PI (* v (* PI v))))
10.0ms
(sqrt (- PI (* v (* PI v))))
10.0ms
(* PI v)

series491.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
229.0ms
(/ 4/3 (sqrt (- PI (* v (* PI v)))))
140.0ms
(sqrt (- PI (* v (* PI v))))
102.0ms
(sqrt (- PI (* v (* PI v))))
21.0ms
(* PI v)

simplify8.5s

Counts
83 → 113
Calls
83 calls:
Slowest
736.0ms
(sqrt (- (pow PI 3) (pow (* v (* PI v)) 3)))
579.0ms
(sqrt (- (pow PI 3) (pow (* v (* PI v)) 3)))
517.0ms
(sqrt (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))))
368.0ms
(+ (* 1/2 (* (pow v 4) (sqrt (/ 1 PI)))) (+ (* 2/3 (* (pow v 2) (sqrt (/ 1 PI)))) (* 4/3 (sqrt (/ 1 PI)))))
334.0ms
(- (+ (* 1/6 (/ 1 (* (pow v 5) (* (pow PI 2) (pow (sqrt (/ -1 PI)) 3))))) (+ (* 2/3 (/ 1 (* (pow v 3) (* PI (sqrt (/ -1 PI)))))) (* 2/3 (/ 1 (* (pow v 5) (* PI (sqrt (/ -1 PI)))))))) (* 4/3 (/ (sqrt (/ -1 PI)) v)))

prune1.4s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.4s7762×body80nan
1.2s8000×body80valid