Details

Time bar (total: 1.1m)

sample101.0ms

Algorithm
intervals
Results
43.0ms292×body80nan
39.0ms256×body80valid

simplify249.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
249.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 3 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
12×add-cbrt-cube add-exp-log
10×pow1
9×times-frac
6×associate-*l*
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
3×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×associate-/r/ *-commutative
1×cbrt-undiv clear-num frac-2neg flip3-- div-exp div-inv flip-- unswap-sqr
Counts
3 → 74
Calls
3 calls:
Slowest
19.0ms
(* v (* PI v))
14.0ms
(/ 4/3 (- PI (* v (* PI v))))
10.0ms
(* PI v)

series158.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
97.0ms
(/ 4/3 (- PI (* v (* PI v))))
31.0ms
(* v (* PI v))
30.0ms
(* PI v)

simplify7.3s

Counts
92 → 83
Calls
92 calls:
Slowest
690.0ms
(/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3)))
445.0ms
(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))
388.0ms
(* (* (* v (* PI v)) (* v (* PI v))) (* v (* PI v)))
335.0ms
(/ (* (* 4/3 4/3) 4/3) (* (* (- PI (* v (* PI v))) (- PI (* v (* PI v)))) (- PI (* v (* PI v)))))
324.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))

prune758.0ms

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×flip3-- add-cbrt-cube add-exp-log flip--
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 274
Calls
4 calls:
Slowest
30.0ms
(/ (/ 4/3 (sqrt (- PI (* v (* PI v))))) (sqrt (- PI (* v (* PI v)))))
10.0ms
(sqrt (- PI (* v (* PI v))))
10.0ms
(sqrt (- PI (* v (* PI v))))
7.0ms
(/ 4/3 (sqrt (- PI (* v (* PI v)))))

series917.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
388.0ms
(sqrt (- PI (* v (* PI v))))
309.0ms
(/ 4/3 (sqrt (- PI (* v (* PI v)))))
111.0ms
(/ (/ 4/3 (sqrt (- PI (* v (* PI v))))) (sqrt (- PI (* v (* PI v)))))
108.0ms
(sqrt (- PI (* v (* PI v))))

simplify49.7s

Counts
456 → 286
Calls
456 calls:
Slowest
718.0ms
(sqrt (- (pow PI 3) (pow (* v (* PI v)) 3)))
693.0ms
(* (* (/ 4/3 (sqrt (- PI (* v (* PI v))))) (/ 4/3 (sqrt (- PI (* v (* PI v)))))) (/ 4/3 (sqrt (- PI (* v (* PI v))))))
674.0ms
(sqrt (- (pow PI 3) (pow (* v (* PI v)) 3)))
643.0ms
(* (* (/ (/ 4/3 (sqrt (- PI (* v (* PI v))))) (sqrt (- PI (* v (* PI v))))) (/ (/ 4/3 (sqrt (- PI (* v (* PI v))))) (sqrt (- PI (* v (* PI v)))))) (/ (/ 4/3 (sqrt (- PI (* v (* PI v))))) (sqrt (- PI (* v (* PI v))))))
605.0ms
(/ 4/3 (sqrt (- (pow PI 3) (pow (* v (* PI v)) 3))))

prune3.3s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.5s7702×body80nan
1.3s8000×body80valid