Details

sample104.0ms

Algorithm

intervals

Results

53.0ms	256×	body	80	valid
32.0ms	230×	body	80	nan

simplify300.0ms

Calls

1 calls:

Slowest

300.0ms

(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 4/3 (- PI (* v (* PI v))))
0.3b	(* PI v)
0.2b	(* v (* PI v))
0.0b	(- PI (* v (* PI v)))

rewrite45.0ms

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`

Calls

4 calls:

Slowest

14.0ms	(/ 4/3 (- PI (* v (* PI v))))
13.0ms	(* v (* PI v))
11.0ms	(* PI v)
5.0ms	(- PI (* v (* PI v)))

series219.0ms

Calls

4 calls:

Slowest

102.0ms	(/ 4/3 (- PI (* v (* PI v))))
59.0ms	(- PI (* v (* PI v)))
37.0ms	(* v (* PI v))
21.0ms	(* PI v)

simplify5.4s

Calls

65 calls:

Slowest

484.0ms	(+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))
393.0ms	(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))
377.0ms	(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))
368.0ms	(/ (exp PI) (exp (* v (* PI v))))
351.0ms	(/ (* (* 4/3 4/3) 4/3) (* (* (- PI (* v (* PI v))) (- PI (* v (* PI v)))) (- PI (* v (* PI v)))))

prune1.0s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (* (cbrt 4/3) (cbrt 4/3)) (/ (- PI (* v (* PI v))) (cbrt 4/3)))
0.3b	(* PI v)
0.2b	(* v (* PI v))
0.0b	(/ (- PI (* v (* PI v))) (cbrt 4/3))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
30×	`cbrt-prod`
28×	`associate-/r*`
25×	`add-exp-log`
18×	`add-cbrt-cube`
11×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-l` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`
1×	`flip3--` `div-sub` `associate-/r/` `flip--` `unswap-sqr`

Calls

4 calls:

Slowest

19.0ms	(* v (* PI v))
19.0ms	(/ (* (cbrt 4/3) (cbrt 4/3)) (/ (- PI (* v (* PI v))) (cbrt 4/3)))
11.0ms	(/ (- PI (* v (* PI v))) (cbrt 4/3))
9.0ms	(* PI v)

series356.0ms

Calls

4 calls:

Slowest

143.0ms	(/ (- PI (* v (* PI v))) (cbrt 4/3))
141.0ms	(/ (* (cbrt 4/3) (cbrt 4/3)) (/ (- PI (* v (* PI v))) (cbrt 4/3)))
44.0ms	(* v (* PI v))
28.0ms	(* PI v)

simplify16.1s

Calls

154 calls:

Slowest

596.0ms	(- (pow PI 3) (pow (* v (* PI v)) 3))
566.0ms	(* (* (* v v) v) (* (* (* PI PI) PI) (* (* v v) v)))
395.0ms	(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))
366.0ms	(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))
355.0ms	(/ (* 4/3 4/3) (/ (* (* (- PI (* v (* PI v))) (- PI (* v (* PI v)))) (- PI (* v (* PI v)))) 4/3))

prune1.9s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.1s	8163×	body	80	nan