Details

sample67.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
21.0ms	267×	body	80	nan

simplify4.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	20
1	32	20
2	90	20
3	271	20
4	781	20
5	1867	20
6	3834	20
done	5000	20

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 3.0 PI) (- 1.0 (* v v)))
0.0b	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.2b	(* 6.0 (* v v))
1.0b	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log` `add-cbrt-cube`
23×	`pow1`
18×	`associate-*r/` `prod-exp` `cbrt-unprod`
14×	`add-sqr-sqrt`
13×	`flip3--` `flip--`
12×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div` `pow-prod-down`
11×	`associate-r`
8×	`frac-times` `associate-/r/`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `sqrt-prod` `-commutative` `associate-/l`
2×	`sub-neg`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

41.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
108.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
29.0ms	(* 6.0 (* v v))
104.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
363.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
28.0ms	(* 6.0 (* v v))
617.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify614.0ms

Counts

135 → 135

Iterations

Useful iterations: done (610.0ms)

Iter	Nodes	Cost
0	330	3068
1	1005	2854
done	5000	2507

prune493.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 2.0 (* 6.0 (* v v))))
0.0b	(* (* 3.0 PI) (- 1.0 (* v v)))
0.0b	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
0.2b	(* 6.0 (* v v))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
15×	`pow1`
14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`prod-exp` `cbrt-unprod`
6×	`prod-diff` `pow-prod-down`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
4×	`expm1-log1p-u` `associate-r/` `associate-l*` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `times-frac` `div-exp` `sqrt-prod` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/r/` `*-commutative`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r*` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

10.0ms	(sqrt (- 2.0 (* 6.0 (* v v))))
29.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
22.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
36.0ms	(* 6.0 (* v v))

series426.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(sqrt (- 2.0 (* 6.0 (* v v))))
128.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
123.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
50.0ms	(* 6.0 (* v v))

simplify3.0s

Counts

110 → 110

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	227	1526
1	644	1429
2	4090	1247
done	5000	1247

prune363.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 4.0 (+ (* 1.0 (* 3.0 PI)) (- (* 3.0 (* (pow v 2) PI)))))
0.2b	(* (pow v 2) PI)
0.2b	(* 6.0 (* v v))
0.2b	(* 3.0 (* (pow v 2) PI))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
24×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-l`
13×	`prod-exp`
11×	`pow1`
9×	`times-frac`
7×	`cbrt-unprod`
5×	`associate-r` `unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 102

Calls

4 calls:

39.0ms	(/ 4.0 (+ (* 1.0 (* 3.0 PI)) (- (* 3.0 (* (pow v 2) PI)))))
32.0ms	(* (pow v 2) PI)
27.0ms	(* 6.0 (* v v))
23.0ms	(* 3.0 (* (pow v 2) PI))

series353.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ 4.0 (+ (* 1.0 (* 3.0 PI)) (- (* 3.0 (* (pow v 2) PI)))))
44.0ms	(* (pow v 2) PI)
36.0ms	(* 6.0 (* v v))
78.0ms	(* 3.0 (* (pow v 2) PI))

simplify1.8s

Counts

114 → 114

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	193	1538
1	484	1422
2	2230	1192
done	5000	1190

prune636.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify15.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	25
1	31	25
2	39	25
done	39	25

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
863.0ms	8126×	body	80	nan