Details

sample44.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
14.0ms	270×	body	80	nan

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	20
1	32	20
2	90	20
3	268	20
4	633	20
5	1191	20
6	1478	20
7	1496	20
done	1496	20

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize22.0ms

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))))))

rewrite276.0ms

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:

34.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
112.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
27.0ms	(* 6.0 (* v v))
96.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
459.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
48.0ms	(* 6.0 (* v v))
630.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify2.4s

Counts

135 → 135

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	330	3068
1	932	2820
2	3839	2441
done	5001	2432

prune514.0ms

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

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 173

Calls

4 calls:

40.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
41.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
62.0ms	(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
19.0ms	(* 6.0 (* v v))

series1.0s

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
179.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
665.0ms	(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
46.0ms	(* 6.0 (* v v))

simplify2.2s

Counts

185 → 185

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	378	4647
1	977	4300
2	3556	3934
done	5000	3925

prune545.0ms

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 (* 3.0 PI)) (- (* 1.0 1.0) (pow v 4)))
0.0b	(/ (* (/ (/ 4.0 (* 3.0 PI)) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.0b	(* (/ (/ 4.0 (* 3.0 PI)) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v)))
0.2b	(* 6.0 (* v v))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

130×	`times-frac`
88×	`add-sqr-sqrt`
52×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
51×	`associate-l`
45×	`difference-of-squares`
20×	`cbrt-undiv` `div-exp`
16×	`div-inv`
15×	`unpow-prod-down` `sqr-pow`
14×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
11×	`pow1`
8×	`associate-/l*`
6×	`sqrt-prod` `associate-/r/` `associate-/l/`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `associate-r/` `associate-r*` `pow-prod-down` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-2neg` `sqrt-div` `associate-l/` `clear-num` `-commutative`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 218

Calls

4 calls:

36.0ms	(/ (/ 4.0 (* 3.0 PI)) (- (* 1.0 1.0) (pow v 4)))
56.0ms	(/ (* (/ (/ 4.0 (* 3.0 PI)) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
143.0ms	(* (/ (/ 4.0 (* 3.0 PI)) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v)))
17.0ms	(* 6.0 (* v v))

series1.3s

Counts

4 → 12

Calls

4 calls:

261.0ms	(/ (/ 4.0 (* 3.0 PI)) (- (* 1.0 1.0) (pow v 4)))
741.0ms	(/ (* (/ (/ 4.0 (* 3.0 PI)) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
251.0ms	(* (/ (/ 4.0 (* 3.0 PI)) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v)))
49.0ms	(* 6.0 (* v v))

simplify1.1s

Counts

230 → 230

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	491	5686
1	1639	5408
done	5000	4663

prune1.3s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	28
1	25	28
done	25	28

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	7862×	body	80	nan
848.0ms	8000×	body	80	valid