Details

sample40.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
13.0ms	262×	body	80	nan

simplify3.1s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize20.0ms

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)))))
0.1b	(* 6.0 (* v v))
1.0b	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite282.0ms

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)))
115.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
19.0ms	(* 6.0 (* v v))
109.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
469.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
51.0ms	(* 6.0 (* v v))
664.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify2.8s

Counts

135 → 135

Iterations

Useful iterations: done (2.8s)

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

prune501.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.0b	(sqrt (- 2.0 (* 6.0 (* v v))))
0.0b	(* (* 3.0 PI) (- 1.0 (* v v)))
0.1b	(* 6.0 (* v v))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

75.0ms	(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
7.0ms	(sqrt (- 2.0 (* 6.0 (* v v))))
47.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
18.0ms	(* 6.0 (* v v))

series984.0ms

Counts

4 → 12

Calls

4 calls:

671.0ms	(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
90.0ms	(sqrt (- 2.0 (* 6.0 (* v v))))
174.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
48.0ms	(* 6.0 (* v v))

simplify2.1s

Counts

175 → 175

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	379	4432
1	982	4088
2	3548	3792
done	5000	3783

prune656.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 6.0 (* v v))
0.1b	(* 6.0 (* v v))
0.1b	(* 6.0 (* v v))
0.1b	(* 6.0 (* v v))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `associate-r` `*-commutative` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

19.0ms	(* 6.0 (* v v))
35.0ms	(* 6.0 (* v v))
20.0ms	(* 6.0 (* v v))
34.0ms	(* 6.0 (* v v))

series160.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 6.0 (* v v))
53.0ms	(* 6.0 (* v v))
41.0ms	(* 6.0 (* v v))
30.0ms	(* 6.0 (* v v))

simplify4.1s

Counts

96 → 96

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	36	696
1	80	684
2	216	564
3	450	564
4	673	564
5	1860	564
done	5000	564

prune507.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify9.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	26	49
1	33	49
done	33	49

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	7995×	body	80	nan
794.0ms	8000×	body	80	valid