Details

sample34.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
9.0ms	244×	body	80	nan

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	10
1	91	10
2	263	10
3	620	10
4	1138	10
5	1470	10
6	1510	10
7	1510	10

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.0b

Counts

2 → 1

localize11.0ms

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))))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

397×	`add-sqr-sqrt`
252×	`associate-l`
166×	`associate-r`
162×	`times-frac`
152×	`*-un-lft-identity`
127×	`unswap-sqr`
108×	`add-cube-cbrt`
70×	`sqrt-prod`
60×	`difference-of-squares`
54×	`associate-/r*`
37×	`add-exp-log` `add-cbrt-cube`
31×	`*-commutative`
23×	`pow1`
22×	`distribute-lft-out--`
18×	`associate-*r/` `prod-exp` `cbrt-unprod`
15×	`swap-sqr`
13×	`flip3--` `flip--`
12×	`sqrt-div` `pow-prod-down`
8×	`frac-times` `associate-/r/`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `add-log-exp`
3×	`associate-/l*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 400

Calls

4 calls:

15.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
38.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
10.0ms	(* 6.0 (* v v))
53.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
285.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
25.0ms	(* 6.0 (* v v))
647.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify102.0ms

Algorithm

egg-herbie

Counts

412 → 412

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	1725	5218
1	5002	5055

prune744.0ms

Filtered

412 candidates to 265 candidates (35.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	411	1	412
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	412	1	413

Merged error: 0b

Counts

413 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

11402×	`add-sqr-sqrt`
10207×	`times-frac`
6197×	`associate-l`
4917×	`*-un-lft-identity`
4217×	`add-cube-cbrt`
3606×	`cbrt-prod`
3547×	`unswap-sqr`
3502×	`associate-r`
1305×	`sqrt-prod`
1301×	`swap-sqr`
962×	`difference-of-squares`
628×	`*-commutative`
350×	`distribute-lft-out--`
161×	`add-cbrt-cube`
91×	`cbrt-unprod`
88×	`associate-/r` `associate-/l`
77×	`add-exp-log`
63×	`div-inv`
55×	`cbrt-undiv`
34×	`prod-exp`
33×	`associate-/l/`
23×	`pow1`
20×	`div-exp`
18×	`associate-*r/`
13×	`flip3--` `flip--`
12×	`sqrt-div` `pow-prod-down`
8×	`frac-times` `associate-/r/`
4×	`associate-*l/` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 5593

Calls

4 calls:

191.0ms	(/ (/ 4.0 (* (cbrt 3.0) (cbrt 3.0))) (* (* (* (cbrt 3.0) PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
45.0ms	(* (* (* (cbrt 3.0) PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
17.0ms	(* (* (cbrt 3.0) PI) (- 1.0 (* v v)))
10.0ms	(* 6.0 (* v v))

series1.0s

Counts

4 → 12

Calls

4 calls:

542.0ms	(/ (/ 4.0 (* (cbrt 3.0) (cbrt 3.0))) (* (* (* (cbrt 3.0) PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
317.0ms	(* (* (* (cbrt 3.0) PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
158.0ms	(* (* (cbrt 3.0) PI) (- 1.0 (* v v)))
26.0ms	(* 6.0 (* v v))

simplify1.5s

Algorithm

egg-herbie

Counts

5605 → 5605

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5629	160009

prune15.9s

Filtered

5605 candidates to 3448 candidates (38.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	5605	0	5605
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	5605	1	5606

Merged error: 0b

Counts

5606 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	15
1	23	15

end0.0ms

sample782.0ms

Algorithm

intervals

Results

302.0ms	8000×	body	80	valid
288.0ms	7957×	body	80	nan