Details

sample30.0ms

Algorithm

intervals

Results

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

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	10
1	91	10
2	275	10
3	672	10
4	1303	10
5	1737	10
6	1802	10
7	1802	10

prune3.0ms

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))))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

469×	`add-sqr-sqrt`
270×	`associate-l`
212×	`*-un-lft-identity`
184×	`associate-r`
168×	`add-cube-cbrt`
162×	`times-frac`
133×	`unswap-sqr`
90×	`prod-diff`
70×	`sqrt-prod`
60×	`difference-of-squares`
54×	`associate-/r*`
47×	`distribute-rgt-in` `distribute-lft-in`
37×	`add-exp-log` `*-commutative` `add-cbrt-cube`
33×	`swap-sqr`
23×	`pow1`
22×	`distribute-lft-out--`
18×	`associate-*r/` `prod-exp` `cbrt-unprod`
13×	`flip3--` `flip--`
12×	`sqrt-div` `pow-prod-down`
8×	`frac-times` `associate-/r/`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`sub-neg`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 498

Calls

4 calls:

21.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
36.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
9.0ms	(* 6.0 (* v v))
50.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series859.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
284.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
26.0ms	(* 6.0 (* v v))
443.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify119.0ms

Algorithm

egg-herbie

Counts

510 → 510

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2234	6830
1	5002	6352

prune779.0ms

Filtered

510 candidates to 279 candidates (45.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	509	1	510
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	510	1	511

Merged error: 0b

Counts

511 → 1

localize11.0ms

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

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

1085×	`add-sqr-sqrt`
933×	`times-frac`
588×	`*-un-lft-identity`
464×	`add-cube-cbrt`
406×	`associate-r`
388×	`associate-l`
225×	`unswap-sqr`
195×	`sqrt-prod`
170×	`difference-of-squares`
90×	`prod-diff`
71×	`*-commutative`
62×	`distribute-lft-out--`
53×	`swap-sqr`
47×	`distribute-rgt-in` `distribute-lft-in`
45×	`associate-/r*`
44×	`div-inv`
37×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*r/`
16×	`pow1` `associate-/l*`
13×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`
12×	`sqrt-div`
9×	`cbrt-undiv` `div-exp` `associate-/l/`
8×	`frac-times` `associate-/r/`
7×	`pow-prod-down`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `clear-num`

Counts

4 → 865

Calls

4 calls:

52.0ms	(/ (/ 4.0 3.0) (* (* PI (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
33.0ms	(* (* PI (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
14.0ms	(* PI (- 1.0 (* v v)))
9.0ms	(* 6.0 (* v v))

series789.0ms

Counts

4 → 12

Calls

4 calls:

458.0ms	(/ (/ 4.0 3.0) (* (* PI (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
227.0ms	(* (* PI (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
77.0ms	(* PI (- 1.0 (* v v)))
26.0ms	(* 6.0 (* v v))

simplify222.0ms

Algorithm

egg-herbie

Counts

877 → 877

Iterations

Useful iterations: 1 (71.0ms)

Iter	Nodes	Cost
0	3588	14389
1	5001	13932

prune1.4s

Filtered

877 candidates to 453 candidates (48.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	877	0	877
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	877	1	878

Merged error: 0b

Counts

878 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample766.0ms

Algorithm

intervals

Results

302.0ms	8000×	body	80	valid
287.0ms	7957×	body	80	nan