Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	274×	body	80	nan
9.0ms	256×	body	80	valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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 (0.0%)

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

localize14.0ms

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))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

7.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
14.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms	(* 6.0 (* v v))
13.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series823.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
267.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
31.0ms	(* 6.0 (* v v))
423.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify115.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	888	1350
1	4408	1176
2	5002	1174

prune269.0ms

Filtered

121 candidates to 78 candidates (64.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	2	122

Merged error: 0b

Counts

122 → 2

localize11.0ms

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
44×	`add-sqr-sqrt`
42×	`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×	`pow-prod-down`
5×	`associate-r`
4×	`associate-l` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-div` `clear-num` `*-commutative`
1×	`associate-/l/` `difference-of-squares` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

7.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
14.0ms	(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
8.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
6.0ms	(* 6.0 (* v v))

series665.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
429.0ms	(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
98.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
29.0ms	(* 6.0 (* v v))

simplify110.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	937	2186
1	4457	2002
2	5001	1982

prune557.0ms

Filtered

171 candidates to 109 candidates (63.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	172	1	173

Merged error: 0b

Counts

173 → 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	(* 3.0 (* PI (- 1.0 (* v v))))
0.0b	(/ 4.0 (* 3.0 (* PI (- 1.0 (* v v)))))
0.2b	(* 6.0 (* v v))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
43×	`add-sqr-sqrt`
42×	`add-cube-cbrt` `*-un-lft-identity`
37×	`add-exp-log` `add-cbrt-cube`
36×	`associate-*r/`
30×	`sqrt-prod`
18×	`associate-/r/`
14×	`pow1`
12×	`prod-exp` `cbrt-unprod` `associate-/l*`
10×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
9×	`div-inv`
8×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-/r*`
6×	`associate-l` `pow-prod-down`
4×	`sub-neg` `add-log-exp`
2×	`frac-2neg` `sqrt-div` `associate-r` `clear-num` `*-commutative`
1×	`associate-/l/` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

14.0ms	(/ (/ 4.0 (* 3.0 (* PI (- 1.0 (* v v))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
7.0ms	(* 3.0 (* PI (- 1.0 (* v v))))
8.0ms	(/ 4.0 (* 3.0 (* PI (- 1.0 (* v v)))))
6.0ms	(* 6.0 (* v v))

series654.0ms

Counts

4 → 12

Calls

4 calls:

426.0ms	(/ (/ 4.0 (* 3.0 (* PI (- 1.0 (* v v))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
100.0ms	(* 3.0 (* PI (- 1.0 (* v v))))
97.0ms	(/ 4.0 (* 3.0 (* PI (- 1.0 (* v v)))))
29.0ms	(* 6.0 (* v v))

simplify108.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	925	2205
1	4048	2021
2	5002	2001

prune366.0ms

Filtered

174 candidates to 108 candidates (62.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	174	1	175

Merged error: 0b

Counts

175 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample762.0ms

Algorithm

intervals

Results

298.0ms	8000×	body	80	valid
282.0ms	8022×	body	80	nan