Details

analyze114.0ms (2.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

sample27.0ms (0.7%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	80	valid
0.0ms	1×	body	80	nan

simplify38.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5222	28

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.4b

Counts

2 → 1

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(* 5.0 (* v v))
0.2b	(* PI t)
0.3b	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
0.5b	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*r/`
16×	`pow1`
13×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`flip3--` `sqrt-div` `associate-r` `associate-/r/` `flip--`
7×	`associate-l` `pow-prod-down`
4×	`cbrt-undiv` `frac-times` `div-exp` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`associate-*l/` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `sqrt-prod` `div-inv`

Counts

4 → 94

Calls

4 calls:

16.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
10.0ms	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
5.0ms	(* 5.0 (* v v))
3.0ms	(* PI t)

series72.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
21.0ms	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
3.0ms	(* 5.0 (* v v))
2.0ms	(* PI t)

simplify72.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4981	1908
1	4981	1908

prune295.0ms (7.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 0.1b

Counts

107 → 10

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(* 5.0 (* v v))
0.3b	(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
0.4b	(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.4b	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite44.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log` `associate-*r/` `add-cbrt-cube`
16×	`pow1`
13×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
9×	`flip3--` `associate-l` `flip--`
8×	`associate-/r/`
7×	`pow-prod-down`
6×	`associate-r`
4×	`cbrt-undiv` `frac-times` `div-exp` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`associate-*l/` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `sqrt-prod` `div-inv`

Counts

4 → 96

Calls

4 calls:

16.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
11.0ms	(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
8.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
5.0ms	(* 5.0 (* v v))

series88.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
21.0ms	(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
19.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
3.0ms	(* 5.0 (* v v))

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5016	2144

prune286.0ms (7.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	109	9	118

Merged error: 0.1b

Counts

118 → 9

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(* (* v v) 5.0)
0.3b	(/ 1 (/ (* (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) PI) (/ (- 1.0 (* (* v v) 5.0)) (- 1.0 (* v v)))))
0.4b	(* (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) PI)
0.4b	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite53.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

189×	`times-frac`
89×	`add-exp-log`
83×	`add-sqr-sqrt`
68×	`add-cube-cbrt` `*-un-lft-identity`
45×	`add-cbrt-cube`
41×	`div-exp`
25×	`prod-exp`
23×	`associate-/r*`
17×	`pow1`
16×	`cbrt-undiv`
13×	`associate-/r/` `cbrt-unprod`
12×	`difference-of-squares`
10×	`associate-r`
9×	`div-inv`
8×	`associate-*r/`
7×	`rec-exp` `1-exp` `pow-prod-down`
6×	`flip3--` `flip--`
5×	`associate-l`
4×	`sqrt-div` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`associate-*l/` `unswap-sqr`
1×	`pow-flip` `frac-2neg` `clear-num` `sqrt-prod` `inv-pow`

Counts

4 → 196

Calls

4 calls:

17.0ms	(/ 1 (/ (* (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) PI) (/ (- 1.0 (* (* v v) 5.0)) (- 1.0 (* v v)))))
9.0ms	(* (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) PI)
8.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
8.0ms	(* (* v v) 5.0)

series116.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ 1 (/ (* (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) PI) (/ (- 1.0 (* (* v v) 5.0)) (- 1.0 (* v v)))))
22.0ms	(* (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) PI)
20.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
3.0ms	(* (* v v) 5.0)

simplify74.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4983	6189
1	4983	6189

prune936.0ms (23.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	204	4	208
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	207	10	217

Merged error: 0.0b

Counts

217 → 10

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(* (* v v) 5.0)
0.3b	(/ 1 (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.4b	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
0.4b	(* (/ 1 (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (/ (- 1.0 (* (* v v) 5.0)) (* PI (- 1.0 (* v v)))))

rewrite48.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`add-exp-log`
52×	`add-cbrt-cube`
44×	`prod-exp`
30×	`div-exp`
20×	`cbrt-unprod`
18×	`add-sqr-sqrt`
16×	`pow1` `associate-r`
15×	`associate-*r/`
14×	`cbrt-undiv`
13×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
9×	`times-frac`
8×	`rec-exp` `1-exp`
6×	`sqrt-div` `pow-prod-down` `associate-/r/`
4×	`flip3--` `flip--` `add-log-exp`
3×	`-commutative` `div-inv` `associate-/l` `unswap-sqr`
2×	`pow-flip`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `sqrt-prod` `inv-pow`

Counts

4 → 131

Calls

4 calls:

20.0ms	(* (/ 1 (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (/ (- 1.0 (* (* v v) 5.0)) (* PI (- 1.0 (* v v)))))
9.0ms	(/ 1 (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
8.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
6.0ms	(* (* v v) 5.0)

series121.0ms (3%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (/ 1 (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (/ (- 1.0 (* (* v v) 5.0)) (* PI (- 1.0 (* v v)))))
29.0ms	(/ 1 (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
20.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
3.0ms	(* (* v v) 5.0)

simplify56.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5084	2841

prune371.0ms (9.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	137	6	143
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	145	8	153

Merged error: 0b

Counts

153 → 8

regimes286.0ms (7.2%)

Accuracy

Total 0.3b remaining (95.7%)

Threshold costs 0.3b (95.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	30
1	80	30

end0.0ms (0%)

sample713.0ms (17.9%)

Algorithm

1×

intervals

Results

558.0ms	8000×	body	80	valid
1.0ms	9×	body	80	nan

Details

analyze114.0ms (2.9%)

sample27.0ms (0.7%)

simplify38.0ms (0.9%)

prune7.0ms (0.2%)

localize20.0ms (0.5%)

rewrite38.0ms (1%)

series72.0ms (1.8%)

simplify72.0ms (1.8%)

prune295.0ms (7.4%)

localize16.0ms (0.4%)

rewrite44.0ms (1.1%)

series88.0ms (2.2%)

simplify57.0ms (1.4%)

prune286.0ms (7.2%)

localize18.0ms (0.4%)

rewrite53.0ms (1.3%)

series116.0ms (2.9%)

simplify74.0ms (1.9%)

prune936.0ms (23.5%)

localize21.0ms (0.5%)

rewrite48.0ms (1.2%)

series121.0ms (3%)

simplify56.0ms (1.4%)

prune371.0ms (9.3%)

regimes286.0ms (7.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample713.0ms (17.9%)

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