Details

analyze258.0ms (7.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

sample23.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	80	valid
5.0ms	258×	pre	80	true
0.0ms	2×	body	80	invalid

simplify505.0ms (15.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4963	13
1	4963	13

prune11.0ms (0.3%)

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: 0.1b

Counts

2 → 2

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(* m (- 1.0 m))
0.0b	(/ (* m (- 1.0 m)) v)
0.1b	(* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m))

rewrite32.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 79

Calls

3 calls:

16.0ms	(* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m))
7.0ms	(/ (* m (- 1.0 m)) v)
6.0ms	(* m (- 1.0 m))

series27.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

15.0ms	(* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m))
6.0ms	(/ (* m (- 1.0 m)) v)
5.0ms	(* m (- 1.0 m))

simplify29.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5256	1059

prune177.0ms (5.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Merged error: 0b

Counts

90 → 7

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/ v (- 1.0 m))
0.0b	(/ m (/ v (- 1.0 m)))
0.1b	(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))

rewrite55.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac`
118×	`add-sqr-sqrt`
109×	`*-un-lft-identity`
73×	`add-cube-cbrt`
26×	`associate-/r*`
20×	`difference-of-squares`
18×	`distribute-lft-out--`
12×	`add-exp-log` `add-cbrt-cube`
11×	`flip3--` `associate-/r/` `flip--`
7×	`associate-l`
6×	`div-inv` `associate-/l*`
5×	`pow1` `associate-r`
4×	`cbrt-undiv` `frac-times` `div-exp`
3×	`add-log-exp`
2×	`sub-neg` `frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 173

Calls

3 calls:

32.0ms	(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
8.0ms	(/ m (/ v (- 1.0 m)))
7.0ms	(/ v (- 1.0 m))

series19.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
6.0ms	(/ v (- 1.0 m))
5.0ms	(/ m (/ v (- 1.0 m)))

simplify58.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4981	2579
1	4981	2579

prune297.0ms (8.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	182	7	189

Merged error: 0b

Counts

189 → 7

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 m) v)
0.1b	(* (* (- (* (/ (- 1.0 m) v) m) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
0.1b	(* (- (* (/ (- 1.0 m) v) m) 1.0) (+ (sqrt 1.0) (sqrt m)))
0.3b	(* (/ (- 1.0 m) v) m)

rewrite56.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 158

Calls

4 calls:

21.0ms	(* (* (- (* (/ (- 1.0 m) v) m) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
14.0ms	(* (- (* (/ (- 1.0 m) v) m) 1.0) (+ (sqrt 1.0) (sqrt m)))
9.0ms	(* (/ (- 1.0 m) v) m)
6.0ms	(/ (- 1.0 m) v)

series44.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (* (- (* (/ (- 1.0 m) v) m) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
16.0ms	(* (- (* (/ (- 1.0 m) v) m) 1.0) (+ (sqrt 1.0) (sqrt m)))
5.0ms	(* (/ (- 1.0 m) v) m)
4.0ms	(/ (- 1.0 m) v)

simplify106.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4979	3036
1	4979	3036

prune411.0ms (12.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	171	6	177

Merged error: 0b

Counts

177 → 6

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(* m (- 1.0 m))
0.0b	(/ (* m (- 1.0 m)) v)
0.1b	(* (* (- (/ (* m (- 1.0 m)) v) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
0.1b	(* (- (/ (* m (- 1.0 m)) v) 1.0) (+ (sqrt 1.0) (sqrt m)))

rewrite58.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

22.0ms	(* (* (- (/ (* m (- 1.0 m)) v) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
16.0ms	(* (- (/ (* m (- 1.0 m)) v) 1.0) (+ (sqrt 1.0) (sqrt m)))
9.0ms	(/ (* m (- 1.0 m)) v)
6.0ms	(* m (- 1.0 m))

series40.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (- (/ (* m (- 1.0 m)) v) 1.0) (+ (sqrt 1.0) (sqrt m)))
14.0ms	(* (* (- (/ (* m (- 1.0 m)) v) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
5.0ms	(/ (* m (- 1.0 m)) v)
4.0ms	(* m (- 1.0 m))

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5067	2706

prune323.0ms (9.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	143	6	149

Merged error: 0b

Counts

149 → 6

regimes144.0ms (4.3%)

Accuracy

Total 0.1b remaining (76.5%)

Threshold costs 0.1b (76.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	13
1	28	13

end0.0ms (0%)

sample548.0ms (16.4%)

Algorithm

1×

intervals

Results

258.0ms	8000×	body	80	valid
153.0ms	8061×	pre	80	true
2.0ms	61×	body	80	invalid

Details

analyze258.0ms (7.8%)

sample23.0ms (0.7%)

simplify505.0ms (15.2%)

prune11.0ms (0.3%)

localize9.0ms (0.3%)

rewrite32.0ms (1%)

series27.0ms (0.8%)

simplify29.0ms (0.9%)

prune177.0ms (5.3%)

localize7.0ms (0.2%)

rewrite55.0ms (1.7%)

series19.0ms (0.6%)

simplify58.0ms (1.7%)

prune297.0ms (8.9%)

localize15.0ms (0.5%)

rewrite56.0ms (1.7%)

series44.0ms (1.3%)

simplify106.0ms (3.2%)

prune411.0ms (12.3%)

localize12.0ms (0.4%)

rewrite58.0ms (1.7%)

series40.0ms (1.2%)

simplify67.0ms (2%)

prune323.0ms (9.7%)

regimes144.0ms (4.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample548.0ms (16.4%)

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