Details

analyze254.0ms (7.5%)

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

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	80	valid
5.0ms	259×	pre	80	true
0.0ms	3×	body	80	invalid

simplify512.0ms (15.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4963	13
1	4963	13

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: 0.1b

Counts

2 → 1

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite41.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

14.0ms	(* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m))
9.0ms	(/ (* m (- 1.0 m)) v)
8.0ms	(- (/ (* m (- 1.0 m)) v) 1.0)
6.0ms	(* m (- 1.0 m))

series31.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (* m (- 1.0 m)) v)
8.0ms	(* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m))
5.0ms	(- (/ (* m (- 1.0 m)) v) 1.0)
5.0ms	(* m (- 1.0 m))

simplify36.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5334	1273

prune180.0ms (5.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	5	105

Merged error: 0.0b

Counts

105 → 5

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(* m (- (pow 1.0 3) (pow m 3)))
0.1b	(* (- (/ (* m (- (pow 1.0 3) (pow m 3))) (* v (+ (* m m) (* 1.0 (+ m 1.0))))) 1.0) (- 1.0 m))
0.1b	(/ (* m (- (pow 1.0 3) (pow m 3))) (* v (+ (* m m) (* 1.0 (+ m 1.0)))))
0.1b	(* v (+ (* m m) (* 1.0 (+ m 1.0))))

rewrite74.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
33×	`associate-r`
24×	`*-un-lft-identity`
22×	`add-exp-log` `add-cbrt-cube`
18×	`difference-of-squares`
12×	`unpow-prod-down` `cube-prod`
11×	`associate-l`
10×	`pow1` `add-cube-cbrt` `associate-*r/`
8×	`flip3--` `flip--` `sqr-pow`
7×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`cbrt-undiv` `frac-times` `sub-neg` `div-exp` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`
2×	`flip3-+` `associate-*l/` `associate-/r/` `flip-+` `associate-/l/`
1×	`difference-cubes` `frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 123

Calls

4 calls:

26.0ms	(* (- (/ (* m (- (pow 1.0 3) (pow m 3))) (* v (+ (* m m) (* 1.0 (+ m 1.0))))) 1.0) (- 1.0 m))
21.0ms	(/ (* m (- (pow 1.0 3) (pow m 3))) (* v (+ (* m m) (* 1.0 (+ m 1.0)))))
16.0ms	(* m (- (pow 1.0 3) (pow m 3)))
6.0ms	(* v (+ (* m m) (* 1.0 (+ m 1.0))))

series52.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (- (/ (* m (- (pow 1.0 3) (pow m 3))) (* v (+ (* m m) (* 1.0 (+ m 1.0))))) 1.0) (- 1.0 m))
14.0ms	(/ (* m (- (pow 1.0 3) (pow m 3))) (* v (+ (* m m) (* 1.0 (+ m 1.0)))))
10.0ms	(* v (+ (* m m) (* 1.0 (+ m 1.0))))
9.0ms	(* m (- (pow 1.0 3) (pow m 3)))

simplify68.0ms (2%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4968	2615
1	4968	2615

prune381.0ms (11.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	135	5	140

Merged error: 0.0b

Counts

140 → 5

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite55.0ms (1.6%)

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:

21.0ms	(* (* (- (/ (* 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)))
7.0ms	(/ (* m (- 1.0 m)) v)
6.0ms	(* m (- 1.0 m))

series44.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (- (/ (* 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))

simplify60.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5067	2706

prune337.0ms (10%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	143	5	148

Merged error: 0.0b

Counts

148 → 5

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- 1.0 m))
0.1b	(cbrt (- 1.0 m))
0.1b	(cbrt (- 1.0 m))
0.1b	(* (cbrt (- 1.0 m)) (cbrt (- 1.0 m)))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

10.0ms	(* (cbrt (- 1.0 m)) (cbrt (- 1.0 m)))
3.0ms	(cbrt (- 1.0 m))
3.0ms	(cbrt (- 1.0 m))
3.0ms	(cbrt (- 1.0 m))

series29.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (cbrt (- 1.0 m)) (cbrt (- 1.0 m)))
6.0ms	(cbrt (- 1.0 m))
6.0ms	(cbrt (- 1.0 m))
6.0ms	(cbrt (- 1.0 m))

simplify47.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4908	1133
1	4908	1133

prune401.0ms (11.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	112	6	118

Merged error: 0b

Counts

118 → 6

regimes113.0ms (3.3%)

Accuracy

Total 0.6b remaining (96.6%)

Threshold costs 0.6b (96.6%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	27
1	49	27

end0.0ms (0%)

sample558.0ms (16.5%)

Algorithm

1×

intervals

Results

263.0ms	8000×	body	80	valid
158.0ms	8062×	pre	80	true
2.0ms	62×	body	80	invalid

Details

analyze254.0ms (7.5%)

sample24.0ms (0.7%)

simplify512.0ms (15.1%)

prune7.0ms (0.2%)

localize9.0ms (0.3%)

rewrite41.0ms (1.2%)

series31.0ms (0.9%)

simplify36.0ms (1.1%)

prune180.0ms (5.3%)

localize16.0ms (0.5%)

rewrite74.0ms (2.2%)

series52.0ms (1.5%)

simplify68.0ms (2%)

prune381.0ms (11.3%)

localize12.0ms (0.4%)

rewrite55.0ms (1.6%)

series44.0ms (1.3%)

simplify60.0ms (1.8%)

prune337.0ms (10%)

localize20.0ms (0.6%)

rewrite22.0ms (0.7%)

series29.0ms (0.9%)

simplify47.0ms (1.4%)

prune401.0ms (11.8%)

regimes113.0ms (3.3%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample558.0ms (16.5%)

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