Details

analyze296.0ms (13.5%)

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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
6.2%	93.6%	0.1%	6
15.6%	84.3%	0.1%	7
29.6%	70.2%	0.1%	8
33.5%	63.2%	3.3%	9
43.3%	49.5%	7.2%	10
52.1%	39.2%	8.7%	11
54.5%	34.2%	11.3%	12
60.6%	25.6%	13.8%	13
65.2%	20.4%	14.4%	14

sample16.0ms (0.7%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
0.0ms	18×	body	80	invalid

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	345	9
1	345	9

prune6.0ms (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: 0.0b

Counts

2 → 1

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(* (- 1.0 x) z)
0.0b	(+ (* x y) (* (- 1.0 x) z))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity`
5×	`associate-l`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

6.0ms	(* (- 1.0 x) z)
4.0ms	(+ (* x y) (* (- 1.0 x) z))

series12.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(+ (* x y) (* (- 1.0 x) z))
4.0ms	(* (- 1.0 x) z)

simplify39.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5197	345

prune62.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Merged error: 0b

Counts

40 → 4

localize16.0ms (0.8%)

Local error

Found 3 expressions with local error:

0.0b	(+ (* x y) (/ (* z (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))
4.3b	(* z (- (pow 1.0 3) (pow x 3)))
13.6b	(/ (* z (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))

rewrite49.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

19.0ms	(/ (* z (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
17.0ms	(* z (- (pow 1.0 3) (pow x 3)))
11.0ms	(+ (* x y) (/ (* z (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))

series67.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ (* z (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
22.0ms	(+ (* x y) (/ (* z (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))
13.0ms	(* z (- (pow 1.0 3) (pow x 3)))

simplify28.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5505	1398

prune204.0ms (9.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	89	4	93

Merged error: 0b

Counts

93 → 4

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) z)
0.0b	(sqrt (* (- 1.0 x) z))
0.0b	(sqrt (* (- 1.0 x) z))
0.3b	(* (sqrt (* (- 1.0 x) z)) (sqrt (* (- 1.0 x) z)))

rewrite33.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`pow1`
32×	`sqrt-pow1`
23×	`pow-prod-down`
20×	`associate-*l/`
16×	`add-sqr-sqrt` `sqrt-div`
12×	`*-un-lft-identity` `pow1/2`
10×	`add-cube-cbrt` `pow-prod-up`
9×	`flip3--` `associate-l` `flip--`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-r`
6×	`sqrt-prod` `pow-sqr`
4×	`frac-times` `swap-sqr` `add-log-exp`
2×	`associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 105

Calls

4 calls:

13.0ms	(* (sqrt (* (- 1.0 x) z)) (sqrt (* (- 1.0 x) z)))
8.0ms	(* (- 1.0 x) z)
5.0ms	(sqrt (* (- 1.0 x) z))
4.0ms	(sqrt (* (- 1.0 x) z))

series41.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (sqrt (* (- 1.0 x) z)) (sqrt (* (- 1.0 x) z)))
12.0ms	(sqrt (* (- 1.0 x) z))
12.0ms	(sqrt (* (- 1.0 x) z))
4.0ms	(* (- 1.0 x) z)

simplify40.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5321	865

prune193.0ms (8.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	117	4	121

Merged error: 0b

Counts

121 → 4

localize15.0ms (0.7%)

Local error

Found 4 expressions with local error:

3.5b	(* (- 1.0 x) (* z (* z (- x 1.0))))
4.8b	(* x (* x (* y y)))
7.9b	(* x (* y y))
28.0b	(/ (+ (* x (* x (* y y))) (* (- 1.0 x) (* z (* z (- x 1.0))))) (+ (* x y) (* z (- x 1.0))))

rewrite56.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

22.0ms	(* (- 1.0 x) (* z (* z (- x 1.0))))
12.0ms	(/ (+ (* x (* x (* y y))) (* (- 1.0 x) (* z (* z (- x 1.0))))) (+ (* x y) (* z (- x 1.0))))
10.0ms	(* x (* x (* y y)))
5.0ms	(* x (* y y))

series79.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (+ (* x (* x (* y y))) (* (- 1.0 x) (* z (* z (- x 1.0))))) (+ (* x y) (* z (- x 1.0))))
8.0ms	(* (- 1.0 x) (* z (* z (- x 1.0))))
6.0ms	(* x (* y y))
6.0ms	(* x (* x (* y y)))

simplify60.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5003	2197

prune193.0ms (8.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	122	4	126

Merged error: 0b

Counts

126 → 4

regimes187.0ms (8.6%)

Accuracy

Total 0.0b remaining (53.3%)

Threshold costs 0.0b (53.3%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms (0%)

sample453.0ms (20.7%)

Algorithm

1×

intervals

Results

245.0ms	8000×	body	80	valid
19.0ms	639×	body	80	invalid

Details

analyze296.0ms (13.5%)

sample16.0ms (0.7%)

simplify13.0ms (0.6%)

prune6.0ms (0.3%)

localize6.0ms (0.3%)

rewrite10.0ms (0.5%)

series12.0ms (0.5%)

simplify39.0ms (1.8%)

prune62.0ms (2.8%)

localize16.0ms (0.8%)

rewrite49.0ms (2.2%)

series67.0ms (3.1%)

simplify28.0ms (1.3%)

prune204.0ms (9.3%)

localize8.0ms (0.4%)

rewrite33.0ms (1.5%)

series41.0ms (1.9%)

simplify40.0ms (1.8%)

prune193.0ms (8.9%)

localize15.0ms (0.7%)

rewrite56.0ms (2.6%)

series79.0ms (3.6%)

simplify60.0ms (2.8%)

prune193.0ms (8.8%)

regimes187.0ms (8.6%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample453.0ms (20.7%)

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