Details

analyze258.0ms (15.4%)

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
36.7%	60.8%	2.5%	9
43.3%	49.9%	6.8%	10
49.7%	40.8%	9.5%	11
58.2%	30.4%	11.4%	12
61.3%	24.7%	14%	13
65%	19.9%	15.1%	14

sample14.0ms (0.9%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	80	valid
0.0ms	19×	body	80	invalid

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	7
1	51	7

prune5.0ms (0.3%)

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: 0.0b

Counts

2 → 1

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite12.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 36

Calls

2 calls:

5.0ms	(+ x (* y (+ z x)))
5.0ms	(* y (+ z x))

series12.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(+ x (* y (+ z x)))
6.0ms	(* y (+ z x))

simplify53.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4950	318
1	4950	318

prune62.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	5	43

Merged error: 0b

Counts

43 → 5

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

rewrite8.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`sum-log`
2×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `flip-+`
1×	`associate-+l+`

Counts

2 → 24

Calls

2 calls:

5.0ms	(+ (+ x (* y z)) (* y x))
3.0ms	(+ x (* y z))

series13.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(+ (+ x (* y z)) (* y x))
6.0ms	(+ x (* y z))

simplify31.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5063	269

prune45.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	30	5	35

Merged error: 0b

Counts

35 → 5

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(* y (+ x z))
0.0b	(+ x (cbrt (pow (* y (+ x z)) 3)))
0.3b	(pow (* y (+ x z)) 3)
32.1b	(cbrt (pow (* y (+ x z)) 3))

rewrite20.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`associate-*r/` `add-log-exp`
4×	`cube-div` `flip3-+` `associate-r` `flip-+`
3×	`pow-unpow` `associate-l`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/3` `sum-log` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

6.0ms	(* y (+ x z))
6.0ms	(pow (* y (+ x z)) 3)
4.0ms	(+ x (cbrt (pow (* y (+ x z)) 3)))
2.0ms	(cbrt (pow (* y (+ x z)) 3))

series32.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow (* y (+ x z)) 3)
9.0ms	(+ x (cbrt (pow (* y (+ x z)) 3)))
6.0ms	(cbrt (pow (* y (+ x z)) 3))
6.0ms	(* y (+ x z))

simplify22.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5088	725

prune130.0ms (7.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	90	5	95

Merged error: 0b

Counts

95 → 5

localize12.0ms (0.7%)

Local error

Found 4 expressions with local error:

4.0b	(- (* x x) (* y (* y (* (+ x z) (+ x z)))))
5.3b	(* y (* y (* (+ x z) (+ x z))))
9.3b	(* y (* (+ x z) (+ x z)))
24.9b	(/ (- (* x x) (* y (* y (* (+ x z) (+ x z))))) (- x (* y (+ x z))))

rewrite41.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

13.0ms	(* y (* y (* (+ x z) (+ x z))))
10.0ms	(* y (* (+ x z) (+ x z)))
7.0ms	(/ (- (* x x) (* y (* y (* (+ x z) (+ x z))))) (- x (* y (+ x z))))
5.0ms	(- (* x x) (* y (* y (* (+ x z) (+ x z)))))

series80.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (- (* x x) (* y (* y (* (+ x z) (+ x z))))) (- x (* y (+ x z))))
22.0ms	(- (* x x) (* y (* y (* (+ x z) (+ x z)))))
8.0ms	(* y (* y (* (+ x z) (+ x z))))
8.0ms	(* y (* (+ x z) (+ x z)))

simplify64.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4999	2130
1	4999	2130

prune142.0ms (8.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	131	5	136

Merged error: 0b

Counts

136 → 5

regimes202.0ms (12%)

Accuracy

Total 0.0b remaining (60.5%)

Threshold costs 0.0b (60.5%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	7
1	9	7

end0.0ms (0%)

sample391.0ms (23.4%)

Algorithm

1×

intervals

Results

195.0ms	8000×	body	80	valid
18.0ms	619×	body	80	invalid

Details

analyze258.0ms (15.4%)

sample14.0ms (0.9%)

simplify4.0ms (0.2%)

prune5.0ms (0.3%)

localize5.0ms (0.3%)

rewrite12.0ms (0.7%)

series12.0ms (0.7%)

simplify53.0ms (3.2%)

prune62.0ms (3.7%)

localize6.0ms (0.4%)

rewrite8.0ms (0.5%)

series13.0ms (0.8%)

simplify31.0ms (1.8%)

prune45.0ms (2.7%)

localize9.0ms (0.5%)

rewrite20.0ms (1.2%)

series32.0ms (1.9%)

simplify22.0ms (1.3%)

prune130.0ms (7.8%)

localize12.0ms (0.7%)

rewrite41.0ms (2.4%)

series80.0ms (4.8%)

simplify64.0ms (3.8%)

prune142.0ms (8.5%)

regimes202.0ms (12%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample391.0ms (23.4%)

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