Details

analyze85.0ms (4.6%)

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample20.0ms (1.1%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

valid

simplify94.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4828	17
1	4828	17

prune7.0ms (0.4%)

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: 0.2b

Counts

2 → 1

localize11.0ms (0.6%)

Local error

Found 3 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite20.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1` `add-exp-log`
8×	`add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `pow-to-exp` `pow-pow` `flip3-+` `associate-r` `pow-exp` `sum-log` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`

Counts

3 → 47

Calls

3 calls:

8.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
5.0ms	(* 4.0 (* b b))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series44.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

23.0ms	(pow (+ (* a a) (* b b)) 2.0)
15.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
6.0ms	(* 4.0 (* b b))

simplify81.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5297	649

prune117.0ms (6.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	2	57

Merged error: 0b

Counts

57 → 2

localize13.0ms (0.7%)

Local error

Found 2 expressions with local error:

0.0b	(* 2 (* (* a a) (* b b)))
1.4b	(* (* a a) (* b b))

rewrite24.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`pow1`
32×	`add-exp-log` `add-cbrt-cube`
27×	`pow-prod-down`
21×	`prod-exp` `cbrt-unprod`
4×	`pow-plus` `associate-l` `pow-prod-up`
3×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`pow2` `associate-r` `pow-sqr` `*-commutative` `add-log-exp`
1×	`unswap-sqr`

Counts

2 → 56

Calls

2 calls:

13.0ms	(* 2 (* (* a a) (* b b)))
9.0ms	(* (* a a) (* b b))

series15.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(* 2 (* (* a a) (* b b)))
7.0ms	(* (* a a) (* b b))

simplify50.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5112	380

prune137.0ms (7.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	2	64

Merged error: 0b

Counts

64 → 2

localize17.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.1b	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
29.8b	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite28.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`unpow-prod-down`
20×	`cbrt-prod`
18×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cube-prod`
12×	`add-exp-log`
10×	`pow1` `add-cbrt-cube`
7×	`sqr-pow`
6×	`pow-unpow`
5×	`pow-exp`
4×	`add-log-exp`
3×	`pow-to-exp` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`pow1/3` `associate-r` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

7.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))
7.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
6.0ms	(* 4.0 (* b b))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series96.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
34.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))
22.0ms	(pow (+ (* a a) (* b b)) 2.0)
3.0ms	(* 4.0 (* b b))

simplify108.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4894	1380
1	4894	1380

prune239.0ms (12.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	110	2	112

Merged error: 0b

Counts

112 → 2

regimes136.0ms (7.3%)

Accuracy

Total 1.0b remaining (98.5%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms (0%)

sample509.0ms (27.5%)

Algorithm

1×

intervals

Results

367.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Details

analyze85.0ms (4.6%)

sample20.0ms (1.1%)

simplify94.0ms (5.1%)

prune7.0ms (0.4%)

localize11.0ms (0.6%)

rewrite20.0ms (1.1%)

series44.0ms (2.4%)

simplify81.0ms (4.4%)

prune117.0ms (6.3%)

localize13.0ms (0.7%)

rewrite24.0ms (1.3%)

series15.0ms (0.8%)

simplify50.0ms (2.7%)

prune137.0ms (7.4%)

localize17.0ms (0.9%)

rewrite28.0ms (1.5%)

series96.0ms (5.2%)

simplify108.0ms (5.8%)

prune239.0ms (12.9%)

regimes136.0ms (7.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample509.0ms (27.5%)

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