Details

analyze121.0ms (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
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
81.1%	18.7%	0.1%	9
81.1%	18.7%	0.1%	10
81.1%	15.6%	3.3%	11
84.3%	10.9%	4.8%	12
84.3%	10.9%	4.8%	13
84.3%	8.6%	7.2%	14

sample17.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
0.0ms	14×	body	80	invalid

simplify17.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	366	9
1	366	9

prune6.0ms (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: 0.0b

Counts

2 → 1

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(- (/ (* x y) 2.0) (/ z 8.0))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
3×	`*-un-lft-identity` `add-log-exp`
2×	`difference-of-squares`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `times-frac` `diff-log` `frac-sub` `add-cbrt-cube` `flip--` `distribute-lft-out--`

Counts

1 → 15

Calls

1 calls:

10.0ms

(- (/ (* x y) 2.0) (/ z 8.0))

series8.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

8.0ms

(- (/ (* x y) 2.0) (/ z 8.0))

simplify36.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5081	254

prune42.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	2	19

Merged error: 0.0b

Counts

19 → 2

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (* x (/ y 2.0)) (/ z 8.0))
0.1b	(sqrt (- (* x (/ y 2.0)) (/ z 8.0)))
0.1b	(sqrt (- (* x (/ y 2.0)) (/ z 8.0)))
0.3b	(* (sqrt (- (* x (/ y 2.0)) (/ z 8.0))) (sqrt (- (* x (/ y 2.0)) (/ z 8.0))))

rewrite43.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`sqrt-div`
28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
11×	`flip3--` `frac-sub` `flip--`
10×	`sqrt-pow1` `pow1/2`
9×	`frac-times`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`unswap-sqr`
3×	`pow-prod-down` `associate-*l/` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `sub-neg` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

18.0ms	(* (sqrt (- (* x (/ y 2.0)) (/ z 8.0))) (sqrt (- (* x (/ y 2.0)) (/ z 8.0))))
7.0ms	(sqrt (- (* x (/ y 2.0)) (/ z 8.0)))
7.0ms	(sqrt (- (* x (/ y 2.0)) (/ z 8.0)))
7.0ms	(- (* x (/ y 2.0)) (/ z 8.0))

series51.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (- (* x (/ y 2.0)) (/ z 8.0)))
17.0ms	(sqrt (- (* x (/ y 2.0)) (/ z 8.0)))
10.0ms	(* (sqrt (- (* x (/ y 2.0)) (/ z 8.0))) (sqrt (- (* x (/ y 2.0)) (/ z 8.0))))
7.0ms	(- (* x (/ y 2.0)) (/ z 8.0))

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4937	1926
1	4937	1926

prune238.0ms (9.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	118	4	122

Merged error: 0.0b

Counts

122 → 4

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

3.6b	(- (* x (* x (* (/ y 2.0) (/ y 2.0)))) (* (/ z 8.0) (/ z 8.0)))
5.2b	(* x (* x (* (/ y 2.0) (/ y 2.0))))
9.6b	(* x (* (/ y 2.0) (/ y 2.0)))
28.9b	(/ (- (* x (* x (* (/ y 2.0) (/ y 2.0)))) (* (/ z 8.0) (/ z 8.0))) (+ (* x (/ y 2.0)) (/ z 8.0)))

rewrite57.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`associate-*r/`
49×	`add-exp-log` `add-cbrt-cube`
24×	`prod-exp` `cbrt-unprod`
18×	`pow1` `frac-sub`
15×	`add-sqr-sqrt`
14×	`frac-times` `add-cube-cbrt` `-un-lft-identity` `associate-l/`
11×	`associate-/l/`
9×	`cbrt-undiv` `times-frac` `div-exp` `pow-prod-down`
6×	`associate-l` `add-log-exp`
3×	`associate-/r` `associate-/r/` `associate-/l`
2×	`flip3--` `associate-r` `*-commutative` `flip--`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `frac-add` `clear-num` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

20.0ms	(/ (- (* x (* x (* (/ y 2.0) (/ y 2.0)))) (* (/ z 8.0) (/ z 8.0))) (+ (* x (/ y 2.0)) (/ z 8.0)))
12.0ms	(- (* x (* x (* (/ y 2.0) (/ y 2.0)))) (* (/ z 8.0) (/ z 8.0)))
11.0ms	(* x (* x (* (/ y 2.0) (/ y 2.0))))
9.0ms	(* x (* (/ y 2.0) (/ y 2.0)))

series56.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (- (* x (* x (* (/ y 2.0) (/ y 2.0)))) (* (/ z 8.0) (/ z 8.0))) (+ (* x (/ y 2.0)) (/ z 8.0)))
18.0ms	(- (* x (* x (* (/ y 2.0) (/ y 2.0)))) (* (/ z 8.0) (/ z 8.0)))
7.0ms	(* x (* x (* (/ y 2.0) (/ y 2.0))))
7.0ms	(* x (* (/ y 2.0) (/ y 2.0)))

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4980	2275
1	4980	2275

prune275.0ms (10.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	132	4	136

Merged error: 0.0b

Counts

136 → 4

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(/ (/ z 8.0) (+ (/ z 8.0) (* x (/ y 2.0))))
0.1b	(/ x (+ (/ z 8.0) (* x (/ y 2.0))))
9.6b	(* x (* (/ y 2.0) (/ y 2.0)))
11.6b	(* (/ x (+ (/ z 8.0) (* x (/ y 2.0)))) (* x (* (/ y 2.0) (/ y 2.0))))

rewrite55.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`times-frac`
85×	`add-exp-log` `add-cbrt-cube`
63×	`add-sqr-sqrt`
62×	`add-cube-cbrt` `*-un-lft-identity`
39×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
19×	`associate-l`
18×	`pow1` `associate-*r/`
16×	`associate-/l*`
9×	`pow-prod-down` `associate-/r/`
7×	`div-inv`
6×	`frac-times` `associate-/r*`
4×	`associate-*l/` `add-log-exp`
3×	`flip3-+` `frac-add` `flip-+`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative`
1×	`associate-/l/` `unswap-sqr`

Counts

4 → 190

Calls

4 calls:

20.0ms	(* (/ x (+ (/ z 8.0) (* x (/ y 2.0)))) (* x (* (/ y 2.0) (/ y 2.0))))
10.0ms	(/ (/ z 8.0) (+ (/ z 8.0) (* x (/ y 2.0))))
8.0ms	(* x (* (/ y 2.0) (/ y 2.0)))
7.0ms	(/ x (+ (/ z 8.0) (* x (/ y 2.0))))

series63.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (/ x (+ (/ z 8.0) (* x (/ y 2.0)))) (* x (* (/ y 2.0) (/ y 2.0))))
19.0ms	(/ x (+ (/ z 8.0) (* x (/ y 2.0))))
15.0ms	(/ (/ z 8.0) (+ (/ z 8.0) (* x (/ y 2.0))))
7.0ms	(* x (* (/ y 2.0) (/ y 2.0)))

simplify58.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4984	3721
1	4984	3721

prune599.0ms (22.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	203	3	206

Merged error: 0.0b

Counts

206 → 3

regimes300.0ms (11.5%)

Accuracy

Total 0.0b remaining (70.4%)

Threshold costs 0.0b (70.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	27	9

end0.0ms (0%)

sample436.0ms (16.6%)

Algorithm

1×

intervals

Results

247.0ms	8000×	body	80	valid
14.0ms	482×	body	80	invalid

Details

analyze121.0ms (4.6%)

sample17.0ms (0.6%)

simplify17.0ms (0.6%)

prune6.0ms (0.2%)

localize6.0ms (0.2%)

rewrite10.0ms (0.4%)

series8.0ms (0.3%)

simplify36.0ms (1.4%)

prune42.0ms (1.6%)

localize9.0ms (0.3%)

rewrite43.0ms (1.6%)

series51.0ms (1.9%)

simplify47.0ms (1.8%)

prune238.0ms (9.1%)

localize13.0ms (0.5%)

rewrite57.0ms (2.2%)

series56.0ms (2.1%)

simplify47.0ms (1.8%)

prune275.0ms (10.5%)

localize14.0ms (0.5%)

rewrite55.0ms (2.1%)

series63.0ms (2.4%)

simplify58.0ms (2.2%)

prune599.0ms (22.8%)

regimes300.0ms (11.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample436.0ms (16.6%)

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