Details

analyze81.0ms (2.7%)

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
12.5%	87.4%	0.1%	5
46.8%	53.1%	0.1%	6
70.2%	29.7%	0.1%	7
76.5%	23.4%	0.1%	8
83.5%	16.4%	0.1%	9
87%	12.9%	0.1%	10
91.1%	8.8%	0.1%	11
93.2%	6.7%	0.1%	12
95.4%	4.5%	0.1%	13
96.5%	3.4%	0.1%	14

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

valid

simplify54.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5284	17

prune5.0ms (0.2%)

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: 18.6b

Counts

2 → 1

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(* (+ x y) (+ x y))
0.1b	(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
18.3b	(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

rewrite46.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`frac-times` `flip3-+` `flip-+`
31×	`add-exp-log` `add-cbrt-cube`
30×	`associate-*l/`
27×	`*-un-lft-identity`
26×	`associate-/r/`
18×	`associate-*r/`
15×	`pow1`
13×	`prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`associate-r` `distribute-lft-out`
8×	`add-cube-cbrt`
6×	`cbrt-undiv` `swap-sqr` `div-exp`
5×	`associate-l`
4×	`pow-prod-down`
3×	`add-log-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `unswap-sqr`
1×	`pow2` `frac-2neg` `times-frac` `pow-plus` `clear-num` `associate-/r` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l`

Counts

3 → 140

Calls

3 calls:

17.0ms	(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))
15.0ms	(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
8.0ms	(* (+ x y) (+ x y))

series33.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))
8.0ms	(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
3.0ms	(* (+ x y) (+ x y))

simplify61.0ms (2%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5000	2686

prune298.0ms (10%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	136	13	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	136	14	150

Merged error: 8.1b

Counts

150 → 14

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.7b	(pow (cbrt (+ x y)) 4)
18.3b	(/ (* x y) (* (* (pow (cbrt (+ x y)) 4) (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (+ x y) 1.0)))

rewrite40.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-exp-log`
40×	`cbrt-div` `prod-exp`
32×	`associate-*r/` `add-cbrt-cube`
29×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`associate-/r/`
16×	`div-exp` `cbrt-unprod`
15×	`*-un-lft-identity`
14×	`associate-*l/`
12×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`cbrt-undiv`
7×	`unpow-prod-down`
5×	`pow1` `pow-to-exp` `pow-exp`
4×	`add-log-exp`
3×	`pow-unpow` `pow1/3` `distribute-lft-out`
2×	`pow-pow`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

25.0ms	(/ (* x y) (* (* (pow (cbrt (+ x y)) 4) (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (+ x y) 1.0)))
4.0ms	(pow (cbrt (+ x y)) 4)
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))

series148.0ms (5%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (cbrt (+ x y)) 4)
32.0ms	(cbrt (+ x y))
30.0ms	(cbrt (+ x y))
22.0ms	(/ (* x y) (* (* (pow (cbrt (+ x y)) 4) (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (+ x y) 1.0)))

simplify81.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4954	1968
1	4954	1968

prune271.0ms (9.1%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	119	20	139

Merged error: 5.7b

Counts

139 → 20

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (pow (cbrt (+ x y)) 6)) (/ y (+ (+ x y) 1.0)))
0.6b	(cbrt (+ x y))
0.6b	(pow (cbrt (+ x y)) 6)
18.4b	(/ x (pow (cbrt (+ x y)) 6))

rewrite49.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity`
94×	`times-frac`
93×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
60×	`unpow-prod-down`
38×	`cbrt-prod`
37×	`associate-l`
34×	`add-exp-log`
21×	`associate-r`
18×	`add-cbrt-cube` `distribute-lft-out`
13×	`div-exp`
11×	`associate-/r*`
10×	`unswap-sqr` `sqr-pow`
8×	`prod-exp`
7×	`pow1`
5×	`cbrt-undiv`
4×	`pow-to-exp` `pow-exp` `cbrt-unprod` `add-log-exp`
3×	`pow-unpow` `div-inv` `associate-/l*`
2×	`cbrt-div` `pow-pow` `flip3-+` `pow1/3` `associate-/r/` `flip-+`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 189

Calls

4 calls:

27.0ms	(* (/ x (pow (cbrt (+ x y)) 6)) (/ y (+ (+ x y) 1.0)))
7.0ms	(/ x (pow (cbrt (+ x y)) 6))
4.0ms	(pow (cbrt (+ x y)) 6)
3.0ms	(cbrt (+ x y))

series113.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(pow (cbrt (+ x y)) 6)
33.0ms	(cbrt (+ x y))
22.0ms	(* (/ x (pow (cbrt (+ x y)) 6)) (/ y (+ (+ x y) 1.0)))
12.0ms	(/ x (pow (cbrt (+ x y)) 6))

simplify54.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5020	2674

prune559.0ms (18.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	189	12	201
Fresh	16	1	17
Picked	1	0	1
Done	1	1	2
Total	207	14	221

Merged error: 0.0b

Counts

221 → 14

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/ y (+ (+ x y) 1.0))
0.0b	(/ 1 (+ x y))
0.1b	(* (/ 1 (+ x y)) (/ x (+ x y)))
0.1b	(* (* (/ 1 (+ x y)) (/ x (+ x y))) (/ y (+ (+ x y) 1.0)))

rewrite58.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`add-exp-log` `*-un-lft-identity`
73×	`times-frac`
65×	`add-sqr-sqrt`
61×	`add-cbrt-cube`
48×	`add-cube-cbrt`
42×	`prod-exp`
39×	`associate-r`
36×	`div-exp`
31×	`distribute-lft-out`
22×	`cbrt-unprod`
19×	`cbrt-undiv` `associate-l`
12×	`pow1`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`rec-exp` `1-exp`
6×	`frac-times` `associate-l/` `associate-/l` `unswap-sqr`
5×	`flip3-+` `flip-+` `div-inv`
4×	`associate-*r/` `pow-prod-down` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `inv-pow`

Counts

4 → 207

Calls

4 calls:

19.0ms	(* (* (/ 1 (+ x y)) (/ x (+ x y))) (/ y (+ (+ x y) 1.0)))
18.0ms	(* (/ 1 (+ x y)) (/ x (+ x y)))
7.0ms	(/ y (+ (+ x y) 1.0))
5.0ms	(/ 1 (+ x y))

series37.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (* (/ 1 (+ x y)) (/ x (+ x y))) (/ y (+ (+ x y) 1.0)))
9.0ms	(* (/ 1 (+ x y)) (/ x (+ x y)))
6.0ms	(/ y (+ (+ x y) 1.0))
4.0ms	(/ 1 (+ x y))

simplify70.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5010	2595

prune277.0ms (9.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	8	4	12
Picked	1	0	1
Done	0	1	1
Total	222	11	233

Merged error: 0b

Counts

233 → 11

regimes177.0ms (6%)

Accuracy

Total 0.1b remaining (84%)

Threshold costs 0.1b (84%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	12	17

end0.0ms (0%)

sample399.0ms (13.4%)

Algorithm

1×

intervals

Results

275.0ms

8000×

body

valid

Details

analyze81.0ms (2.7%)

sample19.0ms (0.6%)

simplify54.0ms (1.8%)

prune5.0ms (0.2%)

localize8.0ms (0.3%)

rewrite46.0ms (1.5%)

series33.0ms (1.1%)

simplify61.0ms (2%)

prune298.0ms (10%)

localize15.0ms (0.5%)

rewrite40.0ms (1.4%)

series148.0ms (5%)

simplify81.0ms (2.7%)

prune271.0ms (9.1%)

localize10.0ms (0.3%)

rewrite49.0ms (1.7%)

series113.0ms (3.8%)

simplify54.0ms (1.8%)

prune559.0ms (18.8%)

localize9.0ms (0.3%)

rewrite58.0ms (2%)

series37.0ms (1.3%)

simplify70.0ms (2.3%)

prune277.0ms (9.3%)

regimes177.0ms (6%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample399.0ms (13.4%)

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