Details

analyze70.0ms (1.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	80	valid
0.0ms	8×	body	80	nan
0.0ms	5×	body	80	invalid

simplify140.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	4908	20
1	4908	20

prune10.0ms (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: 0.1b

Counts

2 → 2

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) 9.0)
0.1b	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
0.2b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

rewrite55.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

26.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
10.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
9.0ms	(* (- a (/ 1.0 3.0)) 9.0)
8.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

series35.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
12.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
5.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
3.0ms	(* (- a (/ 1.0 3.0)) 9.0)

simplify32.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5787	1905

prune289.0ms (6.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	108	7	115

Merged error: 0.0b

Counts

115 → 7

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.2b	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

rewrite138.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

441×	`times-frac`
343×	`add-sqr-sqrt`
261×	`*-un-lft-identity`
258×	`sqrt-prod`
205×	`add-cube-cbrt`
54×	`difference-of-squares`
36×	`associate-/l*`
27×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3--` `flip--`
9×	`div-inv`
7×	`pow1`
6×	`associate-l`
4×	`cbrt-undiv` `frac-times` `div-exp` `associate-r` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

4 → 355

Calls

4 calls:

76.0ms	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
20.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
9.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
7.0ms	(sqrt (- a (/ 1.0 3.0)))

series44.0ms (1%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
14.0ms	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
10.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
4.0ms	(sqrt (- a (/ 1.0 3.0)))

simplify93.0ms (2%)

Algorithm

1×	egg-herbie

Counts

367 → 367

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4988	7942
1	4988	7942

prune1.4s (31.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	366	1	367
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	367	7	374

Merged error: 0.0b

Counts

374 → 7

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ (* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0))) 1))
0.3b	(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0)))

rewrite80.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
103×	`times-frac`
78×	`*-un-lft-identity`
68×	`sqrt-prod`
54×	`add-cube-cbrt`
39×	`associate-l`
32×	`add-exp-log`
25×	`associate-r`
20×	`add-cbrt-cube`
18×	`difference-of-squares`
16×	`unswap-sqr`
11×	`pow1`
10×	`div-exp`
9×	`prod-exp` `associate-/r*` `distribute-lft-out--`
6×	`flip3--` `sqrt-div` `flip--`
5×	`cbrt-undiv` `frac-times` `cbrt-unprod`
4×	`associate-/r/` `add-log-exp`
3×	`rec-exp` `pow-flip` `flip3-+` `1-exp` `associate-r/` `associate-l/` `flip-+` `div-inv` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `clear-num` `inv-pow`

Counts

4 → 202

Calls

4 calls:

28.0ms	(* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0)))
24.0ms	(* (- a (/ 1.0 3.0)) (+ (* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0))) 1))
10.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
9.0ms	(sqrt (- a (/ 1.0 3.0)))

series41.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0)))
14.0ms	(* (- a (/ 1.0 3.0)) (+ (* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0))) 1))
4.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
4.0ms	(sqrt (- a (/ 1.0 3.0)))

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4984	3469
1	4984	3469

prune868.0ms (18.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	2	2	4
Picked	0	1	1
Done	1	1	2
Total	216	5	221

Merged error: 0b

Counts

221 → 5

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.0b	(+ (* (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt 9.0))) (- a (/ 1.0 3.0)))
0.3b	(* (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt 9.0)))

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
26×	`sqrt-prod`
24×	`times-frac`
23×	`*-un-lft-identity`
22×	`associate-r`
19×	`add-cube-cbrt`
14×	`sqrt-div`
12×	`flip3--` `flip--`
10×	`frac-add`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `frac-times` `associate-*l/` `unswap-sqr`
4×	`difference-of-squares`
3×	`associate-*r/`
2×	`prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `sub-neg` `rem-sqrt-square` `associate-+r+` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `*-commutative` `flip-+` `div-inv` `distribute-lft-out`

Counts

3 → 98

Calls

3 calls:

18.0ms	(+ (* (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt 9.0))) (- a (/ 1.0 3.0)))
17.0ms	(* (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt 9.0)))
7.0ms	(sqrt (- a (/ 1.0 3.0)))

series34.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

19.0ms	(* (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt 9.0)))
12.0ms	(+ (* (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt 9.0))) (- a (/ 1.0 3.0)))
3.0ms	(sqrt (- a (/ 1.0 3.0)))

simplify34.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5570	2228

prune283.0ms (6.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	5	112

Merged error: 0b

Counts

112 → 5

regimes141.0ms (3%)

Accuracy

Total 0.1b remaining (84.1%)

Threshold costs 0.1b (84.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	20
1	35	20

end0.0ms (0%)

sample601.0ms (13%)

Algorithm

1×

intervals

Results

437.0ms	8000×	body	80	valid
13.0ms	247×	body	80	invalid
13.0ms	262×	body	80	nan

Details

analyze70.0ms (1.5%)

sample25.0ms (0.5%)

simplify140.0ms (3%)

prune10.0ms (0.2%)

localize10.0ms (0.2%)

rewrite55.0ms (1.2%)

series35.0ms (0.8%)

simplify32.0ms (0.7%)

prune289.0ms (6.3%)

localize12.0ms (0.3%)

rewrite138.0ms (3%)

series44.0ms (1%)

simplify93.0ms (2%)

prune1.4s (31.3%)

localize15.0ms (0.3%)

rewrite80.0ms (1.7%)

series41.0ms (0.9%)

simplify68.0ms (1.5%)

prune868.0ms (18.8%)

localize10.0ms (0.2%)

rewrite46.0ms (1%)

series34.0ms (0.7%)

simplify34.0ms (0.7%)

prune283.0ms (6.1%)

regimes141.0ms (3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample601.0ms (13%)

Profiling