Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

sample26.0ms (0.3%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify137.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune6.0ms (0.1%)

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: 2.9b

Counts

2 → 1

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite115.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

39.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
8.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)

series59.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
21.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)

simplify157.0ms (2%)

Algorithm

1×	egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4973	23485
1	4973	23485

prune3.0s (39.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	467	10	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	468	10	478

Merged error: 1.1b

Counts

478 → 10

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 1.0 2.0)))
0.0b	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 1.0 2.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 1.0 2.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.7b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 1.0 2.0))))

rewrite82.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`times-frac`
65×	`*-un-lft-identity`
54×	`add-exp-log`
49×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
34×	`add-cbrt-cube`
24×	`div-exp`
18×	`associate-/r/`
15×	`associate-r`
14×	`cbrt-undiv`
13×	`flip3-+` `flip-+` `associate-/l*`
12×	`prod-exp`
11×	`distribute-lft-out`
10×	`associate-/r*`
9×	`div-inv`
7×	`pow1` `associate-/l/`
6×	`cbrt-unprod`
4×	`frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `add-log-exp`
3×	`frac-2neg` `clear-num` `unswap-sqr`
2×	`associate-*r/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 181

Calls

4 calls:

27.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 1.0 2.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
21.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 1.0 2.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
18.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 1.0 2.0))))
7.0ms	(/ 1 (+ (+ alpha beta) (* 1.0 2.0)))

series60.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 1.0 2.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
20.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 1.0 2.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
12.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 1.0 2.0))))
5.0ms	(/ 1 (+ (+ alpha beta) (* 1.0 2.0)))

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5351	5555

prune531.0ms (6.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	193	10	203

Merged error: 1.1b

Counts

203 → 10

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0)) (+ (+ alpha beta) (* 1.0 2.0)))
0.2b	(* (sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0)) (+ (+ alpha beta) (* 1.0 2.0))))
2.6b	(sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0))
2.6b	(sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0))

rewrite60.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
46×	`times-frac`
45×	`sqrt-prod`
38×	`add-cube-cbrt`
27×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div` `distribute-lft-out`
8×	`pow1`
7×	`flip3-+` `associate-l` `flip-+` `associate-/l*`
6×	`unswap-sqr`
4×	`associate-/r/` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 137

Calls

4 calls:

26.0ms	(* (sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0)) (+ (+ alpha beta) (* 1.0 2.0))))
15.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0)) (+ (+ alpha beta) (* 1.0 2.0)))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0))

series79.0ms (1%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0)) (+ (+ alpha beta) (* 1.0 2.0)))
14.0ms	(sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0))
12.0ms	(* (sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0)) (+ (+ alpha beta) (* 1.0 2.0))))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* alpha beta)) 1.0))

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4994	3486
1	4994	3486

prune482.0ms (6.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	149	10	159

Merged error: 1.1b

Counts

159 → 10

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))) (cbrt (/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))))
2.7b	(/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))
2.7b	(/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))
2.7b	(/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))

rewrite86.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

137×	`*-un-lft-identity`
102×	`times-frac`
96×	`cbrt-prod`
95×	`add-sqr-sqrt`
71×	`add-cube-cbrt`
30×	`distribute-lft-out`
27×	`swap-sqr`
21×	`associate-r` `associate-l`
14×	`associate-/r/`
12×	`add-exp-log` `associate-/l*`
11×	`pow1`
10×	`flip3-+` `add-cbrt-cube` `flip-+`
9×	`associate-/r*` `unswap-sqr`
7×	`div-inv`
6×	`pow1/3` `associate-/l/`
4×	`cbrt-div` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 204

Calls

4 calls:

33.0ms	(* (cbrt (/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))) (cbrt (/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))))
16.0ms	(/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))

series83.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cbrt (/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))) (cbrt (/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))))
16.0ms	(/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* alpha beta)) 1.0) (+ (+ alpha beta) (* 1.0 2.0)))

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4963	6843
1	4963	6843

prune1.6s (20.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	216	10	226

Merged error: 1.1b

Counts

226 → 10

regimes141.0ms (1.8%)

Accuracy

Total 1.0b remaining (48.7%)

Threshold costs 0b (0%)

bsearch17.0ms (0.2%)

Steps

Iters	Range		Point
8	2.856170016854068e+195	3.85392169788566e+198	6.064453308972152e+195

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	42
1	28	42

end0.0ms (0%)

sample719.0ms (9.3%)

Algorithm

1×

intervals

Results

457.0ms	8000×	body	80	valid
129.0ms	8000×	pre	80	true

Details

analyze3.0ms (0%)

sample26.0ms (0.3%)

simplify137.0ms (1.8%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite115.0ms (1.5%)

series59.0ms (0.8%)

simplify157.0ms (2%)

prune3.0s (39.5%)

localize18.0ms (0.2%)

rewrite82.0ms (1.1%)

series60.0ms (0.8%)

simplify56.0ms (0.7%)

prune531.0ms (6.9%)

localize19.0ms (0.3%)

rewrite60.0ms (0.8%)

series79.0ms (1%)

simplify55.0ms (0.7%)

prune482.0ms (6.3%)

localize19.0ms (0.2%)

rewrite86.0ms (1.1%)

series83.0ms (1.1%)

simplify82.0ms (1.1%)

prune1.6s (20.2%)

regimes141.0ms (1.8%)

bsearch17.0ms (0.2%)

simplify1.0ms (0%)

end0.0ms (0%)

sample719.0ms (9.3%)

Profiling