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

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune9.0ms (0.1%)

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: 3.9b

Counts

2 → 2

localize16.0ms (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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite116.0ms (1.2%)

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:

37.0ms	(/ (/ (/ (+ (+ (+ 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)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
9.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)

series63.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
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))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)

simplify187.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4973	23485
1	4973	23485

prune2.7s (27.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	470	7	477
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	472	7	479

Merged error: 0.3b

Counts

479 → 7

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
2.6b	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
3.6b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
3.6b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite82.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`*-un-lft-identity`
109×	`times-frac`
80×	`distribute-lft-out`
57×	`sqrt-prod`
55×	`add-sqr-sqrt`
51×	`add-cube-cbrt`
39×	`associate-/l*`
18×	`flip3-+` `flip-+`
16×	`associate-/r/`
15×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-div`
9×	`associate-/r*`
8×	`frac-times`
7×	`associate-l`
6×	`pow1`
5×	`associate-r` `div-inv` `associate-/l/`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative`

Counts

4 → 207

Calls

4 calls:

31.0ms	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
14.0ms	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
14.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
13.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series66.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
20.0ms	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 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))))

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5369	6744

prune1.7s (17%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	219	7	226

Merged error: 0.3b

Counts

226 → 7

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
0.1b	(* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
0.6b	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
3.6b	(/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite108.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`*-un-lft-identity`
68×	`distribute-lft-out`
54×	`add-exp-log` `times-frac`
36×	`add-sqr-sqrt`
35×	`associate-l`
34×	`frac-times` `add-cbrt-cube`
31×	`add-cube-cbrt`
29×	`flip3-+` `flip-+`
24×	`associate-*r/`
22×	`prod-exp`
21×	`associate-/r/`
17×	`pow1`
14×	`div-exp`
12×	`cbrt-unprod`
11×	`associate-*l/`
8×	`cbrt-undiv` `associate-/l*`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow-flip` `div-inv`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`inv-pow`

Counts

4 → 204

Calls

4 calls:

30.0ms	(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
28.0ms	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
23.0ms	(* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
16.0ms	(/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series105.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
25.0ms	(* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
22.0ms	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
16.0ms	(/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5657	6876

prune704.0ms (7.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	215	8	223

Merged error: 0.1b

Counts

223 → 8

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3)
3.6b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
3.6b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
11.6b	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3))

rewrite58.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

253×	`*-un-lft-identity`
195×	`sqrt-prod`
160×	`times-frac`
100×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
89×	`distribute-lft-out`
70×	`unpow-prod-down` `cube-prod`
20×	`associate-/r*`
10×	`add-exp-log` `cube-mult` `sqrt-div` `unpow3` `sqr-pow`
8×	`pow1` `associate-/l*`
7×	`add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`cube-div` `add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-pow1` `pow1/2` `div-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-exp` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `sqrt-pow2` `div-inv` `rem-cube-cbrt`

Counts

4 → 276

Calls

4 calls:

19.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3))
9.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms	(pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3)

series76.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3))
23.0ms	(pow (sqrt (+ alpha (+ beta (* 1.0 2.0)))) 3)
13.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
9.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5682	7892

prune2.5s (26%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	288	8	296

Merged error: 0.1b

Counts

296 → 8

regimes139.0ms (1.4%)

Accuracy

Total 1.2b remaining (91.6%)

Threshold costs 0b (0%)

bsearch20.0ms (0.2%)

Steps

Iters	Range		Point
8	1.0578060595355942e+161	3.7288831224075566e+164	1.0706985136143749e+161

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	88
1	48	88

end0.0ms (0%)

sample727.0ms (7.5%)

Algorithm

1×

intervals

Results

459.0ms	8000×	body	80	valid
132.0ms	8000×	pre	80	true

Details

analyze3.0ms (0%)

sample26.0ms (0.3%)

simplify114.0ms (1.2%)

prune9.0ms (0.1%)

localize16.0ms (0.2%)

rewrite116.0ms (1.2%)

series63.0ms (0.6%)

simplify187.0ms (1.9%)

prune2.7s (27.3%)

localize21.0ms (0.2%)

rewrite82.0ms (0.8%)

series66.0ms (0.7%)

simplify62.0ms (0.6%)

prune1.7s (17%)

localize20.0ms (0.2%)

rewrite108.0ms (1.1%)

series105.0ms (1.1%)

simplify67.0ms (0.7%)

prune704.0ms (7.2%)

localize26.0ms (0.3%)

rewrite58.0ms (0.6%)

series76.0ms (0.8%)

simplify74.0ms (0.8%)

prune2.5s (26%)

regimes139.0ms (1.4%)

bsearch20.0ms (0.2%)

simplify2.0ms (0%)

end0.0ms (0%)

sample727.0ms (7.5%)

Profiling