Details

analyze301.0ms (6.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4977	50
1	4977	50
0	2	2
1	2	2

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

Compiler

Compiled 18 to 10 computations (44.4% saved)

sample17.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 35 to 21 computations (40% saved)

simplify137.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4953	25
1	4953	25

prune2.0ms (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

Error

16.3b

Counts

2 → 1

Compiler

Compiled 34 to 18 computations (47.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
0.0b	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
16.1b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

rewrite62.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`flip3-+_binary64_12016` `flip-+_binary64_11987` `frac-times_binary64_12023`
31×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
30×	`associate-*l/_binary64_11956`
27×	`*-un-lft-identity_binary64_12013`
26×	`associate-/r/_binary64_11959`
18×	`associate-*r/_binary64_11955`
15×	`pow1_binary64_12074`
13×	`cbrt-unprod_binary64_12046` `prod-exp_binary64_12062`
11×	`add-sqr-sqrt_binary64_12035`
9×	`distribute-lft-out_binary64_11964` `associate-r_binary64_11953`
8×	`add-cube-cbrt_binary64_12048`
6×	`div-exp_binary64_12064` `swap-sqr_binary64_11980` `cbrt-undiv_binary64_12047`
5×	`associate-l_binary64_11954`
4×	`pow-prod-down_binary64_12084`
3×	`add-log-exp_binary64_12052`
2×	`distribute-lft-in_binary64_11962` `*-commutative_binary64_11944` `unswap-sqr_binary64_11981` `distribute-rgt-in_binary64_11963`
1×	`times-frac_binary64_12019` `pow-prod-up_binary64_12083` `associate-/r_binary64_11957` `pow-plus_binary64_12076` `clear-num_binary64_12012` `div-inv_binary64_12010` `pow-sqr_binary64_11986` `frac-2neg_binary64_12024` `associate-/l_binary64_11958` `pow2_binary64_12094`

Counts

3 → 140

Calls

3 calls:

19.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
17.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
9.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

series152.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

105.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
32.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
15.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify96.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5027	3629

prune168.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	143	6	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	143	7	150

Error

5.8b

Counts

150 → 7

Compiler

Compiled 4147 to 1623 computations (60.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (+.f64 (+.f64 x y) 1))
0.0b	(pow.f64 (+.f64 x y) 2)
0.1b	(*.f64 (/.f64 x (pow.f64 (+.f64 x y) 2)) (/.f64 y (+.f64 (+.f64 x y) 1)))
17.5b	(/.f64 x (pow.f64 (+.f64 x y) 2))

rewrite66.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64_12013`
97×	`times-frac_binary64_12019`
88×	`add-sqr-sqrt_binary64_12035`
59×	`add-cube-cbrt_binary64_12048`
36×	`add-exp-log_binary64_12051`
34×	`unpow-prod-down_binary64_12092`
31×	`associate-l_binary64_11954`
29×	`distribute-lft-out_binary64_11964`
21×	`associate-r_binary64_11953`
20×	`add-cbrt-cube_binary64_12049`
14×	`associate-/r*_binary64_11957` `div-exp_binary64_12064`
10×	`unswap-sqr_binary64_11981` `sqr-pow_binary64_11985` `unpow2_binary64_12078`
8×	`prod-exp_binary64_12062`
7×	`pow1_binary64_12074`
6×	`cbrt-undiv_binary64_12047` `associate-/l*_binary64_11958`
4×	`associate-/r/_binary64_11959` `add-log-exp_binary64_12052` `div-inv_binary64_12010` `pow-to-exp_binary64_12082` `cbrt-unprod_binary64_12046` `pow-exp_binary64_12081`
3×	`pow-unpow_binary64_12090`
2×	`flip3-+_binary64_12016` `clear-num_binary64_12012` `flip-+_binary64_11987` `frac-2neg_binary64_12024`
1×	`-commutative_binary64_11944` `pow-prod-down_binary64_12084` `associate-l/_binary64_11956` `pow-pow_binary64_12085` `associate-*r/_binary64_11955` `frac-times_binary64_12023`

Counts

4 → 195

Calls

4 calls:

28.0ms	(*.f64 (/.f64 x (pow.f64 (+.f64 x y) 2)) (/.f64 y (+.f64 (+.f64 x y) 1)))
7.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
7.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
4.0ms	(pow.f64 (+.f64 x y) 2)

series186.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(*.f64 (/.f64 x (pow.f64 (+.f64 x y) 2)) (/.f64 y (+.f64 (+.f64 x y) 1)))
50.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
27.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
14.0ms	(pow.f64 (+.f64 x y) 2)

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4969	3903
1	4969	3903

prune212.0ms (4.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	203	4	207
Fresh	3	2	5
Picked	0	1	1
Done	1	0	1
Total	207	7	214

Error

0.0b

Counts

214 → 7

Compiler

Compiled 4621 to 2134 computations (53.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (+.f64 (+.f64 x y) 1))
0.0b	(/.f64 x (+.f64 x y))
0.1b	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
0.1b	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))

rewrite297.0ms (6.7%)

Algorithm

1×	rewrite-expression-head

Rules

313×	`*-un-lft-identity_binary64_12013`
303×	`times-frac_binary64_12019`
163×	`add-sqr-sqrt_binary64_12035`
142×	`add-cube-cbrt_binary64_12048`
89×	`distribute-lft-out_binary64_11964`
78×	`associate-l_binary64_11954`
34×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
28×	`associate-/r/_binary64_11959`
24×	`associate-/l*_binary64_11958`
21×	`associate-r_binary64_11953`
14×	`flip3-+_binary64_12016` `div-exp_binary64_12064` `div-inv_binary64_12010` `flip-+_binary64_11987` `cbrt-undiv_binary64_12047`
13×	`associate-/r*_binary64_11957`
6×	`unswap-sqr_binary64_11981` `pow1_binary64_12074` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062`
4×	`add-log-exp_binary64_12052`
3×	`clear-num_binary64_12012` `frac-2neg_binary64_12024`
1×	`-commutative_binary64_11944` `pow-prod-down_binary64_12084` `associate-l/_binary64_11956` `associate-*r/_binary64_11955` `frac-times_binary64_12023` `associate-/l/_binary64_11960`

Counts

4 → 310

Calls

4 calls:

196.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
47.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
7.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
5.0ms	(/.f64 x (+.f64 x y))

series201.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
43.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
27.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
24.0ms	(/.f64 x (+.f64 x y))

simplify133.0ms (3%)

Algorithm

1×	egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4985	7177
1	4985	7177

prune302.0ms (6.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	318	4	322
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	322	7	329

Error

Counts

329 → 7

Compiler

Compiled 8404 to 2590 computations (69.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (+.f64 (+.f64 x y) 1))
0.0b	(/.f64 x (+.f64 x y))
0.0b	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
0.1b	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))) (+.f64 x y))

rewrite71.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity_binary64_12013`
62×	`times-frac_binary64_12019`
54×	`add-sqr-sqrt_binary64_12035`
42×	`add-cube-cbrt_binary64_12048`
38×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
30×	`distribute-lft-out_binary64_11964`
21×	`associate-r_binary64_11953`
18×	`associate-l_binary64_11954`
15×	`div-exp_binary64_12064` `cbrt-undiv_binary64_12047`
13×	`associate-/r*_binary64_11957`
10×	`associate-/r/_binary64_11959`
8×	`cbrt-unprod_binary64_12046` `prod-exp_binary64_12062`
7×	`associate-/l*_binary64_11958`
6×	`pow1_binary64_12074`
5×	`flip3-+_binary64_12016` `div-inv_binary64_12010` `flip-+_binary64_11987`
4×	`add-log-exp_binary64_12052` `unswap-sqr_binary64_11981`
3×	`clear-num_binary64_12012` `frac-2neg_binary64_12024` `associate-/l/_binary64_11960`
2×	`associate-l/_binary64_11956` `associate-r/_binary64_11955` `frac-times_binary64_12023`
1×	`*-commutative_binary64_11944` `pow-prod-down_binary64_12084`

Counts

4 → 167

Calls

4 calls:

25.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
17.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))) (+.f64 x y))
8.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
5.0ms	(/.f64 x (+.f64 x y))

series221.0ms (5%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))) (+.f64 x y))
70.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
29.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
24.0ms	(/.f64 x (+.f64 x y))

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4972	3340
1	4972	3340

prune145.0ms (3.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	179	7	186

Error

Counts

186 → 7

Compiler

Compiled 4071 to 1379 computations (66.1% saved)

regimes241.0ms (5.4%)

Accuracy

Total 0.1b remaining (91.3%)

Threshold costs 0.1b (91.3%)

Compiler

Compiled 3501 to 1946 computations (44.4% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

Compiler

Compiled 34 to 18 computations (47.1% saved)

end0.0ms (0%)

sample1.2s (27.7%)

Algorithm

1×

intervals

Results

280.0ms

8000×

body

128

valid

Compiler

Compiled 1191 to 663 computations (44.3% saved)

Details

analyze301.0ms (6.8%)

sample17.0ms (0.4%)

simplify137.0ms (3.1%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite62.0ms (1.4%)

series152.0ms (3.4%)

simplify96.0ms (2.2%)

prune168.0ms (3.8%)

localize10.0ms (0.2%)

rewrite66.0ms (1.5%)

series186.0ms (4.2%)

simplify84.0ms (1.9%)

prune212.0ms (4.8%)

localize8.0ms (0.2%)

rewrite297.0ms (6.7%)

series201.0ms (4.5%)

simplify133.0ms (3%)

prune302.0ms (6.8%)

localize8.0ms (0.2%)

rewrite71.0ms (1.6%)

series221.0ms (5%)

simplify78.0ms (1.8%)

prune145.0ms (3.3%)

regimes241.0ms (5.4%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.2s (27.7%)

Profiling