Details

analyze71.0ms (1.5%)

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

Compiler

Compiled 18 to 10 computations (44.4% saved)

sample20.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 35 to 21 computations (40% saved)

simplify300.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	4936	25
1	4936	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

Merged error: 21.2b

Counts

2 → 1

Compiler

Compiled 34 to 18 computations (47.1% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
0.1b	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
20.9b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

rewrite69.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`frac-times_binary64_12473` `flip3-+_binary64_12466` `flip-+_binary64_12437`
31×	`add-exp-log_binary64_12501` `add-cbrt-cube_binary64_12499`
30×	`associate-*l/_binary64_12406`
27×	`*-un-lft-identity_binary64_12463`
26×	`associate-/r/_binary64_12409`
18×	`associate-*r/_binary64_12405`
15×	`pow1_binary64_12524`
13×	`prod-exp_binary64_12512` `cbrt-unprod_binary64_12496`
11×	`add-sqr-sqrt_binary64_12485`
9×	`distribute-lft-out_binary64_12414` `associate-r_binary64_12403`
8×	`add-cube-cbrt_binary64_12498`
6×	`cbrt-undiv_binary64_12497` `swap-sqr_binary64_12430` `div-exp_binary64_12514`
5×	`associate-l_binary64_12404`
4×	`pow-prod-down_binary64_12534`
3×	`add-log-exp_binary64_12502`
2×	`unswap-sqr_binary64_12431` `*-commutative_binary64_12394` `distribute-rgt-in_binary64_12413` `distribute-lft-in_binary64_12412`
1×	`clear-num_binary64_12462` `times-frac_binary64_12469` `pow-sqr_binary64_12436` `frac-2neg_binary64_12474` `pow-prod-up_binary64_12533` `pow-plus_binary64_12526` `associate-/l_binary64_12408` `pow2_binary64_12544` `div-inv_binary64_12460` `associate-/r_binary64_12407`

Counts

3 → 140

Calls

3 calls:

21.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
19.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
10.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

series299.0ms (6.1%)

Counts

3 → 9

Calls

3 calls:

213.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
58.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
28.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify95.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4957	3602
1	4957	3602

prune366.0ms (7.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	140	9	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	9	150

Merged error: 8.1b

Counts

150 → 9

Compiler

Compiled 7920 to 3907 computations (50.7% saved)

localize9.0ms (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)))
19.9b	(/.f64 x (pow.f64 (+.f64 x y) 2))

rewrite74.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64_12463`
97×	`times-frac_binary64_12469`
88×	`add-sqr-sqrt_binary64_12485`
59×	`add-cube-cbrt_binary64_12498`
36×	`add-exp-log_binary64_12501`
34×	`unpow-prod-down_binary64_12542`
31×	`associate-l_binary64_12404`
29×	`distribute-lft-out_binary64_12414`
21×	`associate-r_binary64_12403`
20×	`add-cbrt-cube_binary64_12499`
14×	`associate-/r*_binary64_12407` `div-exp_binary64_12514`
10×	`unswap-sqr_binary64_12431` `unpow2_binary64_12528` `sqr-pow_binary64_12435`
8×	`prod-exp_binary64_12512`
7×	`pow1_binary64_12524`
6×	`cbrt-undiv_binary64_12497` `associate-/l*_binary64_12408`
4×	`cbrt-unprod_binary64_12496` `associate-/r/_binary64_12409` `pow-to-exp_binary64_12532` `pow-exp_binary64_12531` `div-inv_binary64_12460` `add-log-exp_binary64_12502`
3×	`pow-unpow_binary64_12540`
2×	`clear-num_binary64_12462` `frac-2neg_binary64_12474` `flip3-+_binary64_12466` `flip-+_binary64_12437`
1×	`pow-pow_binary64_12535` `-commutative_binary64_12394` `associate-l/_binary64_12406` `pow-prod-down_binary64_12534` `frac-times_binary64_12473` `associate-*r/_binary64_12405`

Counts

4 → 195

Calls

4 calls:

34.0ms	(*.f64 (/.f64 x (pow.f64 (+.f64 x y) 2)) (/.f64 y (+.f64 (+.f64 x y) 1)))
8.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
7.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
5.0ms	(pow.f64 (+.f64 x y) 2)

series404.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(*.f64 (/.f64 x (pow.f64 (+.f64 x y) 2)) (/.f64 y (+.f64 (+.f64 x y) 1)))
95.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
59.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
29.0ms	(pow.f64 (+.f64 x y) 2)

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5312	3903

prune471.0ms (9.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	198	9	207
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	205	11	216

Merged error: 0.0b

Counts

216 → 11

Compiler

Compiled 9315 to 4968 computations (46.7% 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 x (+.f64 x y)) (+.f64 x y))
0.1b	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))

rewrite128.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

313×	`*-un-lft-identity_binary64_12463`
303×	`times-frac_binary64_12469`
163×	`add-sqr-sqrt_binary64_12485`
142×	`add-cube-cbrt_binary64_12498`
89×	`distribute-lft-out_binary64_12414`
78×	`associate-l_binary64_12404`
34×	`add-exp-log_binary64_12501` `add-cbrt-cube_binary64_12499`
28×	`associate-/r/_binary64_12409`
24×	`associate-/l*_binary64_12408`
21×	`associate-r_binary64_12403`
14×	`cbrt-undiv_binary64_12497` `flip3-+_binary64_12466` `div-inv_binary64_12460` `div-exp_binary64_12514` `flip-+_binary64_12437`
13×	`associate-/r*_binary64_12407`
6×	`prod-exp_binary64_12512` `pow1_binary64_12524` `unswap-sqr_binary64_12431` `cbrt-unprod_binary64_12496`
4×	`add-log-exp_binary64_12502`
3×	`clear-num_binary64_12462` `frac-2neg_binary64_12474`
1×	`associate-/l/_binary64_12410` `-commutative_binary64_12394` `associate-l/_binary64_12406` `pow-prod-down_binary64_12534` `frac-times_binary64_12473` `associate-*r/_binary64_12405`

Counts

4 → 310

Calls

4 calls:

53.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
12.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
8.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
6.0ms	(/.f64 x (+.f64 x y))

series414.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
94.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
56.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
52.0ms	(/.f64 x (+.f64 x y))

simplify127.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4944	7177
1	4944	7177

prune469.0ms (9.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	318	4	322
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	325	8	333

Merged error: 0b

Counts

333 → 8

Compiler

Compiled 11594 to 4295 computations (63% 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))

rewrite78.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity_binary64_12463`
62×	`times-frac_binary64_12469`
54×	`add-sqr-sqrt_binary64_12485`
42×	`add-cube-cbrt_binary64_12498`
38×	`add-exp-log_binary64_12501` `add-cbrt-cube_binary64_12499`
30×	`distribute-lft-out_binary64_12414`
21×	`associate-r_binary64_12403`
18×	`associate-l_binary64_12404`
15×	`cbrt-undiv_binary64_12497` `div-exp_binary64_12514`
13×	`associate-/r*_binary64_12407`
10×	`associate-/r/_binary64_12409`
8×	`prod-exp_binary64_12512` `cbrt-unprod_binary64_12496`
7×	`associate-/l*_binary64_12408`
6×	`pow1_binary64_12524`
5×	`flip3-+_binary64_12466` `div-inv_binary64_12460` `flip-+_binary64_12437`
4×	`unswap-sqr_binary64_12431` `add-log-exp_binary64_12502`
3×	`clear-num_binary64_12462` `associate-/l/_binary64_12410` `frac-2neg_binary64_12474`
2×	`associate-l/_binary64_12406` `frac-times_binary64_12473` `associate-r/_binary64_12405`
1×	`*-commutative_binary64_12394` `pow-prod-down_binary64_12534`

Counts

4 → 167

Calls

4 calls:

25.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
22.0ms	(/.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))
6.0ms	(/.f64 x (+.f64 x y))

series497.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))) (+.f64 x y))
159.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
61.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
53.0ms	(/.f64 x (+.f64 x y))

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4968	3322
1	4968	3322

prune168.0ms (3.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	179	8	187

Merged error: 0b

Counts

187 → 8

Compiler

Compiled 4322 to 1527 computations (64.7% saved)

regimes45.0ms (0.9%)

Compiler: Compiled 496 to 262 computations (47.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample652.0ms (13.2%)

Algorithm

1×

intervals

Results

286.0ms

8000×

body

128

valid

Compiler

Compiled 300 to 160 computations (46.7% saved)

Details

analyze71.0ms (1.5%)

sample20.0ms (0.4%)

simplify300.0ms (6.1%)

prune2.0ms (0.1%)

localize11.0ms (0.2%)

rewrite69.0ms (1.4%)

series299.0ms (6.1%)

simplify95.0ms (1.9%)

prune366.0ms (7.4%)

localize9.0ms (0.2%)

rewrite74.0ms (1.5%)

series404.0ms (8.2%)

simplify62.0ms (1.3%)

prune471.0ms (9.6%)

localize8.0ms (0.2%)

rewrite128.0ms (2.6%)

series414.0ms (8.4%)

simplify127.0ms (2.6%)

prune469.0ms (9.5%)

localize8.0ms (0.2%)

rewrite78.0ms (1.6%)

series497.0ms (10.1%)

simplify78.0ms (1.6%)

prune168.0ms (3.4%)

regimes45.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample652.0ms (13.2%)

Profiling