Details

analyze77.0ms (1.8%)

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)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 35 to 21 computations (40% saved)

simplify291.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

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)

localize8.0ms (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)))

rewrite72.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`flip3-+_binary64_6483` `frac-times_binary64_6490` `flip-+_binary64_6454`
31×	`add-exp-log_binary64_6515` `add-cbrt-cube_binary64_6513`
30×	`associate-*l/_binary64_6425`
27×	`*-un-lft-identity_binary64_6480`
26×	`associate-/r/_binary64_6428`
18×	`associate-*r/_binary64_6424`
15×	`pow1_binary64_6538`
13×	`prod-exp_binary64_6526` `cbrt-unprod_binary64_6510`
11×	`add-sqr-sqrt_binary64_6501`
9×	`associate-r_binary64_6422` `distribute-lft-out_binary64_6433`
8×	`add-cube-cbrt_binary64_6512`
6×	`cbrt-undiv_binary64_6511` `div-exp_binary64_6528` `swap-sqr_binary64_6447`
5×	`associate-l_binary64_6423`
4×	`pow-prod-down_binary64_6548`
3×	`add-log-exp_binary64_6516`
2×	`unswap-sqr_binary64_6448` `distribute-lft-in_binary64_6431` `distribute-rgt-in_binary64_6432` `*-commutative_binary64_6413`
1×	`div-inv_binary64_6477` `clear-num_binary64_6479` `associate-/r_binary64_6426` `associate-/l_binary64_6427` `pow-prod-up_binary64_6547` `frac-2neg_binary64_6491` `pow-plus_binary64_6540` `pow2_binary64_6558` `times-frac_binary64_6486` `pow-sqr_binary64_6453`

Counts

3 → 140

Calls

3 calls:

24.0ms	(/.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))
9.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

series299.0ms (7%)

Counts

3 → 9

Calls

3 calls:

214.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
60.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
25.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify89.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4962	3602
1	4962	3602

prune176.0ms (4.1%)

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 4183 to 1657 computations (60.4% 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)))
19.9b	(/.f64 x (pow.f64 (+.f64 x y) 2))

rewrite75.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64_6480`
97×	`times-frac_binary64_6486`
88×	`add-sqr-sqrt_binary64_6501`
59×	`add-cube-cbrt_binary64_6512`
36×	`add-exp-log_binary64_6515`
34×	`unpow-prod-down_binary64_6556`
31×	`associate-l_binary64_6423`
29×	`distribute-lft-out_binary64_6433`
21×	`associate-r_binary64_6422`
20×	`add-cbrt-cube_binary64_6513`
14×	`associate-/r*_binary64_6426` `div-exp_binary64_6528`
10×	`sqr-pow_binary64_6452` `unswap-sqr_binary64_6448` `unpow2_binary64_6542`
8×	`prod-exp_binary64_6526`
7×	`pow1_binary64_6538`
6×	`cbrt-undiv_binary64_6511` `associate-/l*_binary64_6427`
4×	`div-inv_binary64_6477` `pow-exp_binary64_6545` `associate-/r/_binary64_6428` `cbrt-unprod_binary64_6510` `add-log-exp_binary64_6516` `pow-to-exp_binary64_6546`
3×	`pow-unpow_binary64_6554`
2×	`flip3-+_binary64_6483` `clear-num_binary64_6479` `frac-2neg_binary64_6491` `flip-+_binary64_6454`
1×	`pow-pow_binary64_6549` `pow-prod-down_binary64_6548` `associate-r/_binary64_6424` `frac-times_binary64_6490` `associate-l/_binary64_6425` `*-commutative_binary64_6413`

Counts

4 → 195

Calls

4 calls:

29.0ms	(*.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))
8.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
5.0ms	(pow.f64 (+.f64 x y) 2)

series397.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(*.f64 (/.f64 x (pow.f64 (+.f64 x y) 2)) (/.f64 y (+.f64 (+.f64 x y) 1)))
90.0ms	(/.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)

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5307	3903

prune221.0ms (5.2%)

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 4723 to 2193 computations (53.6% 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)))

rewrite120.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

313×	`*-un-lft-identity_binary64_6480`
303×	`times-frac_binary64_6486`
163×	`add-sqr-sqrt_binary64_6501`
142×	`add-cube-cbrt_binary64_6512`
89×	`distribute-lft-out_binary64_6433`
78×	`associate-l_binary64_6423`
34×	`add-exp-log_binary64_6515` `add-cbrt-cube_binary64_6513`
28×	`associate-/r/_binary64_6428`
24×	`associate-/l*_binary64_6427`
21×	`associate-r_binary64_6422`
14×	`div-inv_binary64_6477` `flip3-+_binary64_6483` `cbrt-undiv_binary64_6511` `div-exp_binary64_6528` `flip-+_binary64_6454`
13×	`associate-/r*_binary64_6426`
6×	`unswap-sqr_binary64_6448` `prod-exp_binary64_6526` `pow1_binary64_6538` `cbrt-unprod_binary64_6510`
4×	`add-log-exp_binary64_6516`
3×	`clear-num_binary64_6479` `frac-2neg_binary64_6491`
1×	`associate-/l/_binary64_6429` `pow-prod-down_binary64_6548` `associate-r/_binary64_6424` `frac-times_binary64_6490` `associate-l/_binary64_6425` `*-commutative_binary64_6413`

Counts

4 → 310

Calls

4 calls:

49.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
13.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
11.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
6.0ms	(/.f64 x (+.f64 x y))

series416.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
92.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
56.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
51.0ms	(/.f64 x (+.f64 x y))

simplify131.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4946	7177
1	4946	7177

prune317.0ms (7.4%)

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 8506 to 2657 computations (68.8% saved)

localize9.0ms (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))

rewrite79.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity_binary64_6480`
62×	`times-frac_binary64_6486`
54×	`add-sqr-sqrt_binary64_6501`
42×	`add-cube-cbrt_binary64_6512`
38×	`add-exp-log_binary64_6515` `add-cbrt-cube_binary64_6513`
30×	`distribute-lft-out_binary64_6433`
21×	`associate-r_binary64_6422`
18×	`associate-l_binary64_6423`
15×	`cbrt-undiv_binary64_6511` `div-exp_binary64_6528`
13×	`associate-/r*_binary64_6426`
10×	`associate-/r/_binary64_6428`
8×	`prod-exp_binary64_6526` `cbrt-unprod_binary64_6510`
7×	`associate-/l*_binary64_6427`
6×	`pow1_binary64_6538`
5×	`div-inv_binary64_6477` `flip3-+_binary64_6483` `flip-+_binary64_6454`
4×	`unswap-sqr_binary64_6448` `add-log-exp_binary64_6516`
3×	`clear-num_binary64_6479` `associate-/l/_binary64_6429` `frac-2neg_binary64_6491`
2×	`associate-r/_binary64_6424` `frac-times_binary64_6490` `associate-l/_binary64_6425`
1×	`pow-prod-down_binary64_6548` `*-commutative_binary64_6413`

Counts

4 → 167

Calls

4 calls:

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

series458.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))) (+.f64 x y))
150.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
55.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
49.0ms	(/.f64 x (+.f64 x y))

simplify90.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4960	3322
1	4960	3322

prune145.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

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

Merged error: 0b

Counts

187 → 8

Compiler

Compiled 4059 to 1391 computations (65.7% saved)

regimes43.0ms (1%)

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%)

sample655.0ms (15.3%)

Algorithm

1×

intervals

Results

305.0ms

8000×

body

128

valid

Compiler

Compiled 300 to 160 computations (46.7% saved)

Details

analyze77.0ms (1.8%)

sample21.0ms (0.5%)

simplify291.0ms (6.8%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite72.0ms (1.7%)

series299.0ms (7%)

simplify89.0ms (2.1%)

prune176.0ms (4.1%)

localize10.0ms (0.2%)

rewrite75.0ms (1.8%)

series397.0ms (9.3%)

simplify67.0ms (1.6%)

prune221.0ms (5.2%)

localize8.0ms (0.2%)

rewrite120.0ms (2.8%)

series416.0ms (9.7%)

simplify131.0ms (3.1%)

prune317.0ms (7.4%)

localize9.0ms (0.2%)

rewrite79.0ms (1.8%)

series458.0ms (10.7%)

simplify90.0ms (2.1%)

prune145.0ms (3.4%)

regimes43.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample655.0ms (15.3%)

Profiling