Details

analyze78.0ms (1.6%)

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)

sample16.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 35 to 21 computations (40% saved)

simplify304.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	4936	25
1	4936	25

prune2.0ms (0%)

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: 22.0b

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))
21.7b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

rewrite71.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`flip3-+_binary64_12810` `flip-+_binary64_12781` `frac-times_binary64_12817`
31×	`add-cbrt-cube_binary64_12843` `add-exp-log_binary64_12845`
30×	`associate-*l/_binary64_12750`
27×	`*-un-lft-identity_binary64_12807`
26×	`associate-/r/_binary64_12753`
18×	`associate-*r/_binary64_12749`
15×	`pow1_binary64_12868`
13×	`prod-exp_binary64_12856` `cbrt-unprod_binary64_12840`
11×	`add-sqr-sqrt_binary64_12829`
9×	`distribute-lft-out_binary64_12758` `associate-r_binary64_12747`
8×	`add-cube-cbrt_binary64_12842`
6×	`div-exp_binary64_12858` `swap-sqr_binary64_12774` `cbrt-undiv_binary64_12841`
5×	`associate-l_binary64_12748`
4×	`pow-prod-down_binary64_12878`
3×	`add-log-exp_binary64_12846`
2×	`*-commutative_binary64_12738` `distribute-rgt-in_binary64_12757` `unswap-sqr_binary64_12775` `distribute-lft-in_binary64_12756`
1×	`div-inv_binary64_12804` `pow-plus_binary64_12870` `clear-num_binary64_12806` `associate-/l_binary64_12752` `times-frac_binary64_12813` `pow2_binary64_12888` `pow-prod-up_binary64_12877` `associate-/r_binary64_12751` `pow-sqr_binary64_12780` `frac-2neg_binary64_12818`

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)))
18.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
10.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

series304.0ms (6.2%)

Counts

3 → 9

Calls

3 calls:

207.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
71.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
26.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify89.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4957	3602
1	4957	3602

prune449.0ms (9.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	141	8	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	8	150

Merged error: 9.2b

Counts

150 → 8

Compiler

Compiled 10566 to 5338 computations (49.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x y) 2)
0.0b	(/.f64 y (+.f64 (+.f64 x y) 1))
0.2b	(*.f64 (/.f64 x (pow.f64 (+.f64 x y) 2)) (/.f64 y (+.f64 (+.f64 x y) 1)))
19.7b	(/.f64 x (pow.f64 (+.f64 x y) 2))

rewrite70.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64_12807`
97×	`times-frac_binary64_12813`
88×	`add-sqr-sqrt_binary64_12829`
59×	`add-cube-cbrt_binary64_12842`
36×	`add-exp-log_binary64_12845`
34×	`unpow-prod-down_binary64_12886`
31×	`associate-l_binary64_12748`
29×	`distribute-lft-out_binary64_12758`
21×	`associate-r_binary64_12747`
20×	`add-cbrt-cube_binary64_12843`
14×	`div-exp_binary64_12858` `associate-/r*_binary64_12751`
10×	`unpow2_binary64_12872` `sqr-pow_binary64_12779` `unswap-sqr_binary64_12775`
8×	`prod-exp_binary64_12856`
7×	`pow1_binary64_12868`
6×	`associate-/l*_binary64_12752` `cbrt-undiv_binary64_12841`
4×	`pow-exp_binary64_12875` `associate-/r/_binary64_12753` `cbrt-unprod_binary64_12840` `div-inv_binary64_12804` `pow-to-exp_binary64_12876` `add-log-exp_binary64_12846`
3×	`pow-unpow_binary64_12884`
2×	`clear-num_binary64_12806` `flip3-+_binary64_12810` `flip-+_binary64_12781` `frac-2neg_binary64_12818`
1×	`pow-prod-down_binary64_12878` `-commutative_binary64_12738` `associate-r/_binary64_12749` `associate-*l/_binary64_12750` `frac-times_binary64_12817` `pow-pow_binary64_12879`

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))
7.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
5.0ms	(pow.f64 (+.f64 x y) 2)

series394.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(*.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))
57.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
30.0ms	(pow.f64 (+.f64 x y) 2)

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5312	3903

prune511.0ms (10.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	198	9	207
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	205	10	215

Merged error: 0.0b

Counts

215 → 10

Compiler

Compiled 10972 to 5822 computations (46.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x y))
0.0b	(/.f64 y (+.f64 (+.f64 x y) 1))
0.1b	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
0.2b	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))

rewrite119.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

313×	`*-un-lft-identity_binary64_12807`
303×	`times-frac_binary64_12813`
163×	`add-sqr-sqrt_binary64_12829`
142×	`add-cube-cbrt_binary64_12842`
89×	`distribute-lft-out_binary64_12758`
78×	`associate-l_binary64_12748`
34×	`add-cbrt-cube_binary64_12843` `add-exp-log_binary64_12845`
28×	`associate-/r/_binary64_12753`
24×	`associate-/l*_binary64_12752`
21×	`associate-r_binary64_12747`
14×	`div-exp_binary64_12858` `div-inv_binary64_12804` `flip3-+_binary64_12810` `flip-+_binary64_12781` `cbrt-undiv_binary64_12841`
13×	`associate-/r*_binary64_12751`
6×	`prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `pow1_binary64_12868` `unswap-sqr_binary64_12775`
4×	`add-log-exp_binary64_12846`
3×	`clear-num_binary64_12806` `frac-2neg_binary64_12818`
1×	`pow-prod-down_binary64_12878` `-commutative_binary64_12738` `associate-r/_binary64_12749` `associate-*l/_binary64_12750` `associate-/l/_binary64_12754` `frac-times_binary64_12817`

Counts

4 → 310

Calls

4 calls:

52.0ms	(*.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 (8.5%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
88.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
55.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
51.0ms	(/.f64 x (+.f64 x y))

simplify129.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4944	7177
1	4944	7177

prune417.0ms (8.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	318	4	322
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	325	7	332

Merged error: 0b

Counts

332 → 7

Compiler

Compiled 10498 to 3767 computations (64.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite77.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity_binary64_12807`
62×	`times-frac_binary64_12813`
54×	`add-sqr-sqrt_binary64_12829`
42×	`add-cube-cbrt_binary64_12842`
38×	`add-cbrt-cube_binary64_12843` `add-exp-log_binary64_12845`
30×	`distribute-lft-out_binary64_12758`
21×	`associate-r_binary64_12747`
18×	`associate-l_binary64_12748`
15×	`div-exp_binary64_12858` `cbrt-undiv_binary64_12841`
13×	`associate-/r*_binary64_12751`
10×	`associate-/r/_binary64_12753`
8×	`prod-exp_binary64_12856` `cbrt-unprod_binary64_12840`
7×	`associate-/l*_binary64_12752`
6×	`pow1_binary64_12868`
5×	`div-inv_binary64_12804` `flip3-+_binary64_12810` `flip-+_binary64_12781`
4×	`add-log-exp_binary64_12846` `unswap-sqr_binary64_12775`
3×	`clear-num_binary64_12806` `associate-/l/_binary64_12754` `frac-2neg_binary64_12818`
2×	`associate-r/_binary64_12749` `associate-l/_binary64_12750` `frac-times_binary64_12817`
1×	`pow-prod-down_binary64_12878` `*-commutative_binary64_12738`

Counts

4 → 167

Calls

4 calls:

23.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
23.0ms	(/.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))

series463.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))) (+.f64 x y))
146.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
59.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
51.0ms	(/.f64 x (+.f64 x y))

simplify81.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4968	3322
1	4968	3322

prune178.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	179	7	186

Merged error: 0b

Counts

186 → 7

Compiler

Compiled 4640 to 1680 computations (63.8% saved)

regimes35.0ms (0.7%)

Compiler: Compiled 302 to 174 computations (42.4% 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%)

sample584.0ms (11.9%)

Algorithm

1×

intervals

Results

292.0ms

8000×

body

128

valid

Compiler

Compiled 203 to 116 computations (42.9% saved)

Details

analyze78.0ms (1.6%)

sample16.0ms (0.3%)

simplify304.0ms (6.2%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite71.0ms (1.5%)

series304.0ms (6.2%)

simplify89.0ms (1.8%)

prune449.0ms (9.2%)

localize9.0ms (0.2%)

rewrite70.0ms (1.4%)

series394.0ms (8.1%)

simplify66.0ms (1.3%)

prune511.0ms (10.4%)

localize8.0ms (0.2%)

rewrite119.0ms (2.4%)

series414.0ms (8.5%)

simplify129.0ms (2.6%)

prune417.0ms (8.5%)

localize9.0ms (0.2%)

rewrite77.0ms (1.6%)

series463.0ms (9.5%)

simplify81.0ms (1.7%)

prune178.0ms (3.6%)

regimes35.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample584.0ms (11.9%)

Profiling