Details

analyze81.0ms (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)

simplify153.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4935	25
1	4935	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: 22.2b

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))
22.0b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

rewrite70.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64`
31×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
30×	`associate-*l/_binary64`
27×	`*-un-lft-identity_binary64`
26×	`associate-/r/_binary64`
18×	`associate-*r/_binary64`
15×	`pow1_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`distribute-lft-out_binary64` `associate-r_binary64`
8×	`add-cube-cbrt_binary64`
6×	`swap-sqr_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
5×	`associate-l_binary64`
4×	`pow-prod-down_binary64`
3×	`add-log-exp_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

3 → 140

Calls

3 calls:

22.0ms	(/.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))
11.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

series304.0ms (6.1%)

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)))
65.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
25.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify95.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4956	3602
1	4956	3602

prune438.0ms (8.8%)

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: 9.7b

Counts

150 → 9

Compiler

Compiled 9615 to 4997 computations (48% 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)))
21.2b	(/.f64 x (pow.f64 (+.f64 x y) 2))

rewrite75.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64`
97×	`times-frac_binary64`
88×	`add-sqr-sqrt_binary64`
59×	`add-cube-cbrt_binary64`
36×	`add-exp-log_binary64`
34×	`unpow-prod-down_binary64`
31×	`associate-l_binary64`
29×	`distribute-lft-out_binary64`
21×	`associate-r_binary64`
20×	`add-cbrt-cube_binary64`
14×	`associate-/r*_binary64` `div-exp_binary64`
10×	`unpow2_binary64` `sqr-pow_binary64` `unswap-sqr_binary64`
8×	`prod-exp_binary64`
7×	`pow1_binary64`
6×	`cbrt-undiv_binary64` `associate-/l*_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `div-inv_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

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

series400.0ms (8%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(*.f64 (/.f64 x (pow.f64 (+.f64 x y) 2)) (/.f64 y (+.f64 (+.f64 x y) 1)))
96.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
60.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
31.0ms	(pow.f64 (+.f64 x y) 2)

simplify61.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5311	3903

prune475.0ms (9.5%)

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 9955 to 5361 computations (46.1% 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)))

rewrite122.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

313×	`*-un-lft-identity_binary64`
303×	`times-frac_binary64`
163×	`add-sqr-sqrt_binary64`
142×	`add-cube-cbrt_binary64`
89×	`distribute-lft-out_binary64`
78×	`associate-l_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`associate-/r/_binary64`
24×	`associate-/l*_binary64`
21×	`associate-r_binary64`
14×	`flip3-+_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
13×	`associate-/r*_binary64`
6×	`pow1_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

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)))
13.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
9.0ms	(/.f64 x (+.f64 x y))
8.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))

series420.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
89.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
57.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
50.0ms	(/.f64 x (+.f64 x y))

simplify128.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4943	7177
1	4943	7177

prune373.0ms (7.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	319	3	322
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	325	8	333

Merged error: 0.0b

Counts

333 → 8

Compiler

Compiled 9802 to 3352 computations (65.8% 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 x (+.f64 x y)) (/.f64 (/.f64 y (+.f64 (+.f64 x y) 1)) (+.f64 x y)))
0.1b	(/.f64 (/.f64 y (+.f64 (+.f64 x y) 1)) (+.f64 x y))

rewrite145.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

411×	`*-un-lft-identity_binary64`
351×	`times-frac_binary64`
177×	`add-sqr-sqrt_binary64`
156×	`add-cube-cbrt_binary64`
143×	`distribute-lft-out_binary64`
90×	`associate-r_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`associate-/r/_binary64`
27×	`associate-/l*_binary64`
18×	`associate-l_binary64`
14×	`flip3-+_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
13×	`associate-/r*_binary64`
6×	`pow1_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 334

Calls

4 calls:

63.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 (/.f64 y (+.f64 (+.f64 x y) 1)) (+.f64 x y)))
17.0ms	(/.f64 (/.f64 y (+.f64 (+.f64 x y) 1)) (+.f64 x y))
9.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
6.0ms	(/.f64 x (+.f64 x y))

series438.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 (/.f64 y (+.f64 (+.f64 x y) 1)) (+.f64 x y)))
106.0ms	(/.f64 (/.f64 y (+.f64 (+.f64 x y) 1)) (+.f64 x y))
57.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
53.0ms	(/.f64 x (+.f64 x y))

simplify108.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5008	8578

prune386.0ms (7.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	345	1	346
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	345	9	354

Merged error: 0b

Counts

354 → 9

Compiler

Compiled 9996 to 3439 computations (65.6% saved)

regimes42.0ms (0.8%)

Compiler: Compiled 460 to 248 computations (46.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	13	25

end0.0ms (0%)

sample607.0ms (12.2%)

Algorithm

1×

intervals

Results

281.0ms

8000×

body

128

valid

Compiler

Compiled 282 to 153 computations (45.7% saved)

Details

analyze81.0ms (1.6%)

sample16.0ms (0.3%)

simplify153.0ms (3.1%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite70.0ms (1.4%)

series304.0ms (6.1%)

simplify95.0ms (1.9%)

prune438.0ms (8.8%)

localize9.0ms (0.2%)

rewrite75.0ms (1.5%)

series400.0ms (8%)

simplify61.0ms (1.2%)

prune475.0ms (9.5%)

localize8.0ms (0.2%)

rewrite122.0ms (2.4%)

series420.0ms (8.5%)

simplify128.0ms (2.6%)

prune373.0ms (7.5%)

localize8.0ms (0.2%)

rewrite145.0ms (2.9%)

series438.0ms (8.8%)

simplify108.0ms (2.2%)

prune386.0ms (7.8%)

regimes42.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample607.0ms (12.2%)

Profiling