Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.7s (33.8%)

Results

675.0ms	2070×	body	1024	valid
434.0ms	4339×	body	128	valid
264.0ms	1086×	body	512	valid
96.0ms	569×	body	256	valid
73.0ms	192×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify96.0ms (2%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

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

Error

31.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	3.7b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite161.0ms (3.3%)

Algorithm

2×	egg-rewrite

Rules

146×	`egg`
50×	`egg`

Counts

2 → 196

Calls

2 calls:

79.0ms	(/.f64 x (+.f64 x 1))
78.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	195	19
2	2929	19
3	5058	19
0	5	7
1	109	7
2	1405	7
3	4960	7
4	5167	7

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

605×	`times-frac_binary64`
562×	`fma-def_binary64`
403×	`sub-neg_binary64`
338×	`div-sub_binary64`
220×	`fma-neg_binary64`

Counts

220 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	330
1	124	309
2	358	300
3	965	300
4	2934	300
5	4391	300
6	4964	300

prune235.0ms (4.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	217	5	222
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	218	5	223

Error

0.0b

Counts

223 → 5

Alt Table

Status	Error	Program
	31.3b	(-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	32.4b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (/.f64 1 (+.f64 x 1))) (/.f64 (fma.f64 -1 x -1) (-.f64 x 1)))
▶	29.4b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	31.8b	(fma.f64 (fma.f64 -1 x -1) (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
	29.6b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))

Compiler

Compiled 5767 to 4213 computations (26.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
✓	0.2b	(/.f64 3 (pow.f64 x 3))
✓	0.2b	(/.f64 1 (*.f64 x x))
✓	7.8b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))

series13.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

5.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
3.0ms	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
3.0ms	(/.f64 3 (pow.f64 x 3))
2.0ms	(/.f64 1 (*.f64 x x))

rewrite343.0ms (7%)

Algorithm

4×	egg-rewrite

Rules

125×	`egg`
68×	`egg`
67×	`egg`
46×	`egg`

Counts

4 → 306

Calls

4 calls:

94.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
81.0ms	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
79.0ms	(/.f64 1 (*.f64 x x))
75.0ms	(/.f64 3 (pow.f64 x 3))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	205	11
2	2551	11
3	4754	11
4	4878	11
0	5	7
1	100	4
2	1021	4
3	4826	4
4	5107	4
0	5	7
1	111	7
2	1239	7
3	4787	7
4	4877	7
0	12	22
1	282	17
2	3749	17
3	5325	17

simplify81.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

527×	`times-frac_binary64`
465×	`associate-/r*_binary64`
410×	`associate-*l/_binary64`
374×	`fma-def_binary64`
335×	`fma-neg_binary64`

Counts

342 → 316

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	22	456
1	59	438
2	151	438
3	361	438
4	1016	408
5	3828	390
6	4523	390
7	5055	390

prune247.0ms (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	316	5	321

Error

0.0b

Counts

321 → 5

Alt Table

Status	Error	Program
	31.3b	(-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	32.4b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (/.f64 1 (+.f64 x 1))) (/.f64 (fma.f64 -1 x -1) (-.f64 x 1)))
✓	29.4b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	31.8b	(fma.f64 (fma.f64 -1 x -1) (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
▶	29.6b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))

Compiler

Compiled 7450 to 5684 computations (23.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (pow.f64 x 2))
✓	0.3b	(*.f64 3 (/.f64 1 x))
✓	7.8b	(+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
✓	8.4b	(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))

series12.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

4.0ms	(+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
4.0ms	(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))
2.0ms	(/.f64 1 (pow.f64 x 2))
1.0ms	(*.f64 3 (/.f64 1 x))

rewrite330.0ms (6.7%)

Algorithm

4×	egg-rewrite

Rules

59×	`egg`
56×	`egg`
50×	`egg`
47×	`egg`

Counts

4 → 212

Calls

4 calls:

90.0ms	(+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
81.0ms	(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))
77.0ms	(*.f64 3 (/.f64 1 x))
76.0ms	(/.f64 1 (pow.f64 x 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	23
1	427	23
2	4368	23
3	5900	23
0	11	11
1	249	11
2	2578	11
3	4895	11
4	4821	11
0	6	4
1	121	4
2	1244	4
3	4810	4
4	5001	4
0	6	4
1	124	4
2	1159	4
3	4727	4
4	4943	4

simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

673×	`associate-/r/_binary64`
599×	`fma-def_binary64`
377×	`*-commutative_binary64`
333×	`associate-/r*_binary64`
325×	`associate-l_binary64`

Counts

236 → 219

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	22	195
1	50	195
2	94	195
3	178	195
4	428	189
5	1975	186
6	2922	186
7	3671	186
8	4252	186
9	4929	186

prune190.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	219	5	224

Error

0.0b

Counts

224 → 5

Alt Table

Status	Error	Program
▶	31.3b	(-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	32.4b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (/.f64 1 (+.f64 x 1))) (/.f64 (fma.f64 -1 x -1) (-.f64 x 1)))
✓	29.4b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	50.4b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 (pow.f64 (pow.f64 (.f64 (/.f64 3 x) (cbrt.f64 (/.f64 3 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 3 x)))) (+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
	31.8b	(fma.f64 (fma.f64 -1 x -1) (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))

Compiler

Compiled 6722 to 5421 computations (19.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) x)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 x 1) x))
✓	3.7b	(-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 1 (/.f64 (+.f64 x 1) x))
2.0ms	(/.f64 (+.f64 x 1) x)

rewrite309.0ms (6.3%)

Algorithm

3×	egg-rewrite

Rules

157×	`egg`
56×	`egg`
54×	`egg`

Counts

3 → 267

Calls

3 calls:

111.0ms	(-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
111.0ms	(/.f64 1 (/.f64 (+.f64 x 1) x))
82.0ms	(/.f64 (+.f64 x 1) x)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	221	19
2	3302	19
3	4968	19
4	4949	19
0	6	10
1	137	7
2	1759	7
3	4896	7
4	4980	7
5	4933	7
0	5	7
1	109	7
2	1412	7
3	4864	7
4	5071	7

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

605×	`times-frac_binary64`
562×	`fma-def_binary64`
403×	`sub-neg_binary64`
338×	`div-sub_binary64`
220×	`fma-neg_binary64`

Counts

303 → 293

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	399
1	126	378
2	360	369
3	967	369
4	2936	369
5	4393	369
6	4966	369

prune232.0ms (4.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	293	0	293
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	293	5	298

Error

0.0b

Counts

298 → 5

Alt Table

Status	Error	Program
✓	31.3b	(-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	32.4b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (/.f64 1 (+.f64 x 1))) (/.f64 (fma.f64 -1 x -1) (-.f64 x 1)))
✓	29.4b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	50.4b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 (pow.f64 (pow.f64 (.f64 (/.f64 3 x) (cbrt.f64 (/.f64 3 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 3 x)))) (+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
	31.8b	(fma.f64 (fma.f64 -1 x -1) (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))

Compiler

Compiled 7172 to 5283 computations (26.3% saved)

regimes420.0ms (8.6%)

Accuracy

Total 0.0b remaining (29.5%)

Threshold costs 0.0b (29.5%)

Counts

146 → 3

Compiler

Compiled 5616 to 4372 computations (22.2% saved)

bsearch36.0ms (0.7%)

Steps

Iters	Range		Point
8	232.75796806107857	169867.59613959913	11995.028539617728
8	-9256375.059611818	-7450.127406426313	-18424.40926304694

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	88
1	38	88
2	45	88
3	51	88
4	57	88
5	60	88
6	61	88
7	59	88

end244.0ms (5%)

Compiler: Compiled 234 to 178 computations (23.9% saved)

Details

analyze5.0ms (0.1%)

sample1.7s (33.8%)

simplify96.0ms (2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series5.0ms (0.1%)

rewrite161.0ms (3.3%)

simplify73.0ms (1.5%)

prune235.0ms (4.8%)

localize8.0ms (0.2%)

series13.0ms (0.3%)

rewrite343.0ms (7%)

simplify81.0ms (1.7%)

prune247.0ms (5%)

localize16.0ms (0.3%)

series12.0ms (0.2%)

rewrite330.0ms (6.7%)

simplify80.0ms (1.6%)

prune190.0ms (3.9%)

localize7.0ms (0.2%)

series8.0ms (0.2%)

rewrite309.0ms (6.3%)

simplify82.0ms (1.7%)

prune232.0ms (4.7%)

regimes420.0ms (8.6%)

bsearch36.0ms (0.7%)

simplify6.0ms (0.1%)

end244.0ms (5%)

Profiling