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)

sample1.5s (39.3%)

Results

637.0ms	2085×	body	1024	valid
406.0ms	4400×	body	128	valid
248.0ms	1014×	body	512	valid
92.0ms	537×	body	256	valid
83.0ms	220×	body	2048	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

preprocess69.0ms (1.8%)

Algorithm

2×	egg-herbie

Rules

859×	`fma-neg_binary64`
764×	`fma-def_binary64`
321×	`div-sub_binary64`
169×	`associate-/l*_binary64`
149×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	60	19
5	100	19
6	205	19
7	377	19
8	951	19
9	2127	19
10	2751	19
11	3062	19
12	3879	19
13	4173	19
14	4215	19
15	4217	19
16	4219	19
17	4229	19
18	4229	19
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify59.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
764×	`fma-def_binary64`
321×	`div-sub_binary64`
169×	`associate-/l*_binary64`
149×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	60	19
5	100	19
6	205	19
7	377	19
8	951	19
9	2127	19
10	2751	19
11	3062	19
12	3879	19
13	4173	19
14	4215	19
15	4217	19
16	4219	19
17	4229	19
18	4229	19

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

30.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	4.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	-inf
1.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	inf
1.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	0
1.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))	x	-inf
1.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))	x	inf

rewrite77.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

470×	`fma-def_binary64`
286×	`fma-neg_binary64`
267×	`log-div_binary64`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	195	36
2	3222	36

Stop Event

1×	node limit

Counts

3 → 210

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

405×	`fma-neg_binary64`
344×	`cancel-sign-sub-inv_binary64`
288×	`fma-def_binary64`
287×	`associate-l_binary64`
233×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	475
1	204	443
2	627	430
3	1940	428

Stop Event

1×	node limit

Counts

246 → 250

prune228.0ms (6.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	247	3	250
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	248	3	251

Error

0.0b

Counts

251 → 3

Alt Table

Status	Error	Program
	32.4b	(fma.f64 x (+.f64 3 x) 1)
▶	30.1b	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (.f64 (/.f64 (+.f64 x 1) x) 1)) (.f64 (/.f64 (+.f64 x 1) x) (/.f64 (+.f64 x -1) (+.f64 x 1))))
	30.9b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))

Compiler

Compiled 6096 to 4485 computations (26.4% saved)

localize28.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 (+.f64 x 1) x) (/.f64 (+.f64 x -1) (+.f64 x 1)))
✓	0.0b	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (.f64 (/.f64 (+.f64 x 1) x) 1)) (.f64 (/.f64 (+.f64 x 1) x) (/.f64 (+.f64 x -1) (+.f64 x 1))))
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 x 1))
✓	4.3b	(-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1))

series10.0ms (0.3%)

Counts

4 → 48

Calls

12 calls:

1.0ms	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (.f64 (/.f64 (+.f64 x 1) x) 1)) (.f64 (/.f64 (+.f64 x 1) x) (/.f64 (+.f64 x -1) (+.f64 x 1))))	x	-inf
1.0ms	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (.f64 (/.f64 (+.f64 x 1) x) 1)) (.f64 (/.f64 (+.f64 x 1) x) (/.f64 (+.f64 x -1) (+.f64 x 1))))	x	inf
1.0ms	(-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1))	x	-inf
1.0ms	(-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1))	x	inf
1.0ms	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (.f64 (/.f64 (+.f64 x 1) x) 1)) (.f64 (/.f64 (+.f64 x 1) x) (/.f64 (+.f64 x -1) (+.f64 x 1))))	x	0

rewrite94.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

230×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
139×	`*-un-lft-identity_binary64`
139×	`pow1_binary64`
133×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	88
1	293	64
2	4833	64

Stop Event

1×	node limit

Counts

4 → 183

simplify48.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

402×	`fma-neg_binary64`
290×	`cancel-sign-sub-inv_binary64`
222×	`associate-+l-_binary64`
215×	`fma-def_binary64`
212×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	589
1	206	560
2	595	553
3	1708	547
4	4886	547

Stop Event

1×	node limit

Counts

231 → 225

prune252.0ms (6.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	273	3	276

Error

0.0b

Counts

276 → 3

Alt Table

Status	Error	Program
	30.9b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))
✓	30.1b	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (.f64 (/.f64 (+.f64 x 1) x) 1)) (.f64 (/.f64 (+.f64 x 1) x) (/.f64 (+.f64 x -1) (+.f64 x 1))))
▶	30.1b	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1)) (/.f64 1 (/.f64 x (+.f64 x -1))))

Compiler

Compiled 8656 to 6315 computations (27% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1)) (/.f64 1 (/.f64 x (+.f64 x -1))))
	0.0b	(/.f64 (+.f64 x -1) (+.f64 x 1))
✓	0.0b	(/.f64 1 (/.f64 x (+.f64 x -1)))
	4.3b	(-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1))

series6.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

2.0ms	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1)) (/.f64 1 (/.f64 x (+.f64 x -1))))	x	inf
1.0ms	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1)) (/.f64 1 (/.f64 x (+.f64 x -1))))	x	-inf
1.0ms	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1)) (/.f64 1 (/.f64 x (+.f64 x -1))))	x	0
1.0ms	(/.f64 1 (/.f64 x (+.f64 x -1)))	x	0
1.0ms	(/.f64 1 (/.f64 x (+.f64 x -1)))	x	inf

rewrite67.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

246×	`log1p-udef_binary64`
153×	`add-sqr-sqrt_binary64`
150×	`*-un-lft-identity_binary64`
150×	`pow1_binary64`
143×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	315	35
2	4878	35

Stop Event

1×	node limit

Counts

2 → 86

simplify26.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

532×	`times-frac_binary64`
434×	`cancel-sign-sub-inv_binary64`
367×	`fma-def_binary64`
302×	`associate-/l/_binary64`
198×	`sub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	261
1	96	242
2	271	238
3	810	238
4	2415	235

Stop Event

1×	node limit

Counts

110 → 103

prune182.0ms (4.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	212	4	216

Error

Counts

216 → 4

Alt Table

Status	Error	Program
	30.9b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))
✓	30.1b	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (.f64 (/.f64 (+.f64 x 1) x) 1)) (.f64 (/.f64 (+.f64 x 1) x) (/.f64 (+.f64 x -1) (+.f64 x 1))))
✓	30.1b	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1)) (/.f64 1 (/.f64 x (+.f64 x -1))))
▶	30.6b	(/.f64 (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 -3 x)) (/.f64 -2 (pow.f64 x 3))) (/.f64 1 (/.f64 x (+.f64 x -1))))

Compiler

Compiled 5912 to 4380 computations (25.9% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 2 x) x)
✓	0.3b	(/.f64 -2 (pow.f64 x 3))
✓	4.4b	(/.f64 (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 -3 x)) (/.f64 -2 (pow.f64 x 3))) (/.f64 1 (/.f64 x (+.f64 x -1))))
✓	6.5b	(+.f64 (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 -3 x)) (/.f64 -2 (pow.f64 x 3)))

series13.0ms (0.3%)

Counts

4 → 36

Calls

12 calls:

2.0ms	(+.f64 (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 -3 x)) (/.f64 -2 (pow.f64 x 3)))	x	0
2.0ms	(/.f64 -2 (pow.f64 x 3))	x	0
1.0ms	(/.f64 (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 -3 x)) (/.f64 -2 (pow.f64 x 3))) (/.f64 1 (/.f64 x (+.f64 x -1))))	x	-inf
1.0ms	(+.f64 (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 -3 x)) (/.f64 -2 (pow.f64 x 3)))	x	inf
1.0ms	(/.f64 (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 -3 x)) (/.f64 -2 (pow.f64 x 3))) (/.f64 1 (/.f64 x (+.f64 x -1))))	x	inf

rewrite39.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

220×	`add-sqr-sqrt_binary64`
210×	`pow1_binary64`
209×	`*-un-lft-identity_binary64`
206×	`add-cbrt-cube_binary64`
205×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	70
1	451	63

Stop Event

1×	node limit

Counts

4 → 87

simplify34.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

377×	`fma-def_binary64`
295×	`distribute-neg-frac_binary64`
240×	`sub-neg_binary64`
211×	`associate-/r*_binary64`
186×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	477
1	127	465
2	343	462
3	990	462
4	3190	462

Stop Event

1×	node limit

Counts

123 → 109

prune84.0ms (2.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	109	4	113

Error

Counts

113 → 4

Alt Table

Status	Error	Program
	30.9b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))
✓	30.1b	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (.f64 (/.f64 (+.f64 x 1) x) 1)) (.f64 (/.f64 (+.f64 x 1) x) (/.f64 (+.f64 x -1) (+.f64 x 1))))
✓	30.1b	(/.f64 (-.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) (*.f64 (/.f64 (+.f64 x 1) x) 1)) (/.f64 1 (/.f64 x (+.f64 x -1))))
✓	30.6b	(/.f64 (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 -3 x)) (/.f64 -2 (pow.f64 x 3))) (/.f64 1 (/.f64 x (+.f64 x -1))))

Compiler

Compiled 2808 to 2057 computations (26.7% saved)

regimes736.0ms (19.5%)

Accuracy

Total 0.0b remaining (16.9%)

Threshold costs 0.0b (16.9%)

Counts

246 → 3

Compiler

Compiled 10274 to 7674 computations (25.3% saved)

bsearch43.0ms (1.1%)

Algorithm

2×	binary-search

Calls

2 calls:

19.0ms	x
17.0ms	x

Steps

Iters	Point		Range
16767.2313256428	∈ [	11.162057359689127	,	299408.37602779915	]
-12339.105848947931	∈ [	-30770404.13233236	,	-0.0035811007973851052	]

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`unsub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	106
1	52	106
2	54	106
3	55	106

Stop Event

1×

saturated

end113.0ms (3%)

Stop Event

1×

fuel

Compiler

Compiled 240 to 174 computations (27.5% saved)

Details

analyze5.0ms (0.1%)

sample1.5s (39.3%)

preprocess69.0ms (1.8%)

simplify59.0ms (1.6%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series9.0ms (0.2%)

rewrite77.0ms (2.1%)

simplify30.0ms (0.8%)

prune228.0ms (6.1%)

localize28.0ms (0.7%)

series10.0ms (0.3%)

rewrite94.0ms (2.5%)

simplify48.0ms (1.3%)

prune252.0ms (6.7%)

localize10.0ms (0.3%)

series6.0ms (0.2%)

rewrite67.0ms (1.8%)

simplify26.0ms (0.7%)

prune182.0ms (4.8%)

localize14.0ms (0.4%)

series13.0ms (0.3%)

rewrite39.0ms (1%)

simplify34.0ms (0.9%)

prune84.0ms (2.2%)

regimes736.0ms (19.5%)

bsearch43.0ms (1.1%)

simplify4.0ms (0.1%)

end113.0ms (3%)

Profiling