Details

analyze1.5s (28.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
3.1%	96.6%	0.2%	11
4.7%	95.1%	0.2%	12
8.2%	91.6%	0.2%	13
10.5%	89.2%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (22.1%)

Results

1.0s	8252×	body	128	valid
98.0ms	766×	body	128	invalid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	2048	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess40.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

956×	`div-sub_binary64`
390×	`fma-def_binary64`
299×	`distribute-rgt-in_binary64`
254×	`distribute-lft-in_binary64`
253×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	176
1	138	154
2	292	154
3	605	154
4	1447	154
5	3922	154
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

611×	`times-frac_binary64`
577×	`div-sub_binary64`
529×	`fma-neg_binary64`
259×	`fma-def_binary64`
192×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	41	14
3	82	14
4	188	14
5	381	14
6	902	14
7	2369	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.5b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
▶	1.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

Compiler

Compiled 88 to 52 computations (40.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	3.6b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

series86.0ms (1.7%)

Counts

3 → 144

Calls

36 calls:

4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))	t	0
4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))	y	-inf
4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))	x	0
3.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))	a	-inf
3.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))	a	0

rewrite68.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

280×	`fma-neg_binary64`
252×	`expm1-udef_binary64`
252×	`log1p-udef_binary64`
137×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	257	37
2	4024	37

Stop Event

1×	node limit

Counts

3 → 110

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

627×	`times-frac_binary64`
520×	`sub-neg_binary64`
290×	`associate--l+_binary64`
214×	`associate--r+_binary64`
206×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	4417
1	767	4078
2	2702	3496

Stop Event

1×	node limit

Counts

254 → 222

prune181.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	218	4	222
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	218	6	224

Error

0.0b

Counts

224 → 6

Alt Table

Status	Error	Program
✓	1.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
▶	1.4b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	9.2b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (pow.f64 (cbrt.f64 (-.f64 a t)) 2)) (cbrt.f64 (-.f64 a t))))
	8.9b	(+.f64 x (/.f64 1 (/.f64 (-.f64 a t) (*.f64 y (-.f64 z t)))))
	2.5b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
	1.8b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))

Compiler

Compiled 5462 to 1952 computations (64.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	3.4b	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))

series87.0ms (1.7%)

Counts

3 → 144

Calls

36 calls:

5.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))	t	0
4.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))	t	0
4.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))	x	-inf
3.0ms	(/.f64 (-.f64 a t) (-.f64 z t))	t	0
3.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))	a	-inf

rewrite68.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
141×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`
136×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	263	37
2	4303	37

Stop Event

1×	node limit

Counts

3 → 118

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

805×	`times-frac_binary64`
532×	`sub-neg_binary64`
296×	`associate--l+_binary64`
215×	`associate--r+_binary64`
209×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	4417
1	793	4081
2	2853	3769

Stop Event

1×	node limit

Counts

262 → 230

prune175.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	228	2	230
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	231	5	236

Error

Counts

236 → 5

Alt Table

Status	Error	Program
✓	1.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
	13.5b	(+.f64 x (/.f64 z (/.f64 (-.f64 a t) y)))
	8.9b	(+.f64 x (/.f64 1 (/.f64 (-.f64 a t) (*.f64 y (-.f64 z t)))))
▶	1.5b	(+.f64 x (/.f64 y (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))))
	1.8b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))

Compiler

Compiled 5620 to 1957 computations (65.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))))
✓	0.0b	(/.f64 1 (-.f64 z t))
✓	0.2b	(*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))
✓	3.4b	(/.f64 y (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t))))

series97.0ms (1.9%)

Counts

4 → 168

Calls

42 calls:

6.0ms	(+.f64 x (/.f64 y (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))))	t	-inf
4.0ms	(+.f64 x (/.f64 y (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))))	y	0
4.0ms	(/.f64 y (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t))))	y	-inf
4.0ms	(*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))	z	-inf
3.0ms	(/.f64 y (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t))))	z	inf

rewrite75.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

274×	`expm1-udef_binary64`
274×	`log1p-udef_binary64`
153×	`add-sqr-sqrt_binary64`
146×	`add-cbrt-cube_binary64`
146×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	296	44
2	4472	44

Stop Event

1×	node limit

Counts

4 → 143

simplify88.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
541×	`sub-neg_binary64`
296×	`associate--l+_binary64`
221×	`+-commutative_binary64`
220×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	4909
1	851	4555
2	3043	4435

Stop Event

1×	node limit

Counts

311 → 268

prune185.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	268	5	273

Error

Counts

273 → 5

Alt Table

Status	Error	Program
✓	1.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
	13.5b	(+.f64 x (/.f64 z (/.f64 (-.f64 a t) y)))
	8.9b	(+.f64 x (/.f64 1 (/.f64 (-.f64 a t) (*.f64 y (-.f64 z t)))))
✓	1.5b	(+.f64 x (/.f64 y (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))))
▶	1.8b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))

Compiler

Compiled 6467 to 2320 computations (64.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.0b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
✓	3.6b	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))

series94.0ms (1.8%)

Counts

4 → 168

Calls

42 calls:

5.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))	z	-inf
4.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))	a	-inf
4.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))	x	0
3.0ms	(/.f64 1 (-.f64 a t))	a	inf
3.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))	y	-inf

rewrite71.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`expm1-udef_binary64`
266×	`log1p-udef_binary64`
149×	`add-sqr-sqrt_binary64`
142×	`add-cbrt-cube_binary64`
142×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	290	44
2	4211	44

Stop Event

1×	node limit

Counts

4 → 120

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

641×	`times-frac_binary64`
527×	`sub-neg_binary64`
290×	`associate--l+_binary64`
221×	`+-commutative_binary64`
219×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	4909
1	823	4552
2	2891	3946

Stop Event

1×	node limit

Counts

288 → 246

prune167.0ms (3.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	246	5	251

Error

Counts

251 → 5

Alt Table

Status	Error	Program
✓	1.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
	13.5b	(+.f64 x (/.f64 z (/.f64 (-.f64 a t) y)))
	8.9b	(+.f64 x (/.f64 1 (/.f64 (-.f64 a t) (*.f64 y (-.f64 z t)))))
✓	1.5b	(+.f64 x (/.f64 y (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))))
✓	1.8b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))

Compiler

Compiled 5777 to 2189 computations (62.1% saved)

regimes670.0ms (12.8%)

Accuracy

Total 0.8b remaining (98.2%)

Threshold costs 0.8b (98.2%)

Counts

75 → 3

Compiler

Compiled 9119 to 6005 computations (34.1% saved)

bsearch40.0ms (0.8%)

Algorithm

2×	binary-search

Calls

2 calls:

27.0ms	y
11.0ms	y

Steps

Iters	Point		Range
1.6341701951976104e-198	∈ [	1.5788797085083375e-209	,	3.802531178479766e-198	]
-7.12267444498305e+45	∈ [	-4.969514376109458e+50	,	-7.032934410722043e+45	]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	59
1	31	59
2	36	59
3	38	59
4	39	59

Stop Event

1×

saturated

end85.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 176 to 97 computations (44.9% saved)

Details

analyze1.5s (28.8%)

sample1.2s (22.1%)

preprocess40.0ms (0.8%)

simplify21.0ms (0.4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series86.0ms (1.7%)

rewrite68.0ms (1.3%)

simplify77.0ms (1.5%)

prune181.0ms (3.5%)

localize8.0ms (0.2%)

series87.0ms (1.7%)

rewrite68.0ms (1.3%)

simplify76.0ms (1.5%)

prune175.0ms (3.3%)

localize8.0ms (0.2%)

series97.0ms (1.9%)

rewrite75.0ms (1.4%)

simplify88.0ms (1.7%)

prune185.0ms (3.5%)

localize8.0ms (0.2%)

series94.0ms (1.8%)

rewrite71.0ms (1.4%)

simplify82.0ms (1.6%)

prune167.0ms (3.2%)

regimes670.0ms (12.8%)

bsearch40.0ms (0.8%)

simplify4.0ms (0.1%)

end85.0ms (1.6%)

Profiling