Details

analyze1.5s (25.8%)

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
12.9%	86.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (20.8%)

Results

1.1s	8255×	body	128	valid
90.0ms	725×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess38.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

940×	`div-sub_binary64`
392×	`fma-def_binary64`
305×	`distribute-rgt-in_binary64`
264×	`distribute-lft-in_binary64`
256×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	176
1	138	154
2	294	154
3	617	154
4	1469	154
5	3950	154
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify23.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

575×	`div-sub_binary64`
522×	`times-frac_binary64`
522×	`fma-neg_binary64`
259×	`fma-def_binary64`
198×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	44	14
3	88	14
4	193	14
5	384	14
6	898	14
7	2363	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a z)) x)

Compiler

Compiled 56 to 32 computations (42.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a z))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a z)) x)

series55.0ms (1%)

Counts

2 → 96

Calls

24 calls:

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

rewrite80.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
192×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	226	24
2	3371	24

Stop Event

1×	node limit

Counts

2 → 77

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

771×	`fma-def_binary64`
652×	`times-frac_binary64`
495×	`cancel-sign-sub-inv_binary64`
324×	`sub-neg_binary64`
153×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2928
1	568	2919
2	1954	2272

Stop Event

1×	node limit

Counts

173 → 153

prune113.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	149	5	154

Error

0.0b

Counts

154 → 5

Alt Table

Status	Error	Program
	26.4b	(+.f64 y (+.f64 x (*.f64 (/.f64 y z) (-.f64 a t))))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a z)) x)
	52.5b	(/.f64 y (/.f64 (-.f64 a z) t))
▶	4.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))
	13.6b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 y z) (-.f64 a z)))

Compiler

Compiled 3471 to 1201 computations (65.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))
✓	0.0b	(/.f64 y (-.f64 a z))
✓	11.7b	(*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z))

series101.0ms (1.8%)

Counts

3 → 132

Calls

36 calls:

9.0ms	(*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z))	t	-inf
6.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))	x	-inf
6.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))	t	0
4.0ms	(*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z))	y	inf
3.0ms	(*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z))	a	-inf

rewrite69.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

539×	`fma-def_binary64`
258×	`fma-neg_binary64`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	254	34
2	3913	34

Stop Event

1×	node limit

Counts

3 → 134

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
685×	`times-frac_binary64`
538×	`cancel-sign-sub-inv_binary64`
277×	`sub-neg_binary64`
149×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	3945
1	627	3837
2	1948	3086

Stop Event

1×	node limit

Counts

266 → 233

prune176.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	231	7	238

Error

0.0b

Counts

238 → 7

Alt Table

Status	Error	Program
	26.4b	(+.f64 y (+.f64 x (*.f64 (/.f64 y z) (-.f64 a t))))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a z)) x)
▶	0.6b	(+.f64 x (/.f64 y (/.f64 (-.f64 a z) (-.f64 t z))))
	4.8b	(+.f64 x (.f64 (.f64 y (/.f64 1 (-.f64 a z))) (-.f64 t z)))
✓	4.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))
	13.6b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 y z) (-.f64 a z)))
	13.2b	(fma.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 a z)) 2)) (*.f64 (cbrt.f64 (/.f64 y (-.f64 a z))) (-.f64 t z)) x)

Compiler

Compiled 5421 to 1752 computations (67.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 a z) (-.f64 t z))))
✓	0.0b	(/.f64 (-.f64 a z) (-.f64 t z))
✓	1.4b	(/.f64 y (/.f64 (-.f64 a z) (-.f64 t z)))

series96.0ms (1.7%)

Counts

3 → 144

Calls

36 calls:

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

rewrite72.0ms (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

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
708×	`cancel-sign-sub-inv_binary64`
431×	`sub-neg_binary64`
214×	`associate--l+_binary64`
182×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	4429
1	716	4243
2	2440	3934

Stop Event

1×	node limit

Counts

262 → 230

prune192.0ms (3.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	226	4	230
Fresh	4	0	4
Picked	1	0	1
Done	0	2	2
Total	231	6	237

Error

Counts

237 → 6

Alt Table

Status	Error	Program
	0.7b	(+.f64 x (/.f64 y (*.f64 (-.f64 a z) (/.f64 1 (-.f64 t z)))))
▶	0.6b	(+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 z (-.f64 t z)))))
	0.8b	(+.f64 x (/.f64 y (pow.f64 (/.f64 (-.f64 t z) (-.f64 a z)) -1)))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a z)) x)
	1.3b	(+.f64 x (.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) (pow.f64 (cbrt.f64 (/.f64 (-.f64 a z) (-.f64 t z))) 2)) (cbrt.f64 (.f64 y (/.f64 (-.f64 t z) (-.f64 a z))))))
✓	4.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))

Compiler

Compiled 5751 to 1904 computations (66.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 z (-.f64 t z)))))
✓	0.0b	(-.f64 (/.f64 a (-.f64 t z)) (/.f64 z (-.f64 t z)))
✓	0.0b	(/.f64 z (-.f64 t z))
✓	1.4b	(/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 z (-.f64 t z))))

series233.0ms (4.1%)

Counts

4 → 147

Calls

42 calls:

20.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 z (-.f64 t z)))))	t	inf
17.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 z (-.f64 t z)))))	t	-inf
16.0ms	(/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 z (-.f64 t z))))	t	-inf
14.0ms	(/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 z (-.f64 t z))))	y	-inf
14.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 z (-.f64 t z)))))	t	0

rewrite83.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

284×	`log1p-udef_binary64`
169×	`egg-rr`
154×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	289	46
2	4829	46

Stop Event

1×	node limit

Counts

4 → 169

simplify101.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

686×	`associate-/l*_binary64`
558×	`associate-/r*_binary64`
292×	`fma-def_binary64`
210×	`+-commutative_binary64`
186×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	557	8412
1	2238	7980

Stop Event

1×	node limit

Counts

316 → 323

prune322.0ms (5.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	323	6	329

Error

Counts

329 → 6

Alt Table

Status	Error	Program
	0.7b	(+.f64 x (/.f64 y (*.f64 (-.f64 a z) (/.f64 1 (-.f64 t z)))))
✓	0.6b	(+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 z (-.f64 t z)))))
	0.8b	(+.f64 x (/.f64 y (pow.f64 (/.f64 (-.f64 t z) (-.f64 a z)) -1)))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a z)) x)
	1.3b	(+.f64 x (.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) (pow.f64 (cbrt.f64 (/.f64 (-.f64 a z) (-.f64 t z))) 2)) (cbrt.f64 (.f64 y (/.f64 (-.f64 t z) (-.f64 a z))))))
✓	4.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))

Compiler

Compiled 12824 to 5368 computations (58.1% saved)

regimes934.0ms (16.5%)

Accuracy

Total 1.1b remaining (98.8%)

Threshold costs 0b (0%)

Counts

123 → 1

Compiler

Compiled 16307 to 10643 computations (34.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	17	22
2	26	22
3	30	22
4	32	22

Stop Event

1×

saturated

end92.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 160 to 96 computations (40% saved)

Details

analyze1.5s (25.8%)

sample1.2s (20.8%)

preprocess38.0ms (0.7%)

simplify23.0ms (0.4%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series55.0ms (1%)

rewrite80.0ms (1.4%)

simplify63.0ms (1.1%)

prune113.0ms (2%)

localize7.0ms (0.1%)

series101.0ms (1.8%)

rewrite69.0ms (1.2%)

simplify69.0ms (1.2%)

prune176.0ms (3.1%)

localize7.0ms (0.1%)

series96.0ms (1.7%)

rewrite72.0ms (1.3%)

simplify79.0ms (1.4%)

prune192.0ms (3.4%)

localize8.0ms (0.1%)

series233.0ms (4.1%)

rewrite83.0ms (1.5%)

simplify101.0ms (1.8%)

prune322.0ms (5.7%)

regimes934.0ms (16.5%)

simplify3.0ms (0%)

end92.0ms (1.6%)

Profiling