Details

analyze1.4s (28.3%)

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)

sample1.1s (22.5%)

Results

1.0s	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)

preprocess40.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

932×	`div-sub_binary64`
494×	`fma-def_binary64`
327×	`fma-neg_binary64`
303×	`distribute-rgt-in_binary64`
262×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	176
1	109	176
2	250	154
3	611	154
4	1514	154
5	4194	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

734×	`fma-def_binary64`
533×	`div-sub_binary64`
511×	`fma-neg_binary64`
499×	`times-frac_binary64`
213×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	85	14
4	194	14
5	394	14
6	832	14
7	2375	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
▶	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	13.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series48.0ms (1%)

Counts

2 → 96

Calls

24 calls:

4.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)	x	0
3.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)	a	0
3.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)	z	0
2.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)	z	-inf
2.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)	z	inf

rewrite52.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
193×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	227	24
2	3413	24

Stop Event

1×	node limit

Counts

2 → 77

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-def_binary64`
656×	`times-frac_binary64`
494×	`cancel-sign-sub-inv_binary64`
325×	`sub-neg_binary64`
153×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	2936
1	568	2936
2	1962	2292

Stop Event

1×	node limit

Counts

173 → 153

prune110.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	150	5	155

Error

0.0b

Counts

155 → 5

Alt Table

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

Compiler

Compiled 3465 to 1214 computations (65% 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 a) (-.f64 z t))))
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	1.4b	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

series84.0ms (1.7%)

Counts

3 → 144

Calls

36 calls:

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

rewrite68.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

260×	`expm1-udef_binary64`
260×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	264	37
2	4345	37

Stop Event

1×	node limit

Counts

3 → 118

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
711×	`cancel-sign-sub-inv_binary64`
436×	`sub-neg_binary64`
210×	`associate--l+_binary64`
182×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	4438
1	702	4195
2	2428	4075

Stop Event

1×	node limit

Counts

262 → 230

prune179.0ms (3.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	227	3	230
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	229	6	235

Error

Counts

235 → 6

Alt Table

Status	Error	Program
	1.3b	(+.f64 x (.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z a) (-.f64 z t))) 2)) (cbrt.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))))
	4.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	13.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
▶	0.6b	(+.f64 x (/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))))
	0.7b	(+.f64 x (/.f64 y (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))))

Compiler

Compiled 5815 to 1957 computations (66.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series140.0ms (2.8%)

Counts

4 → 111

Calls

36 calls:

22.0ms	(/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))	t	-inf
13.0ms	(/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))	t	inf
13.0ms	(/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))	t	0
10.0ms	(/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))	y	inf
9.0ms	(/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))	y	-inf

rewrite78.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

292×	`fma-neg_binary64`
238×	`expm1-udef_binary64`
238×	`log1p-udef_binary64`
183×	`egg-rr`
129×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	241	37
2	4056	37

Stop Event

1×	node limit

Counts

4 → 183

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

619×	`associate-/l*_binary64`
506×	`associate-/r*_binary64`
270×	`associate-r_binary64`
190×	`associate--l+_binary64`
181×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	413	5355
1	1610	5149

Stop Event

1×	node limit

Counts

294 → 300

prune281.0ms (5.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	300	6	306

Error

Counts

306 → 6

Alt Table

Status	Error	Program
	1.3b	(+.f64 x (.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z a) (-.f64 z t))) 2)) (cbrt.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))))
	4.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	13.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
✓	0.6b	(+.f64 x (/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))))
▶	0.7b	(+.f64 x (/.f64 y (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))))

Compiler

Compiled 9784 to 3967 computations (59.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))))
✓	0.0b	(/.f64 1 (-.f64 z t))
✓	0.3b	(*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))
✓	1.4b	(/.f64 y (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t))))

series94.0ms (1.9%)

Counts

4 → 168

Calls

42 calls:

6.0ms	(/.f64 y (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t))))	z	inf
5.0ms	(+.f64 x (/.f64 y (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))))	t	0
4.0ms	(+.f64 x (/.f64 y (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))))	x	inf
3.0ms	(+.f64 x (/.f64 y (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))))	z	0
3.0ms	(*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))	z	-inf

rewrite72.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

276×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
147×	`add-cbrt-cube_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	297	44
2	4515	44

Stop Event

1×	node limit

Counts

4 → 143

simplify89.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

848×	`times-frac_binary64`
711×	`cancel-sign-sub-inv_binary64`
445×	`sub-neg_binary64`
210×	`associate--l+_binary64`
196×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	4930
1	761	4669
2	2620	4549

Stop Event

1×	node limit

Counts

311 → 268

prune206.0ms (4.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	268	6	274

Error

Counts

274 → 6

Alt Table

Status	Error	Program
	1.3b	(+.f64 x (.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) (pow.f64 (cbrt.f64 (/.f64 (-.f64 z a) (-.f64 z t))) 2)) (cbrt.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))))
	4.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	13.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
✓	0.6b	(+.f64 x (/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))))
✓	0.7b	(+.f64 x (/.f64 y (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))))

Compiler

Compiled 6489 to 2294 computations (64.6% saved)

regimes539.0ms (10.9%)

Accuracy

Total 1.1b remaining (99.5%)

Threshold costs 0b (0%)

Counts

90 → 1

Compiler

Compiled 9977 to 6575 computations (34.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	17	22
2	27	22
3	33	22
4	37	22
5	38	22

Stop Event

1×

saturated

end81.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 158 to 94 computations (40.5% saved)

Details

analyze1.4s (28.3%)

sample1.1s (22.5%)

preprocess40.0ms (0.8%)

simplify21.0ms (0.4%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series48.0ms (1%)

rewrite52.0ms (1.1%)

simplify54.0ms (1.1%)

prune110.0ms (2.2%)

localize7.0ms (0.1%)

series84.0ms (1.7%)

rewrite68.0ms (1.4%)

simplify78.0ms (1.6%)

prune179.0ms (3.6%)

localize8.0ms (0.2%)

series140.0ms (2.8%)

rewrite78.0ms (1.6%)

simplify75.0ms (1.5%)

prune281.0ms (5.7%)

localize8.0ms (0.2%)

series94.0ms (1.9%)

rewrite72.0ms (1.5%)

simplify89.0ms (1.8%)

prune206.0ms (4.2%)

regimes539.0ms (10.9%)

simplify3.0ms (0.1%)

end81.0ms (1.6%)

Profiling