Details

analyze1.3s (14.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
2.3%	94.4%	3.3%	9
3.5%	90.1%	6.4%	10
4.1%	89.5%	6.4%	11
17.1%	71.1%	11.8%	12
19.8%	64.1%	16.1%	13
21.2%	62.7%	16.1%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.4s (27%)

Results

946.0ms	6330×	body	128	valid
623.0ms	980×	body	1024	valid
255.0ms	594×	body	512	valid
215.0ms	1686×	body	128	invalid
126.0ms	216×	body	1024	invalid
107.0ms	249×	body	512	invalid
100.0ms	347×	body	256	valid
45.0ms	158×	body	256	invalid
5.0ms	5×	body	2048	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess35.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

792×	`times-frac_binary64`
358×	`fma-def_binary64`
193×	`associate-l_binary64`
167×	`associate-r_binary64`
155×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	80
1	62	64
2	94	64
3	194	64
4	482	64
5	1189	64
6	3217	64
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify23.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

522×	`unswap-sqr_binary64`
363×	`fma-def_binary64`
253×	`associate-l_binary64`
215×	`associate-r_binary64`
204×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	19	16
2	28	16
3	57	16
4	138	16
5	332	16
6	893	16
7	3314	16

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

5.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.9b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))

Compiler

Compiled 55 to 31 computations (43.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	0.0b	(/.f64 y (+.f64 y z))
✓	5.8b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series107.0ms (1.2%)

Counts

3 → 84

Calls

21 calls:

19.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))	x	0
13.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))	x	-inf
13.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))	x	inf
10.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))	y	0
6.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))	z	-inf

rewrite65.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

374×	`fma-def_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
198×	`fma-neg_binary64`
187×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	214	33
2	3333	33

Stop Event

1×	node limit

Counts

3 → 110

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

299×	`sub-neg_binary64`
272×	`fma-def_binary64`
271×	`+-commutative_binary64`
255×	`associate-+r+_binary64`
215×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	3559
1	1021	3465
2	4248	3278

Stop Event

1×	node limit

Counts

194 → 199

prune147.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	194	5	199
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	195	5	200

Error

Counts

200 → 5

Alt Table

Status	Error	Program
	6.4b	(fma.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) 2) x)
	30.5b	(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) (sqrt.f64 y)) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) (sqrt.f64 y)) x)
	11.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	1.8b	(+.f64 x (/.f64 1 y))
	32.4b	(pow.f64 (sqrt.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) 2)

Compiler

Compiled 6036 to 2736 computations (54.7% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(+.f64 x (/.f64 1 y))	x	-inf
1.0ms	(+.f64 x (/.f64 1 y))	x	0
1.0ms	(+.f64 x (/.f64 1 y))	x	inf
0.0ms	(+.f64 x (/.f64 1 y))	y	0
0.0ms	(+.f64 x (/.f64 1 y))	y	-inf

rewrite33.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
483×	`prod-diff_binary64`
112×	`log1p-udef_binary64`
64×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1692	7

Stop Event

1×	node limit

Counts

1 → 35

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	138
1	9	138

Stop Event

1×

saturated

Counts

59 → 38

prune28.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	38	5	43

Error

Counts

43 → 5

Alt Table

Status	Error	Program
	30.5b	(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) (sqrt.f64 y)) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) (sqrt.f64 y)) x)
	14.2b	(fma.f64 (cbrt.f64 (pow.f64 y -2)) (/.f64 1 (cbrt.f64 y)) x)
▶	6.4b	(fma.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) 2) x)
	11.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	1.8b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 573 to 353 computations (38.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) 2) x)
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) 2)
✓	0.5b	(cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
	5.8b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series3.4s (37.4%)

Counts

3 → 51

Calls

21 calls:

676.0ms	(fma.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) 2) x)	y	0
587.0ms	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) 2)	y	-inf
542.0ms	(fma.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) 2) x)	y	-inf
493.0ms	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) 2)	y	0
217.0ms	(cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))	y	-inf

rewrite72.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

734×	`prod-diff_binary64`
131×	`add-sqr-sqrt_binary64`
127×	`log1p-expm1-u_binary64`
127×	`expm1-log1p-u_binary64`
124×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	69
1	266	49
2	3583	49

Stop Event

1×	node limit

Counts

3 → 74

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-def_binary64`
444×	`associate-r_binary64`
337×	`associate-l_binary64`
195×	`times-frac_binary64`
192×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	476	5732
1	1612	5379

Stop Event

1×	node limit

Counts

125 → 149

prune365.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	310	0	310
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	310	5	315

Error

Counts

315 → 5

Alt Table

Status	Error	Program
	30.5b	(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) (sqrt.f64 y)) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) (sqrt.f64 y)) x)
	14.2b	(fma.f64 (cbrt.f64 (pow.f64 y -2)) (/.f64 1 (cbrt.f64 y)) x)
✓	6.4b	(fma.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) 2) x)
▶	11.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	1.8b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 18363 to 9245 computations (49.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (exp.f64 (neg.f64 z)) y)
✓	0.0b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))

series20.0ms (0.2%)

Counts

2 → 44

Calls

15 calls:

4.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))	y	inf
2.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))	z	inf
1.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)	z	inf
1.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))	z	-inf
1.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)	z	-inf

rewrite52.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

839×	`expm1-log1p-u_binary64`
766×	`prod-diff_binary64`
91×	`add-sqr-sqrt_binary64`
86×	`log1p-expm1-u_binary64`
85×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	174	15
2	2506	15

Stop Event

1×	node limit

Counts

2 → 68

simplify31.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-neg_binary64`
661×	`fma-def_binary64`
643×	`cancel-sign-sub-inv_binary64`
266×	`associate-/r/_binary64`
203×	`sub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	486
1	91	478
2	210	478
3	556	478
4	1691	472

Stop Event

1×	node limit

Counts

112 → 88

prune64.0ms (0.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	88	5	93

Error

Counts

93 → 5

Alt Table

Status	Error	Program
	30.5b	(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) (sqrt.f64 y)) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) (sqrt.f64 y)) x)
	14.2b	(fma.f64 (cbrt.f64 (pow.f64 y -2)) (/.f64 1 (cbrt.f64 y)) x)
✓	6.4b	(fma.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) 2) x)
✓	11.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	1.8b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 1170 to 467 computations (60.1% saved)

regimes567.0ms (6.3%)

Accuracy

Total 2.1b remaining (98.7%)

Threshold costs 0b (0%)

Counts

96 → 3

Compiler

Compiled 9032 to 5337 computations (40.9% saved)

bsearch3.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(+.f64 x (/.f64 (exp.f64 (*.f64 y (log.f64 (/.f64 y (+.f64 z y))))) y))
0.0ms	(+.f64 x (/.f64 (exp.f64 (*.f64 y (log.f64 (/.f64 y (+.f64 z y))))) y))

Steps

Iters	Point		Range
-8.248944571562772e-242	∈ [	-8.248944571562772e-242	,	6.15235649275633e-309	]
-4.423486912743551e+27	∈ [	-4.423486912743551e+27	,	-2.1202671201594308e+26	]

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	75
1	35	75
2	37	75
3	38	75

Stop Event

1×

saturated

end84.0ms (0.9%)

Stop Event

1×

fuel

Compiler

Compiled 191 to 100 computations (47.6% saved)

Details

analyze1.3s (14.6%)

sample2.4s (27%)

preprocess35.0ms (0.4%)

simplify23.0ms (0.3%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series107.0ms (1.2%)

rewrite65.0ms (0.7%)

simplify78.0ms (0.9%)

prune147.0ms (1.6%)

localize3.0ms (0%)

series4.0ms (0%)

rewrite33.0ms (0.4%)

simplify8.0ms (0.1%)

prune28.0ms (0.3%)

localize12.0ms (0.1%)

series3.4s (37.4%)

rewrite72.0ms (0.8%)

simplify80.0ms (0.9%)

prune365.0ms (4%)

localize5.0ms (0.1%)

series20.0ms (0.2%)

rewrite52.0ms (0.6%)

simplify31.0ms (0.3%)

prune64.0ms (0.7%)

regimes567.0ms (6.3%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end84.0ms (0.9%)

Profiling