Details

analyze706.0ms (10%)

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.1s (15%)

Results

985.0ms	8256×	body	128	valid
58.0ms	495×	body	128	invalid

Compiler

Compiled 40 to 24 computations (40% saved)

preprocess17.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

23×	`fma-def_binary64`
11×	`+-commutative_binary64`
6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	126
1	65	126
2	75	126
0	4	4

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 19 to 11 computations (42.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	18	18
2	22	18

Stop Event

1×

saturated

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

24.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.6b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

Compiler

Compiled 66 to 32 computations (51.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 c c (*.f64 d d))
✓	0.7b	(fma.f64 a c (*.f64 b d))
✓	24.1b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

series84.0ms (1.2%)

Counts

3 → 120

Calls

30 calls:

11.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))	a	inf
11.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))	b	-inf
10.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))	b	0
9.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))	b	inf
9.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))	a	-inf

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
271×	`prod-diff_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
164×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	203	32
2	2570	32

Stop Event

1×	node limit

Counts

3 → 94

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

597×	`associate-*l/_binary64`
518×	`fma-def_binary64`
407×	`associate-/r/_binary64`
354×	`fma-neg_binary64`
278×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1830
1	114	1710
2	356	1626
3	1797	1578

Stop Event

1×	node limit

Counts

214 → 124

prune95.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	116	8	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	8	125

Error

2.2b

Counts

125 → 8

Alt Table

Status	Error	Program
	33.4b	(.f64 (cbrt.f64 (/.f64 (fma.f64 a c (.f64 b d)) (pow.f64 (hypot.f64 c d) 2))) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 a c (*.f64 b d)) (pow.f64 (hypot.f64 c d) 2)) 2)))
	23.7b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 c (/.f64 (fma.f64 d d (.f64 c c)) a)))
	38.2b	(pow.f64 (/.f64 (sqrt.f64 (fma.f64 a c (*.f64 b d))) (hypot.f64 c d)) 2)
	25.0b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 a c (*.f64 b d)) (pow.f64 (hypot.f64 c d) 2))) 3)
	38.2b	(/.f64 a c)
▶	15.7b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))
	32.4b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	35.2b	(/.f64 b d)

Compiler

Compiled 2486 to 889 computations (64.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 c d)
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))
	0.7b	(fma.f64 a c (*.f64 b d))
✓	14.7b	(/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))

series182.0ms (2.6%)

Counts

3 → 120

Calls

30 calls:

17.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))	a	inf
15.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))	b	0
13.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))	b	-inf
13.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))	a	-inf
12.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))	b	-inf

rewrite59.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`log-prod_binary64`
254×	`prod-diff_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
189×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	245	35
2	3129	35

Stop Event

1×	node limit

Counts

3 → 124

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

560×	`times-frac_binary64`
423×	`associate-/l*_binary64`
332×	`fma-def_binary64`
297×	`cancel-sign-sub-inv_binary64`
280×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	2896
1	371	2710
2	1285	2540

Stop Event

1×	node limit

Counts

244 → 210

prune233.0ms (3.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	295	5	300
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	301	7	308

Error

0.0b

Counts

308 → 7

Alt Table

Status	Error	Program
	16.0b	(/.f64 1 (/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))))
	23.7b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 c (/.f64 (fma.f64 d d (.f64 c c)) a)))
	33.5b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	30.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
▶	15.8b	(.f64 (/.f64 1 (hypot.f64 c d)) (.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))
	43.9b	(*.f64 (/.f64 1 (hypot.f64 c d)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
	32.4b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))

Compiler

Compiled 6883 to 2545 computations (63% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 c d)) (.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))
	0.7b	(fma.f64 a c (*.f64 b d))
✓	7.1b	(.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (fma.f64 a c (.f64 b d)) (sqrt.f64 (hypot.f64 c d))))
✓	7.6b	(/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))

series270.0ms (3.8%)

Counts

3 → 128

Calls

36 calls:

14.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))	a	0
14.0ms	(.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (fma.f64 a c (.f64 b d)) (sqrt.f64 (hypot.f64 c d))))	a	-inf
14.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))	b	0
14.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))	a	inf
13.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))	a	-inf

rewrite73.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

275×	`log1p-udef_binary64`
272×	`prod-diff_binary64`
166×	`add-sqr-sqrt_binary64`
160×	`pow1_binary64`
158×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	72
1	335	56
2	4199	56

Stop Event

1×	node limit

Counts

3 → 103

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

425×	`times-frac_binary64`
422×	`fma-def_binary64`
405×	`cancel-sign-sub-inv_binary64`
331×	`associate-l_binary64`
310×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	3290
1	376	3026
2	1343	2876

Stop Event

1×	node limit

Counts

231 → 181

prune149.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	214	7	221

Error

0.0b

Counts

221 → 7

Alt Table

Status	Error	Program
	16.0b	(/.f64 1 (/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))))
	23.7b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 c (/.f64 (fma.f64 d d (.f64 c c)) a)))
	33.5b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	30.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
▶	15.8b	(/.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))
✓	15.8b	(.f64 (/.f64 1 (hypot.f64 c d)) (.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))
	43.9b	(*.f64 (/.f64 1 (hypot.f64 c d)) (neg.f64 (fma.f64 (/.f64 d c) b a)))

Compiler

Compiled 5538 to 2193 computations (60.4% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))
	0.7b	(fma.f64 a c (*.f64 b d))
✓	7.2b	(/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d))))
	7.6b	(/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))

series187.0ms (2.7%)

Counts

2 → 80

Calls

24 calls:

15.0ms	(/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d))))	c	-inf
14.0ms	(/.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))	a	0
14.0ms	(/.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))	a	-inf
14.0ms	(/.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))	b	-inf
12.0ms	(/.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))	a	inf

rewrite67.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

323×	`prod-diff_binary64`
271×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
153×	`pow1_binary64`
151×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	307	42
2	4221	42

Stop Event

1×	node limit

Counts

2 → 90

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-def_binary64`
416×	`cancel-sign-sub-inv_binary64`
285×	`associate-/r/_binary64`
240×	`associate-/l/_binary64`
197×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	3354
1	482	2921
2	2164	2796

Stop Event

1×	node limit

Counts

170 → 142

prune172.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	240	6	246

Error

0.0b

Counts

246 → 6

Alt Table

Status	Error	Program
	16.0b	(/.f64 1 (/.f64 (hypot.f64 c d) (/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))))
	23.7b	(fma.f64 (/.f64 c (fma.f64 c c (.f64 d d))) a (/.f64 d (/.f64 (fma.f64 c c (.f64 d d)) b)))
	33.5b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	30.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
✓	15.8b	(.f64 (/.f64 1 (hypot.f64 c d)) (.f64 (pow.f64 (hypot.f64 c d) -1/2) (/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))))
	43.9b	(*.f64 (/.f64 1 (hypot.f64 c d)) (neg.f64 (fma.f64 (/.f64 d c) b a)))

Compiler

Compiled 6963 to 2817 computations (59.5% saved)

regimes3.1s (44.6%)

Accuracy

Total 10.2b remaining (98.5%)

Threshold costs 0b (0%)

Counts

230 → 5

Compiler

Compiled 23753 to 14199 computations (40.2% saved)

bsearch92.0ms (1.3%)

Algorithm

4×	binary-search

Calls

4 calls:

33.0ms	c
19.0ms	c
17.0ms	c
15.0ms	c

Steps

Iters	Point		Range
7.712883155351153e+76	∈ [	1.3397102745219712e+75	,	8.387711126857237e+76	]
9.158472105652272e-177	∈ [	3.8503495947759214e-177	,	9.547987586876858e-175	]
-2.1020937544048643e-195	∈ [	-4.2676008261053727e-194	,	-2.2743482387472888e-200	]
-3.951719848587527e+140	∈ [	-2.474902145722205e+146	,	-3.1152095905255187e+140	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	111
1	43	111

Stop Event

1×

saturated

end104.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 278 to 133 computations (52.2% saved)

Details

analyze706.0ms (10%)

sample1.1s (15%)

preprocess17.0ms (0.2%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series84.0ms (1.2%)

rewrite49.0ms (0.7%)

simplify51.0ms (0.7%)

prune95.0ms (1.4%)

localize9.0ms (0.1%)

series182.0ms (2.6%)

rewrite59.0ms (0.8%)

simplify55.0ms (0.8%)

prune233.0ms (3.3%)

localize14.0ms (0.2%)

series270.0ms (3.8%)

rewrite73.0ms (1%)

simplify58.0ms (0.8%)

prune149.0ms (2.1%)

localize21.0ms (0.3%)

series187.0ms (2.7%)

rewrite67.0ms (1%)

simplify71.0ms (1%)

prune172.0ms (2.4%)

regimes3.1s (44.6%)

bsearch92.0ms (1.3%)

simplify6.0ms (0.1%)

end104.0ms (1.5%)

Profiling