Details

analyze717.0ms (8.6%)

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)

sample1.0s (12.6%)

Results

973.0ms	8256×	body	128	valid
61.0ms	495×	body	128	invalid

Compiler

Compiled 40 to 24 computations (40% saved)

preprocess16.0ms (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

prune6.0ms (0.1%)

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)

localize8.0ms (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)))

series79.0ms (1%)

Counts

3 → 120

Calls

30 calls:

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

rewrite48.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	203	32
2	2589	32

Stop Event

1×	node limit

Counts

3 → 94

simplify55.0ms (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

prune89.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	7	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Error

2.2b

Counts

125 → 7

Alt Table

Status	Error	Program
	46.7b	(/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a c) 3) (pow.f64 (.f64 b d) 3)) (fma.f64 (.f64 a c) (.f64 a c) (-.f64 (pow.f64 (.f64 b d) 2) (.f64 (.f64 a c) (.f64 b d))))) (fma.f64 c c (*.f64 d d)))
	38.2b	(/.f64 a c)
	35.2b	(/.f64 b 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)))
	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)
▶	15.7b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))

Compiler

Compiled 2478 to 871 computations (64.9% 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))

series171.0ms (2.1%)

Counts

3 → 120

Calls

30 calls:

14.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))	b	0
12.0ms	(/.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	0
12.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))	b	-inf
11.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))	a	-inf

rewrite60.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	246	35
2	3155	35

Stop Event

1×	node limit

Counts

3 → 124

simplify59.0ms (0.7%)

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

prune240.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	294	6	300
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	301	6	307

Error

0.0b

Counts

307 → 6

Alt Table

Status	Error	Program
	20.6b	(.f64 (/.f64 1 (hypot.f64 c d)) (.f64 (cbrt.f64 (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d))) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)) 2))))
	22.1b	(fma.f64 (/.f64 d (fma.f64 d d (.f64 c c))) b (/.f64 a (/.f64 (fma.f64 d d (.f64 c c)) c)))
	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))
	43.9b	(*.f64 (/.f64 1 (hypot.f64 c d)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
▶	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)))))

Compiler

Compiled 6885 to 2540 computations (63.1% 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)))

series273.0ms (3.3%)

Counts

3 → 128

Calls

36 calls:

16.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))	b	-inf
15.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))	a	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	0
14.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (sqrt.f64 (hypot.f64 c d)))	a	inf
13.0ms	(.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)))))	b	-inf

rewrite68.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

275×	`log1p-udef_binary64`
272×	`prod-diff_binary64`
161×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	72
1	335	56
2	4203	56

Stop Event

1×	node limit

Counts

3 → 103

simplify60.0ms (0.7%)

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

prune228.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	214	6	220

Error

0.0b

Counts

220 → 6

Alt Table

Status	Error	Program
▶	20.6b	(.f64 (/.f64 1 (hypot.f64 c d)) (.f64 (cbrt.f64 (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d))) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)) 2))))
	22.1b	(fma.f64 (/.f64 d (fma.f64 d d (.f64 c c))) b (/.f64 a (/.f64 (fma.f64 d d (.f64 c c)) c)))
	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))
	43.9b	(*.f64 (/.f64 1 (hypot.f64 c d)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
✓	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)))))

Compiler

Compiled 5518 to 2175 computations (60.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (/.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))
✓	22.0b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d)) 2))

series334.0ms (4%)

Counts

2 → 64

Calls

24 calls:

45.0ms	(cbrt.f64 (/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d)))	c	-inf
35.0ms	(cbrt.f64 (/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d)))	d	-inf
33.0ms	(cbrt.f64 (/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d)))	a	0
27.0ms	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d)) 2))	c	inf
25.0ms	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d)) 2))	d	inf

rewrite48.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

591×	`log-prod_binary64`
245×	`prod-diff_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
208×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	263	35
2	3124	35

Stop Event

1×	node limit

Counts

2 → 66

simplify113.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

578×	`associate-r_binary64`
476×	`associate-l_binary64`
380×	`fma-def_binary64`
208×	`associate-/r*_binary64`
200×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	396	7071
1	1407	6808

Stop Event

1×	node limit

Counts

130 → 146

prune328.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	382	0	382
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	382	6	388

Error

0.0b

Counts

388 → 6

Alt Table

Status	Error	Program
✓	20.6b	(.f64 (/.f64 1 (hypot.f64 c d)) (.f64 (cbrt.f64 (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d))) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)) 2))))
	22.1b	(fma.f64 (/.f64 d (fma.f64 d d (.f64 c c))) b (/.f64 a (/.f64 (fma.f64 d d (.f64 c c)) c)))
	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))
	43.9b	(*.f64 (/.f64 1 (hypot.f64 c d)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
✓	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)))))

Compiler

Compiled 18674 to 7720 computations (58.7% saved)

regimes4.0s (48.2%)

Accuracy

Total 10.2b remaining (98.4%)

Threshold costs 0b (0%)

Counts

282 → 5

Compiler

Compiled 31418 to 18699 computations (40.5% saved)

bsearch88.0ms (1.1%)

Algorithm

4×	binary-search

Calls

4 calls:

25.0ms	c
20.0ms	c
18.0ms	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

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	121
1	49	119
2	52	119
3	58	119
4	63	119
5	68	119
6	70	119

Stop Event

1×

saturated

end111.0ms (1.3%)

Stop Event

1×

fuel

Compiler

Compiled 301 to 142 computations (52.8% saved)

Details

analyze717.0ms (8.6%)

sample1.0s (12.6%)

preprocess16.0ms (0.2%)

simplify6.0ms (0.1%)

prune6.0ms (0.1%)

localize8.0ms (0.1%)

series79.0ms (1%)

rewrite48.0ms (0.6%)

simplify55.0ms (0.7%)

prune89.0ms (1.1%)

localize9.0ms (0.1%)

series171.0ms (2.1%)

rewrite60.0ms (0.7%)

simplify59.0ms (0.7%)

prune240.0ms (2.9%)

localize14.0ms (0.2%)

series273.0ms (3.3%)

rewrite68.0ms (0.8%)

simplify60.0ms (0.7%)

prune228.0ms (2.7%)

localize16.0ms (0.2%)

series334.0ms (4%)

rewrite48.0ms (0.6%)

simplify113.0ms (1.4%)

prune328.0ms (3.9%)

regimes4.0s (48.2%)

bsearch88.0ms (1.1%)

simplify6.0ms (0.1%)

end111.0ms (1.3%)

Profiling