Details

analyze15.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.2s (39.3%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify32.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
469×	`fma-neg_binary64`
365×	`sub-neg_binary64`
282×	`unsub-neg_binary64`
267×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	24	20
2	58	20
3	138	20
4	328	20
5	848	20
6	2017	20
7	4713	20

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

18.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	18.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
	19.0b	(.f64 (+.f64 x y) (/.f64 (-.f64 x y) (fma.f64 x x (.f64 y y))))

Compiler

Compiled 97 to 46 computations (52.6% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	18.3b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series22.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
7.0ms	(+.f64 (.f64 x x) (.f64 y y))

rewrite60.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

648×	`fma-def_binary64`
273×	`fma-neg_binary64`
211×	`expm1-udef_binary64`
211×	`log1p-udef_binary64`
121×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	237	26
2	3839	26

Stop Event

1×	node limit

Counts

2 → 93

Calls

2 calls:

57.0ms	(+.f64 (.f64 x x) (.f64 y y))
57.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

simplify30.0ms (1%)

Algorithm

1×	egg-herbie

Rules

526×	`associate-*l/_binary64`
422×	`associate-*r/_binary64`
387×	`fma-def_binary64`
331×	`cancel-sign-sub-inv_binary64`
306×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	738
1	111	678
2	333	642
3	1312	609

Stop Event

1×	node limit

Counts

141 → 112

prune72.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Error

0.0b

Counts

114 → 4

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	18.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
	44.8b	(fma.f64 2 (*.f64 (/.f64 y x) (-.f64 (pow.f64 (/.f64 y x) 3) (/.f64 y x))) 1)
	18.3b	(fma.f64 (/.f64 x y) (/.f64 (*.f64 2 x) y) -1)

Compiler

Compiled 2234 to 893 computations (60% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x y)
✓	0.0b	(/.f64 (-.f64 x y) (hypot.f64 x y))
✓	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

series48.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

21.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
11.0ms	(hypot.f64 x y)
8.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
8.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))

rewrite115.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
279×	`egg-rr`
112×	`add-sqr-sqrt_binary64`
106×	`log1p-expm1-u_binary64`
106×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	46
1	214	43
2	3520	43

Stop Event

1×	node limit

Counts

4 → 279

Calls

4 calls:

104.0ms	(hypot.f64 x y)
104.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
104.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
104.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

simplify60.0ms (2%)

Algorithm

1×	egg-herbie

Rules

553×	`times-frac_binary64`
372×	`fma-def_binary64`
296×	`associate-/l*_binary64`
286×	`cancel-sign-sub-inv_binary64`
270×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1812
1	388	1722
2	1344	1606

Stop Event

1×	node limit

Counts

375 → 369

prune305.0ms (10.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	416	2	418
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	418	4	422

Error

Counts

422 → 4

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))
	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	44.8b	(fma.f64 2 (*.f64 (/.f64 y x) (-.f64 (pow.f64 (/.f64 y x) 3) (/.f64 y x))) 1)
	18.3b	(fma.f64 (/.f64 x y) (/.f64 (*.f64 2 x) y) -1)

Compiler

Compiled 15105 to 3921 computations (74% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 x y)
✓	0.0b	(/.f64 (hypot.f64 x y) (-.f64 x y))
✓	0.0b	(*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y))
✓	0.0b	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))

series39.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

22.0ms	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))
9.0ms	(*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y))
8.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))

rewrite66.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`prod-diff_binary64`
200×	`log1p-udef_binary64`
110×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`
104×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	48
1	210	42
2	3295	42

Stop Event

1×	node limit

Counts

3 → 100

Calls

3 calls:

64.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))
64.0ms	(*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y))
64.0ms	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))

simplify52.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

921×	`fma-neg_binary64`
434×	`times-frac_binary64`
258×	`fma-def_binary64`
223×	`associate-/l*_binary64`
203×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1233
1	276	1185
2	933	1102
3	4383	1089

Stop Event

1×	node limit

Counts

172 → 153

prune158.0ms (5.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	251	4	255

Error

Counts

255 → 4

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	44.8b	(fma.f64 2 (*.f64 (/.f64 y x) (-.f64 (pow.f64 (/.f64 y x) 3) (/.f64 y x))) 1)
	18.3b	(fma.f64 (/.f64 x y) (/.f64 (*.f64 2 x) y) -1)

Compiler

Compiled 5352 to 2072 computations (61.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 x y) (hypot.f64 x y))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))
✓	1.9b	(log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))

series48.0ms (1.6%)

Counts

3 → 72

Calls

3 calls:

20.0ms

(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))

14.0ms

(expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))

14.0ms

(log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))

rewrite66.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

975×	`prod-diff_binary64`
118×	`add-sqr-sqrt_binary64`
116×	`egg-rr`
114×	`expm1-log1p-u_binary64`
113×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	231	41
2	3536	41

Stop Event

1×	node limit

Counts

3 → 116

Calls

3 calls:

63.0ms

(expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))

63.0ms

(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))

63.0ms

(log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))

simplify36.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

481×	`times-frac_binary64`
297×	`fma-def_binary64`
282×	`cancel-sign-sub-inv_binary64`
254×	`associate-/r*_binary64`
254×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1448
1	362	1410
2	1283	1298

Stop Event

1×	node limit

Counts

188 → 179

prune248.0ms (8.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	379	1	380
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	380	4	384

Error

Counts

384 → 4

Alt Table

Status	Error	Program
	44.0b	(fma.f64 (/.f64 (/.f64 y (/.f64 x y)) x) -2 1)
✓	0.0b	(/.f64 (+.f64 x y) (*.f64 (/.f64 (hypot.f64 x y) (-.f64 x y)) (hypot.f64 x y)))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	18.3b	(fma.f64 (/.f64 x y) (/.f64 (*.f64 2 x) y) -1)

Compiler

Compiled 14620 to 3539 computations (75.8% saved)

regimes206.0ms (7%)

Accuracy

Total 0.0b remaining (67.4%)

Threshold costs 0.0b (67.4%)

Counts

79 → 1

Compiler

Compiled 3688 to 2216 computations (39.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	12	22
2	17	22
3	19	22
4	20	22

Stop Event

1×

saturated

end63.0ms (2.1%)

Compiler: Compiled 94 to 50 computations (46.8% saved)

Details

analyze15.0ms (0.5%)

sample1.2s (39.3%)

simplify32.0ms (1.1%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series22.0ms (0.7%)

rewrite60.0ms (2%)

simplify30.0ms (1%)

prune72.0ms (2.5%)

localize8.0ms (0.3%)

series48.0ms (1.6%)

rewrite115.0ms (3.9%)

simplify60.0ms (2%)

prune305.0ms (10.4%)

localize9.0ms (0.3%)

series39.0ms (1.3%)

rewrite66.0ms (2.2%)

simplify52.0ms (1.8%)

prune158.0ms (5.4%)

localize11.0ms (0.4%)

series48.0ms (1.6%)

rewrite66.0ms (2.2%)

simplify36.0ms (1.2%)

prune248.0ms (8.5%)

regimes206.0ms (7%)

simplify2.0ms (0.1%)

end63.0ms (2.1%)

Profiling