Details

analyze32.0ms (1%)

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)

sample1.1s (35.6%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 56 to 34 computations (39.3% saved)

preprocess43.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

772×	`fma-def_binary64`
588×	`div-sub_binary64`
352×	`unsub-neg_binary64`
194×	`cancel-sign-sub-inv_binary64`
190×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	43	40
2	103	40
3	250	40
4	569	40
5	1563	40
6	3472	40
7	4656	40
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 17 to 9 computations (47.1% saved)

simplify30.0ms (0.9%)

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

19.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	19.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
	20.5b	(.f64 (+.f64 x y) (/.f64 (-.f64 x y) (fma.f64 x x (.f64 y y))))

Compiler

Compiled 97 to 46 computations (52.6% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	19.6b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series14.0ms (0.4%)

Counts

1 → 24

Calls

6 calls:

3.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))	y	-inf
2.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))	x	0
2.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))	y	0
2.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))	x	-inf
2.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))	x	inf

rewrite52.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	237	19
2	3893	19

Stop Event

1×	node limit

Counts

1 → 46

simplify30.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

527×	`associate-*l/_binary64`
424×	`associate-*r/_binary64`
378×	`fma-def_binary64`
331×	`cancel-sign-sub-inv_binary64`
306×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	534
1	109	510
2	327	474
3	1307	441

Stop Event

1×	node limit

Counts

70 → 60

prune49.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	58	4	62

Error

Counts

62 → 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)))
	41.9b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -2 1)
	21.4b	(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
	20.3b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3))

Compiler

Compiled 1257 to 567 computations (54.9% saved)

localize8.0ms (0.2%)

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 (1.5%)

Counts

4 → 96

Calls

24 calls:

4.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))	y	-inf
4.0ms	(hypot.f64 x y)	x	0
4.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))	x	0
3.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))	x	-inf
3.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))	y	0

rewrite151.0ms (4.8%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
179×	`egg-rr`
114×	`add-sqr-sqrt_binary64`
113×	`pow1_binary64`
112×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	46
1	214	43
2	3523	43

Stop Event

1×	node limit

Counts

4 → 279

simplify55.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

553×	`times-frac_binary64`
374×	`fma-def_binary64`
296×	`associate-/l*_binary64`
286×	`cancel-sign-sub-inv_binary64`
268×	`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

prune291.0ms (9.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	417	1	418
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	418	4	422

Error

Counts

422 → 4

Alt Table

Status	Error	Program
	21.4b	(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
▶	0.0b	(/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (hypot.f64 x y) (+.f64 x y)))
	20.3b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 15096 to 4124 computations (72.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series29.0ms (0.9%)

Counts

2 → 48

Calls

12 calls:

5.0ms	(/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (hypot.f64 x y) (+.f64 x y)))	y	inf
3.0ms	(/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (hypot.f64 x y) (+.f64 x y)))	x	0
3.0ms	(/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (hypot.f64 x y) (+.f64 x y)))	x	-inf
3.0ms	(/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (hypot.f64 x y) (+.f64 x y)))	y	0
3.0ms	(/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (hypot.f64 x y) (+.f64 x y)))	y	-inf

rewrite61.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

832×	`prod-diff_binary64`
118×	`add-sqr-sqrt_binary64`
117×	`pow1_binary64`
116×	`*-un-lft-identity_binary64`
110×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	219	29
2	3695	29

Stop Event

1×	node limit

Counts

2 → 91

simplify45.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

939×	`fma-neg_binary64`
387×	`times-frac_binary64`
246×	`unswap-sqr_binary64`
204×	`sub-neg_binary64`
186×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	924
1	200	876
2	692	822
3	3475	752

Stop Event

1×	node limit

Counts

139 → 127

prune316.0ms (9.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	426	0	426
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	426	4	430

Error

Counts

430 → 4

Alt Table

Status	Error	Program
	21.4b	(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
✓	0.0b	(/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (hypot.f64 x y) (+.f64 x y)))
▶	20.3b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 15501 to 4274 computations (72.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3)
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3))
✓	0.0b	(/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y)))
✓	19.4b	(/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))

series93.0ms (2.9%)

Counts

4 → 96

Calls

24 calls:

18.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3))	x	-inf
8.0ms	(pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3)	x	0
6.0ms	(pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3)	y	inf
5.0ms	(pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3)	x	-inf
5.0ms	(pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3)	y	0

rewrite97.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

237×	`expm1-udef_binary64`
237×	`log1p-udef_binary64`
181×	`fma-neg_binary64`
143×	`add-sqr-sqrt_binary64`
139×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	73
1	305	73
2	4122	73

Stop Event

1×	node limit

Counts

4 → 240

simplify89.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

604×	`times-frac_binary64`
276×	`associate-/l*_binary64`
273×	`sub-neg_binary64`
261×	`associate-/r*_binary64`
205×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1938
1	297	1858
2	941	1770
3	4598	1770

Stop Event

1×	node limit

Counts

336 → 216

prune165.0ms (5.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	216	4	220

Error

Counts

220 → 4

Alt Table

Status	Error	Program
	21.4b	(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
✓	0.0b	(/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (hypot.f64 x y) (+.f64 x y)))
✓	20.3b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) 3))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 5294 to 2577 computations (51.3% saved)

regimes251.0ms (7.9%)

Accuracy

Total 0.0b remaining (56%)

Threshold costs 0.0b (56%)

Counts

93 → 1

Compiler

Compiled 4257 to 2680 computations (37% 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

end68.0ms (2.1%)

Stop Event

1×

fuel

Compiler

Compiled 104 to 54 computations (48.1% saved)

Details

analyze32.0ms (1%)

sample1.1s (35.6%)

preprocess43.0ms (1.3%)

simplify30.0ms (0.9%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series14.0ms (0.4%)

rewrite52.0ms (1.6%)

simplify30.0ms (0.9%)

prune49.0ms (1.5%)

localize8.0ms (0.2%)

series48.0ms (1.5%)

rewrite151.0ms (4.8%)

simplify55.0ms (1.7%)

prune291.0ms (9.1%)

localize7.0ms (0.2%)

series29.0ms (0.9%)

rewrite61.0ms (1.9%)

simplify45.0ms (1.4%)

prune316.0ms (9.9%)

localize10.0ms (0.3%)

series93.0ms (2.9%)

rewrite97.0ms (3%)

simplify89.0ms (2.8%)

prune165.0ms (5.2%)

regimes251.0ms (7.9%)

simplify2.0ms (0.1%)

end68.0ms (2.1%)

Profiling