Details

analyze575.0ms (16.1%)

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%	81.1%	18.9%	7
6.2%	74.9%	18.9%	8
9.4%	65.5%	25.1%	9
15.6%	48.4%	36%	10
20.3%	43.1%	36.6%	11
22.6%	36%	41.4%	12
27.1%	25.1%	47.8%	13
29.5%	22.5%	48%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (34.9%)

Results

966.0ms	8256×	body	128	valid
269.0ms	2617×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess41.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

953×	`fma-def_binary64`
371×	`distribute-rgt-in_binary64`
269×	`unsub-neg_binary64`
250×	`sub-neg_binary64`
215×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	60
1	56	60
2	93	60
3	200	60
4	499	60
5	1448	60
6	3546	60
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify27.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-def_binary64`
584×	`fma-neg_binary64`
283×	`distribute-rgt-in_binary64`
228×	`sub-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	19	15
2	31	15
3	60	15
4	134	15
5	383	15
6	833	15
7	1633	15
8	3632	15

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

24.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.4b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	3.2b	(-.f64 (.f64 y y) (.f64 z z))
✓	25.1b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series52.0ms (1.5%)

Counts

3 → 84

Calls

21 calls:

6.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))	x	0
5.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))	x	-inf
5.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))	z	inf
4.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))	x	inf
4.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))	y	0

rewrite77.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`prod-diff_binary64`
406×	`fma-def_binary64`
256×	`egg-rr`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	37
1	198	37
2	2650	35

Stop Event

1×	node limit

Counts

3 → 256

simplify51.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

714×	`associate-/l*_binary64`
585×	`associate-/r*_binary64`
470×	`fma-def_binary64`
264×	`cancel-sign-sub-inv_binary64`
176×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	1894
1	434	1872
2	1592	1838

Stop Event

1×	node limit

Counts

340 → 342

prune177.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	340	2	342
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	340	3	343

Error

0.2b

Counts

343 → 3

Alt Table

Status	Error	Program
	31.0b	(fma.f64 y x (*.f64 (/.f64 -1/2 (/.f64 (/.f64 y z) z)) x))
✓	24.4b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
▶	28.1b	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))

Compiler

Compiled 7981 to 3043 computations (61.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))
✓	0.1b	(*.f64 (/.f64 z y) z)

series39.0ms (1.1%)

Counts

2 → 60

Calls

15 calls:

7.0ms	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))	x	-inf
4.0ms	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))	x	0
4.0ms	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))	x	inf
3.0ms	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))	y	-inf
2.0ms	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))	y	0

rewrite49.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

888×	`log1p-expm1-u_binary64`
888×	`expm1-log1p-u_binary64`
151×	`prod-diff_binary64`
105×	`add-sqr-sqrt_binary64`
96×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	208	21
2	2690	21

Stop Event

1×	node limit

Counts

2 → 41

simplify39.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

570×	`distribute-rgt-neg-in_binary64`
510×	`distribute-lft-neg-in_binary64`
457×	`fma-def_binary64`
437×	`associate-/l/_binary64`
335×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	705
1	45	705
2	99	705
3	215	705
4	601	705
5	2464	705

Stop Event

1×	node limit

Counts

101 → 50

prune26.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	50	3	53

Error

0.2b

Counts

53 → 3

Alt Table

Status	Error	Program
▶	31.0b	(fma.f64 y x (*.f64 (/.f64 -1/2 (/.f64 (/.f64 y z) z)) x))
✓	24.4b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	28.1b	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))

Compiler

Compiled 695 to 335 computations (51.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 y z) z)
✓	0.6b	(/.f64 -1/2 (/.f64 (/.f64 y z) z))
✓	3.7b	(*.f64 (/.f64 -1/2 (/.f64 (/.f64 y z) z)) x)

series70.0ms (1.9%)

Counts

3 → 84

Calls

21 calls:

10.0ms	(/.f64 (/.f64 y z) z)	z	0
7.0ms	(/.f64 (/.f64 y z) z)	y	-inf
6.0ms	(/.f64 (/.f64 y z) z)	y	inf
6.0ms	(/.f64 (/.f64 y z) z)	y	0
4.0ms	(*.f64 (/.f64 -1/2 (/.f64 (/.f64 y z) z)) x)	x	0

rewrite54.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`log-prod_binary64`
187×	`log-div_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`
160×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	200	30
2	2806	30

Stop Event

1×	node limit

Counts

3 → 103

simplify97.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

697×	`associate-/r/_binary64`
438×	`associate-/l/_binary64`
313×	`*-commutative_binary64`
293×	`associate-l_binary64`
257×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	876
1	27	876
2	59	876
3	148	876
4	483	876
5	1835	876
6	3469	876
7	3951	876
8	4135	876
9	4339	876
10	4552	876
11	4821	876

Stop Event

1×	node limit

Counts

187 → 109

prune52.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	109	3	112

Error

0.2b

Counts

112 → 3

Alt Table

Status	Error	Program
✓	31.0b	(fma.f64 y x (*.f64 (/.f64 -1/2 (/.f64 (/.f64 y z) z)) x))
✓	24.4b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	28.1b	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))

Compiler

Compiled 1834 to 829 computations (54.8% saved)

regimes543.0ms (15.2%)

Accuracy

Total 0.2b remaining (50.3%)

Threshold costs 0.2b (50.3%)

Counts

33 → 2

Compiler

Compiled 3334 to 2324 computations (30.3% saved)

bsearch279.0ms (7.8%)

Algorithm

1×	binary-search

Calls

1 calls:

278.0ms

Steps

Iters	Point		Range
-7.238217623544146e-284	∈ [	-6.973815285744073e-253	,	-4.128868923005719e-284	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-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	20	39
1	27	39
2	29	39
3	30	39

Stop Event

1×

saturated

end52.0ms (1.5%)

Stop Event

1×

done

Compiler

Compiled 102 to 62 computations (39.2% saved)

Details

analyze575.0ms (16.1%)

sample1.2s (34.9%)

preprocess41.0ms (1.1%)

simplify27.0ms (0.7%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series52.0ms (1.5%)

rewrite77.0ms (2.1%)

simplify51.0ms (1.4%)

prune177.0ms (4.9%)

localize7.0ms (0.2%)

series39.0ms (1.1%)

rewrite49.0ms (1.4%)

simplify39.0ms (1.1%)

prune26.0ms (0.7%)

localize9.0ms (0.2%)

series70.0ms (1.9%)

rewrite54.0ms (1.5%)

simplify97.0ms (2.7%)

prune52.0ms (1.5%)

regimes543.0ms (15.2%)

bsearch279.0ms (7.8%)

simplify6.0ms (0.2%)

end52.0ms (1.5%)

Profiling