Details

analyze509.0ms (12.1%)

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
18.7%	81.1%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
45.2%	53.8%	0.9%	9
50.3%	47.8%	1.9%	10
54%	43.6%	2.4%	11
61.7%	32.9%	5.4%	12
64.1%	28.3%	7.6%	13
66.2%	24.7%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.1s (27.4%)

Results

988.0ms	8256×	body	128	valid
147.0ms	1200×	body	128	invalid

Compiler

Compiled 32 to 22 computations (31.3% saved)

preprocess46.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

802×	`times-frac_binary64`
679×	`fma-neg_binary64`
418×	`fma-def_binary64`
329×	`cancel-sign-sub-inv_binary64`
220×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	72
1	71	72
2	154	72
3	269	72
4	474	64
5	890	64
6	1410	64
7	2303	64
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify45.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1128×	`fma-def_binary64`
1073×	`fma-neg_binary64`
226×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
162×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	46	18
3	78	18
4	141	16
5	274	16
6	443	16
7	744	16
8	1785	13
9	3544	13
10	4642	13
11	4838	13
12	4935	13
13	4935	13

Stop Event

1×

saturated

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.8b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))
▶	0.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	2.1b	(*.f64 (/.f64 x y) z)

series44.0ms (1%)

Counts

3 → 96

Calls

24 calls:

4.0ms	(*.f64 (/.f64 x y) z)	x	-inf
3.0ms	(/.f64 (+.f64 x 4) y)	y	inf
3.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))	y	0
3.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))	x	0
2.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))	x	-inf

rewrite70.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

334×	`fma-def_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
202×	`fma-neg_binary64`
184×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	236	27
2	3526	27

Stop Event

1×	node limit

Counts

3 → 176

simplify72.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-neg_binary64`
323×	`fma-def_binary64`
185×	`distribute-rgt-in_binary64`
176×	`cancel-sign-sub-inv_binary64`
160×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	1102
1	78	1102
2	186	952
3	442	860
4	951	790
5	2039	790
6	3042	790
7	3589	790
8	3601	790
9	3601	790

Stop Event

1×

saturated

Counts

272 → 194

prune155.0ms (3.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	189	5	194
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	190	6	196

Error

Counts

196 → 6

Alt Table

Status	Error	Program
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 (/.f64 (*.f64 x z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))
▶	0.8b	(fabs.f64 (fma.f64 (+.f64 x 4) (/.f64 1 y) (*.f64 (/.f64 x y) (neg.f64 z))))
	3.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	30.4b	(fabs.f64 (fma.f64 (*.f64 (/.f64 (neg.f64 x) y) (sqrt.f64 z)) (sqrt.f64 z) (/.f64 (+.f64 x 4) y)))
	2.8b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))
	2.8b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))

Compiler

Compiled 4182 to 2044 computations (51.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (+.f64 x 4) (/.f64 1 y) (*.f64 (/.f64 x y) (neg.f64 z)))
✓	2.1b	(*.f64 (/.f64 x y) (neg.f64 z))

series33.0ms (0.8%)

Counts

2 → 72

Calls

18 calls:

3.0ms	(*.f64 (/.f64 x y) (neg.f64 z))	x	0
3.0ms	(fma.f64 (+.f64 x 4) (/.f64 1 y) (*.f64 (/.f64 x y) (neg.f64 z)))	x	-inf
2.0ms	(fma.f64 (+.f64 x 4) (/.f64 1 y) (*.f64 (/.f64 x y) (neg.f64 z)))	x	inf
2.0ms	(fma.f64 (+.f64 x 4) (/.f64 1 y) (*.f64 (/.f64 x y) (neg.f64 z)))	z	inf
2.0ms	(fma.f64 (+.f64 x 4) (/.f64 1 y) (*.f64 (/.f64 x y) (neg.f64 z)))	z	0

rewrite96.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

346×	`prod-diff_binary64`
218×	`egg-rr`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
129×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	259	23
2	3426	21

Stop Event

1×	node limit

Counts

2 → 218

simplify74.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-neg_binary64`
323×	`fma-def_binary64`
185×	`distribute-rgt-in_binary64`
175×	`cancel-sign-sub-inv_binary64`
160×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	952
1	78	952
2	186	802
3	442	710
4	951	703
5	2055	703
6	3074	703
7	3622	703
8	3634	703
9	3634	703

Stop Event

1×

saturated

Counts

290 → 231

prune205.0ms (4.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	231	6	237

Error

Counts

237 → 6

Alt Table

Status	Error	Program
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 (/.f64 (*.f64 x z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))
✓	0.8b	(fabs.f64 (fma.f64 (+.f64 x 4) (/.f64 1 y) (*.f64 (/.f64 x y) (neg.f64 z))))
	3.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	30.4b	(fabs.f64 (fma.f64 (*.f64 (/.f64 (neg.f64 x) y) (sqrt.f64 z)) (sqrt.f64 z) (/.f64 (+.f64 x 4) y)))
▶	2.8b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))
	2.8b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))

Compiler

Compiled 8403 to 3638 computations (56.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 x z -4) x)
✓	2.7b	(/.f64 (-.f64 (fma.f64 x z -4) x) y)

series19.0ms (0.5%)

Counts

2 → 60

Calls

15 calls:

2.0ms	(/.f64 (-.f64 (fma.f64 x z -4) x) y)	z	-inf
2.0ms	(/.f64 (-.f64 (fma.f64 x z -4) x) y)	z	inf
2.0ms	(/.f64 (-.f64 (fma.f64 x z -4) x) y)	x	-inf
2.0ms	(/.f64 (-.f64 (fma.f64 x z -4) x) y)	y	-inf
2.0ms	(/.f64 (-.f64 (fma.f64 x z -4) x) y)	x	inf

rewrite88.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

541×	`prod-diff_binary64`
279×	`egg-rr`
232×	`fma-def_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	180	19
2	2573	19

Stop Event

1×	node limit

Counts

2 → 279

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

792×	`fma-neg_binary64`
343×	`fma-def_binary64`
206×	`cancel-sign-sub-inv_binary64`
200×	`unsub-neg_binary64`
173×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	826
1	97	790
2	217	546
3	448	546
4	1083	546
5	2255	546
6	3349	546
7	3554	546
8	3560	546
9	3560	546

Stop Event

1×

saturated

Counts

339 → 301

prune278.0ms (6.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	300	1	301
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	302	5	307

Error

Counts

307 → 5

Alt Table

Status	Error	Program
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 (/.f64 (*.f64 x z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))
▶	2.8b	(fabs.f64 (-.f64 (/.f64 (fma.f64 x z -4) y) (/.f64 x y)))
✓	0.8b	(fabs.f64 (fma.f64 (+.f64 x 4) (/.f64 1 y) (*.f64 (/.f64 x y) (neg.f64 z))))
	3.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	30.4b	(fabs.f64 (fma.f64 (*.f64 (/.f64 (neg.f64 x) y) (sqrt.f64 z)) (sqrt.f64 z) (/.f64 (+.f64 x 4) y)))

Compiler

Compiled 9242 to 4538 computations (50.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (fma.f64 x z -4) y) (/.f64 x y))
✓	2.7b	(/.f64 (fma.f64 x z -4) y)

series31.0ms (0.7%)

Counts

2 → 72

Calls

18 calls:

2.0ms	(-.f64 (/.f64 (fma.f64 x z -4) y) (/.f64 x y))	y	inf
2.0ms	(-.f64 (/.f64 (fma.f64 x z -4) y) (/.f64 x y))	x	-inf
2.0ms	(/.f64 (fma.f64 x z -4) y)	y	0
2.0ms	(-.f64 (/.f64 (fma.f64 x z -4) y) (/.f64 x y))	z	-inf
2.0ms	(-.f64 (/.f64 (fma.f64 x z -4) y) (/.f64 x y))	x	inf

rewrite67.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

383×	`fma-def_binary64`
224×	`fma-neg_binary64`
201×	`log-div_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	207	19
2	3184	19

Stop Event

1×	node limit

Counts

2 → 187

simplify64.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-neg_binary64`
328×	`fma-def_binary64`
254×	`cancel-sign-sub-inv_binary64`
191×	`distribute-rgt-in_binary64`
177×	`unsub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	752
1	105	662
2	238	660
3	506	651
4	1130	651
5	2235	651
6	3173	651
7	3629	651
8	3668	651
9	3668	651

Stop Event

1×

saturated

Counts

259 → 204

prune176.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	204	5	209

Error

Counts

209 → 5

Alt Table

Status	Error	Program
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 (/.f64 (*.f64 x z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))
✓	2.8b	(fabs.f64 (-.f64 (/.f64 (fma.f64 x z -4) y) (/.f64 x y)))
✓	0.8b	(fabs.f64 (fma.f64 (+.f64 x 4) (/.f64 1 y) (*.f64 (/.f64 x y) (neg.f64 z))))
	3.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	30.4b	(fabs.f64 (fma.f64 (*.f64 (/.f64 (neg.f64 x) y) (sqrt.f64 z)) (sqrt.f64 z) (/.f64 (+.f64 x 4) y)))

Compiler

Compiled 4220 to 2166 computations (48.7% saved)

regimes798.0ms (19%)

Accuracy

Total 1.6b remaining (98.9%)

Threshold costs 0b (0%)

Counts

159 → 1

Compiler

Compiled 12207 to 8446 computations (30.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	20	18
2	36	18
3	49	18
4	63	18
5	69	18
6	70	18

Stop Event

1×

saturated

end78.0ms (1.9%)

Stop Event

1×

fuel

Compiler

Compiled 116 to 77 computations (33.6% saved)

Details

analyze509.0ms (12.1%)

sample1.1s (27.4%)

preprocess46.0ms (1.1%)

simplify45.0ms (1.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series44.0ms (1%)

rewrite70.0ms (1.7%)

simplify72.0ms (1.7%)

prune155.0ms (3.7%)

localize9.0ms (0.2%)

series33.0ms (0.8%)

rewrite96.0ms (2.3%)

simplify74.0ms (1.8%)

prune205.0ms (4.9%)

localize7.0ms (0.2%)

series19.0ms (0.5%)

rewrite88.0ms (2.1%)

simplify66.0ms (1.6%)

prune278.0ms (6.6%)

localize7.0ms (0.2%)

series31.0ms (0.7%)

rewrite67.0ms (1.6%)

simplify64.0ms (1.5%)

prune176.0ms (4.2%)

regimes798.0ms (19%)

simplify3.0ms (0.1%)

end78.0ms (1.9%)

Profiling