Details

analyze939.0ms (18.3%)

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%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.3s (26.1%)

Results

976.0ms	8256×	body	128	valid
340.0ms	2946×	body	128	invalid

Compiler

Compiled 38 to 24 computations (36.8% saved)

preprocess37.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

679×	`div-sub_binary64`
433×	`cancel-sign-sub-inv_binary64`
405×	`fma-neg_binary64`
352×	`sub-neg_binary64`
272×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	80
1	80	80
2	214	80
3	441	80
4	1098	80
5	3253	80
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

801×	`div-sub_binary64`
796×	`fma-def_binary64`
540×	`times-frac_binary64`
202×	`distribute-rgt-in_binary64`
197×	`fma-neg_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	27	20
2	67	20
3	136	20
4	320	20
5	748	20
6	1891	19
7	4408	19

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y)))
	29.9b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 60 computations (39.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x z) y)
✓	0.1b	(fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y))

series27.0ms (0.5%)

Counts

2 → 72

Calls

18 calls:

4.0ms	(fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y))	x	-inf
2.0ms	(/.f64 (+.f64 x z) y)	z	inf
2.0ms	(fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y))	z	-inf
2.0ms	(fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y))	z	inf
2.0ms	(fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y))	x	inf

rewrite77.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

917×	`prod-diff_binary64`
201×	`egg-rr`
180×	`log1p-udef_binary64`
109×	`add-sqr-sqrt_binary64`
103×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	206	21
2	3135	21

Stop Event

1×	node limit

Counts

2 → 201

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary64`
450×	`fma-neg_binary64`
447×	`cancel-sign-sub-inv_binary64`
299×	`distribute-rgt-in_binary64`
270×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	874
1	51	793
2	93	793
3	203	791
4	564	791
5	2006	791

Stop Event

1×	node limit

Counts

273 → 219

prune124.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	214	5	219
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	215	6	221

Error

0.0b

Counts

221 → 6

Alt Table

Status	Error	Program
	18.4b	(.f64 -1/2 (.f64 -1 (+.f64 y (/.f64 (pow.f64 x 2) y))))
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y)))
	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (-.f64 z x) (/.f64 y (+.f64 z x))) y))
	0.5b	(*.f64 -1/2 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 x z) y)) 3) (-.f64 z x) (neg.f64 y)))
▶	0.1b	(.f64 -1/2 (fma.f64 (.f64 (+.f64 x z) (/.f64 1 y)) (-.f64 z x) (neg.f64 y)))
	51.7b	(*.f64 -1/2 (pow.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) y)) 2))

Compiler

Compiled 6118 to 1924 computations (68.6% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 (+.f64 x z) (/.f64 1 y)) (-.f64 z x) (neg.f64 y))
✓	0.3b	(*.f64 (+.f64 x z) (/.f64 1 y))

series27.0ms (0.5%)

Counts

2 → 72

Calls

18 calls:

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

rewrite79.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

921×	`prod-diff_binary64`
223×	`egg-rr`
121×	`add-sqr-sqrt_binary64`
113×	`add-cbrt-cube_binary64`
113×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	240	21
2	3416	21

Stop Event

1×	node limit

Counts

2 → 223

simplify46.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

579×	`fma-def_binary64`
450×	`fma-neg_binary64`
439×	`cancel-sign-sub-inv_binary64`
299×	`distribute-rgt-in_binary64`
270×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	874
1	51	793
2	93	793
3	203	791
4	564	791
5	2014	791

Stop Event

1×	node limit

Counts

295 → 241

prune137.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	240	1	241
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	242	5	247

Error

0.0b

Counts

247 → 5

Alt Table

Status	Error	Program
	18.4b	(.f64 -1/2 (.f64 -1 (+.f64 y (/.f64 (pow.f64 x 2) y))))
▶	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (-.f64 z x) (/.f64 y (+.f64 z x))) y))
	39.7b	(.f64 -1/2 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 x z) y)) 2) (.f64 (cbrt.f64 (/.f64 (+.f64 x z) y)) (-.f64 z x)) y) (fma.f64 y 1 y)))
✓	0.1b	(.f64 -1/2 (fma.f64 (.f64 (+.f64 x z) (/.f64 1 y)) (-.f64 z x) (neg.f64 y)))
	51.7b	(*.f64 -1/2 (pow.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) y)) 2))

Compiler

Compiled 6663 to 2148 computations (67.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 z x))
✓	0.3b	(/.f64 (-.f64 z x) (/.f64 y (+.f64 z x)))

series38.0ms (0.7%)

Counts

2 → 60

Calls

18 calls:

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

rewrite182.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

923×	`prod-diff_binary64`
408×	`egg-rr`
101×	`add-sqr-sqrt_binary64`
96×	`log1p-expm1-u_binary64`
96×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	190	20
2	3125	20

Stop Event

1×	node limit

Counts

2 → 408

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

744×	`cancel-sign-sub-inv_binary64`
634×	`fma-def_binary64`
378×	`fma-neg_binary64`
374×	`associate-/l/_binary64`
189×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	1020
1	136	1020
2	411	948
3	1912	894

Stop Event

1×	node limit

Counts

468 → 431

prune406.0ms (7.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	428	3	431
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	431	5	436

Error

Counts

436 → 5

Alt Table

Status	Error	Program
	13.5b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (+.f64 z x) (-.f64 z x)) y) y))
▶	0.2b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 z x) (.f64 y (/.f64 1 (+.f64 z x)))) y))
	2.5b	(.f64 -1/2 (-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 z) 2) y) (/.f64 (cbrt.f64 z) (/.f64 1 (+.f64 z x))) (neg.f64 (.f64 (/.f64 (+.f64 z x) y) x))) (fma.f64 (neg.f64 (/.f64 (+.f64 z x) y)) x (*.f64 (/.f64 (+.f64 z x) y) x))) y))
✓	0.1b	(.f64 -1/2 (fma.f64 (.f64 (+.f64 x z) (/.f64 1 y)) (-.f64 z x) (neg.f64 y)))
	51.7b	(*.f64 -1/2 (pow.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) y)) 2))

Compiler

Compiled 23215 to 6400 computations (72.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 z x))
✓	0.3b	(*.f64 y (/.f64 1 (+.f64 z x)))
✓	0.3b	(/.f64 (-.f64 z x) (*.f64 y (/.f64 1 (+.f64 z x))))

series41.0ms (0.8%)

Counts

3 → 96

Calls

24 calls:

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

rewrite192.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

951×	`prod-diff_binary64`
456×	`egg-rr`
115×	`add-sqr-sqrt_binary64`
108×	`add-cbrt-cube_binary64`
108×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	226	27
2	3433	27

Stop Event

1×	node limit

Counts

3 → 456

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
488×	`fma-neg_binary64`
230×	`distribute-neg-frac_binary64`
224×	`distribute-rgt-neg-in_binary64`
222×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	1578
1	181	1578
2	547	1470
3	2457	1416

Stop Event

1×	node limit

Counts

552 → 494

prune430.0ms (8.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	494	0	494
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	494	5	499

Error

Counts

499 → 5

Alt Table

Status	Error	Program
	13.5b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (+.f64 z x) (-.f64 z x)) y) y))
✓	0.2b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 z x) (.f64 y (/.f64 1 (+.f64 z x)))) y))
	2.5b	(.f64 -1/2 (-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 z) 2) y) (/.f64 (cbrt.f64 z) (/.f64 1 (+.f64 z x))) (neg.f64 (.f64 (/.f64 (+.f64 z x) y) x))) (fma.f64 (neg.f64 (/.f64 (+.f64 z x) y)) x (*.f64 (/.f64 (+.f64 z x) y) x))) y))
✓	0.1b	(.f64 -1/2 (fma.f64 (.f64 (+.f64 x z) (/.f64 1 y)) (-.f64 z x) (neg.f64 y)))
	51.7b	(*.f64 -1/2 (pow.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) y)) 2))

Compiler

Compiled 25786 to 6480 computations (74.9% saved)

regimes675.0ms (13.2%)

Accuracy

Total 0.1b remaining (50.9%)

Threshold costs 0.1b (50.9%)

Counts

114 → 1

Compiler

Compiled 15594 to 8790 computations (43.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
14×	`*-commutative_binary64`
12×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	28	24
2	48	24
3	72	22
4	92	22
5	103	22
6	122	22
7	136	22

Stop Event

1×

saturated

end80.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 152 to 91 computations (40.1% saved)

Details

analyze939.0ms (18.3%)

sample1.3s (26.1%)

preprocess37.0ms (0.7%)

simplify31.0ms (0.6%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series27.0ms (0.5%)

rewrite77.0ms (1.5%)

simplify50.0ms (1%)

prune124.0ms (2.4%)

localize9.0ms (0.2%)

series27.0ms (0.5%)

rewrite79.0ms (1.6%)

simplify46.0ms (0.9%)

prune137.0ms (2.7%)

localize7.0ms (0.1%)

series38.0ms (0.7%)

rewrite182.0ms (3.6%)

simplify56.0ms (1.1%)

prune406.0ms (7.9%)

localize9.0ms (0.2%)

series41.0ms (0.8%)

rewrite192.0ms (3.7%)

simplify69.0ms (1.4%)

prune430.0ms (8.4%)

regimes675.0ms (13.2%)

simplify3.0ms (0.1%)

end80.0ms (1.6%)

Profiling