Details

analyze1.1s (30.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
22.2%	77.6%	0.2%	11
40.4%	59.5%	0.2%	12
47.4%	52.4%	0.2%	13
55.3%	44.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.1s (31.8%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 44 to 30 computations (31.8% saved)

preprocess35.0ms (1%)

Algorithm

2×	egg-herbie

Rules

582×	`fma-def_binary64`
534×	`div-sub_binary64`
358×	`times-frac_binary64`
330×	`associate-/l*_binary64`
279×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	175
1	147	175
2	375	175
3	992	154
4	3101	140
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify25.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
471×	`div-sub_binary64`
457×	`associate-*l/_binary64`
448×	`cancel-sign-sub-inv_binary64`
340×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	25
2	76	25
3	193	22
4	558	19
5	1508	19
6	3813	19

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.2%)

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
	12.2b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	0.1b	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))

Compiler

Compiled 110 to 74 computations (32.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))
✓	0.0b	(*.f64 2 (/.f64 z y))
✓	0.0b	(-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))
✓	0.7b	(/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z)))

series81.0ms (2.3%)

Counts

4 → 93

Calls

36 calls:

6.0ms	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))	x	-inf
5.0ms	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))	x	0
5.0ms	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))	x	inf
4.0ms	(-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))	t	-inf
4.0ms	(/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z)))	y	inf

rewrite72.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

275×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`
152×	`add-sqr-sqrt_binary64`
146×	`log1p-expm1-u_binary64`
146×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	299	55
2	4311	55

Stop Event

1×	node limit

Counts

4 → 125

simplify68.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-neg_binary64`
529×	`times-frac_binary64`
334×	`associate-/l*_binary64`
293×	`associate-/r*_binary64`
239×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	94	2292
1	285	2282
2	889	2282
3	4721	2282

Stop Event

1×	node limit

Counts

218 → 166

prune144.0ms (4.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	165	3	168

Error

Counts

168 → 3

Alt Table

Status	Error	Program
▶	12.2b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
	21.8b	(-.f64 x (/.f64 y z))
	25.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 3689 to 1927 computations (47.8% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
✓	0.9b	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))
✓	21.1b	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))

series93.0ms (2.7%)

Counts

3 → 120

Calls

30 calls:

9.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))	x	-inf
8.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))	x	0
8.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))	x	inf
7.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))	z	-inf
6.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))	t	0

rewrite78.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

295×	`log1p-udef_binary64`
163×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
154×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	322	60
2	4650	60

Stop Event

1×	node limit

Counts

3 → 136

simplify54.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

555×	`times-frac_binary64`
359×	`associate-/l*_binary64`
310×	`associate-/r*_binary64`
260×	`associate-r_binary64`
243×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	94	2701
1	300	2691
2	973	2653

Stop Event

1×	node limit

Counts

256 → 180

prune119.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	180	3	183

Error

Counts

183 → 3

Alt Table

Status	Error	Program
✓	12.2b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	21.8b	(-.f64 x (/.f64 y z))
	25.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 5034 to 2679 computations (46.8% saved)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	12.2b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
✓	21.8b	(-.f64 x (/.f64 y z))
▶	25.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 50 to 34 computations (32% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (/.f64 z t) x)

series8.0ms (0.2%)

Counts

1 → 36

Calls

9 calls:

1.0ms	(fma.f64 2 (/.f64 z t) x)	z	-inf
1.0ms	(fma.f64 2 (/.f64 z t) x)	z	inf
1.0ms	(fma.f64 2 (/.f64 z t) x)	x	-inf
1.0ms	(fma.f64 2 (/.f64 z t) x)	x	0
1.0ms	(fma.f64 2 (/.f64 z t) x)	x	inf

rewrite35.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

678×	`log1p-expm1-u_binary64`
678×	`expm1-log1p-u_binary64`
134×	`expm1-udef_binary64`
134×	`log1p-udef_binary64`
118×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	145	8
2	1802	8

Stop Event

1×	node limit

Counts

1 → 26

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`+-commutative_binary64`
1×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	249
1	13	249
2	18	249
3	22	249
4	24	249
5	25	249

Stop Event

1×

saturated

Counts

62 → 29

prune13.0ms (0.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	29	3	32

Error

Counts

32 → 3

Alt Table

Status	Error	Program
✓	12.2b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
✓	21.8b	(-.f64 x (/.f64 y z))
✓	25.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 351 to 194 computations (44.7% saved)

regimes378.0ms (10.8%)

Accuracy

Total -0.1b remaining (-146%)

Threshold costs -0.1b (-146%)

Counts

68 → 1

Compiler

Compiled 7456 to 5428 computations (27.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	21	22
2	27	22
3	31	22
4	34	22
5	35	22

Stop Event

1×

saturated

end54.0ms (1.6%)

Stop Event

1×

done

Compiler

Compiled 78 to 55 computations (29.5% saved)

Details

analyze1.1s (30.7%)

sample1.1s (31.8%)

preprocess35.0ms (1%)

simplify25.0ms (0.7%)

prune5.0ms (0.2%)

localize8.0ms (0.2%)

series81.0ms (2.3%)

rewrite72.0ms (2.1%)

simplify68.0ms (1.9%)

prune144.0ms (4.1%)

localize13.0ms (0.4%)

series93.0ms (2.7%)

rewrite78.0ms (2.2%)

simplify54.0ms (1.6%)

prune119.0ms (3.4%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series8.0ms (0.2%)

rewrite35.0ms (1%)

simplify13.0ms (0.4%)

prune13.0ms (0.4%)

regimes378.0ms (10.8%)

simplify3.0ms (0.1%)

end54.0ms (1.6%)

Profiling