Details

analyze10.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 19 to 15 computations (21.1% saved)

sample936.0ms (44.4%)

Results

919.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 30 computations (21.1% saved)

preprocess34.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

1040×	`fma-neg_binary64`
807×	`times-frac_binary64`
392×	`div-sub_binary64`
208×	`fma-def_binary64`
181×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	25	19
2	45	19
3	82	19
4	130	19
5	207	19
6	376	19
7	623	19
8	1608	19
9	3012	19
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify25.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1040×	`fma-neg_binary64`
807×	`times-frac_binary64`
392×	`div-sub_binary64`
208×	`fma-def_binary64`
181×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	25	19
2	45	19
3	82	19
4	130	19
5	207	19
6	376	19
7	623	19
8	1608	19
9	3012	19

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 62 to 46 computations (25.8% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
✓	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.2b	(fma.f64 x -27061/100000 -230753/100000)
✓	15.0b	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series9.0ms (0.4%)

Counts

4 → 48

Calls

12 calls:

1.0ms	(fma.f64 x 4481/100000 99229/100000)	x	-inf
1.0ms	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))	x	-inf
1.0ms	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))	x	inf
1.0ms	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))	x	0
1.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)	x	-inf

rewrite68.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`unpow-prod-down_binary64`
418×	`log-prod_binary64`
268×	`pow2_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	225	35
2	2521	35

Stop Event

1×	node limit

Counts

4 → 165

simplify38.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-neg_binary64`
432×	`cancel-sign-sub-inv_binary64`
410×	`times-frac_binary64`
285×	`fma-def_binary64`
172×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	473
1	137	433
2	322	389
3	831	371
4	2523	370

Stop Event

1×	node limit

Counts

213 → 197

prune216.0ms (10.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	196	2	198

Error

Counts

198 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
	1.4b	(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x 99229/100000 1)))

Status

Error

Program

▶

0.0b

(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

1.4b

(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x 99229/100000 1)))

Compiler

Compiled 4250 to 3308 computations (22.2% saved)

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x -27061/100000 -230753/100000)
✓	1.4b	(expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	15.0b	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
✓	15.5b	(log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series8.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

1.0ms	(log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))	x	-inf
1.0ms	(log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))	x	inf
1.0ms	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))	x	-inf
1.0ms	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))	x	inf
1.0ms	(log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))	x	0

rewrite61.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

456×	`log-prod_binary64`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
201×	`pow1/3_binary64`
183×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	246	36
2	2730	36

Stop Event

1×	node limit

Counts

3 → 101

simplify34.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

844×	`fma-def_binary64`
259×	`fma-neg_binary64`
242×	`associate-+l-_binary64`
229×	`cancel-sign-sub-inv_binary64`
222×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	556
1	241	544
2	646	510
3	1880	478

Stop Event

1×	node limit

Counts

137 → 146

prune153.0ms (7.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	183	2	185

Error

Counts

185 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
▶	1.4b	(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x 99229/100000 1)))

Status

Error

Program

✓

0.0b

(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

▶

1.4b

(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x 99229/100000 1)))

Compiler

Compiled 3908 to 3034 computations (22.4% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 99229/100000 1)
✓	0.1b	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x 99229/100000 1))
	0.2b	(fma.f64 x -27061/100000 -230753/100000)

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x 99229/100000 1))	x	0
1.0ms	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x 99229/100000 1))	x	inf
1.0ms	(/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x 99229/100000 1))	x	-inf
1.0ms	(fma.f64 x 99229/100000 1)	x	inf
1.0ms	(fma.f64 x 99229/100000 1)	x	-inf

rewrite44.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

789×	`log1p-expm1-u_binary64`
789×	`expm1-log1p-u_binary64`
153×	`log1p-udef_binary64`
87×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	183	17
2	2058	17

Stop Event

1×	node limit

Counts

2 → 56

simplify29.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-def_binary64`
604×	`fma-neg_binary64`
425×	`cancel-sign-sub-inv_binary64`
382×	`associate-/r*_binary64`
189×	`associate-/l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	217
1	101	193
2	251	191
3	710	185
4	2130	182

Stop Event

1×	node limit

Counts

80 → 75

prune79.0ms (3.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	112	2	114

Error

Counts

114 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	1.4b	(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x 99229/100000 1)))

Status

Error

Program

✓

0.0b

(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

✓

1.4b

(+.f64 x (/.f64 (fma.f64 x -27061/100000 -230753/100000) (fma.f64 x 99229/100000 1)))

Compiler

Compiled 1783 to 1401 computations (21.4% saved)

regimes273.0ms (13%)

Accuracy

Total 0.0b remaining (22.9%)

Threshold costs 0.0b (22.9%)

Counts

135 → 1

Compiler

Compiled 4678 to 3612 computations (22.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	17	23

Stop Event

1×

saturated

end56.0ms (2.6%)

Stop Event

1×

done

Compiler

Compiled 63 to 48 computations (23.8% saved)

Details

analyze10.0ms (0.5%)

sample936.0ms (44.4%)

preprocess34.0ms (1.6%)

simplify25.0ms (1.2%)

prune3.0ms (0.1%)

localize8.0ms (0.4%)

series9.0ms (0.4%)

rewrite68.0ms (3.2%)

simplify38.0ms (1.8%)

prune216.0ms (10.3%)

localize12.0ms (0.6%)

series8.0ms (0.4%)

rewrite61.0ms (2.9%)

simplify34.0ms (1.6%)

prune153.0ms (7.3%)

localize7.0ms (0.3%)

series4.0ms (0.2%)

rewrite44.0ms (2.1%)

simplify29.0ms (1.4%)

prune79.0ms (3.7%)

regimes273.0ms (13%)

simplify2.0ms (0.1%)

end56.0ms (2.6%)

Profiling