Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
100%	0%	0%	3

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample746.0ms (46.1%)

Results

715.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	9	8

prune2.0ms (0.2%)

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

14.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.0b	(/.f64 x (fma.f64 x x 1))

Compiler

Compiled 28 to 16 computations (42.9% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	14.0b	(/.f64 x (fma.f64 x x 1))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 x (fma.f64 x x 1))

rewrite89.0ms (5.5%)

Algorithm

2×	batch-egg-rewrite

Rules

462×	`log1p-expm1-u_binary64`
462×	`expm1-log1p-u_binary64`
316×	`unpow-prod-down_binary64`
231×	`log-prod_binary64`
149×	`prod-diff_binary64`

Counts

1 → 67

Calls

1 calls:

88.0ms

(/.f64 x (fma.f64 x x 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	98	8
2	1186	8
3	4899	8
4	5141	8
0	0	0
1	0	0

simplify83.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

675×	`div-sub_binary64`
485×	`times-frac_binary64`
468×	`fma-def_binary64`
300×	`distribute-rgt-neg-in_binary64`
270×	`sub-neg_binary64`

Counts

79 → 79

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	180
1	65	180
2	171	180
3	413	180
4	1056	180
5	2530	180
6	4550	180
7	4854	180
8	5378	180

prune65.0ms (4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	4	80

Error

Counts

80 → 4

Alt Table

Status	Error	Program
	14.0b	(expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x x 1))))
▶	13.1b	(*.f64 x (pow.f64 (hypot.f64 1 x) -2))
	30.5b	(/.f64 1 x)
	32.5b	(-.f64 (+.f64 (pow.f64 x 5) x) (pow.f64 x 3))

Compiler

Compiled 1133 to 763 computations (32.7% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 1 x) -2)
✓	13.1b	(*.f64 x (pow.f64 (hypot.f64 1 x) -2))

series8.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(pow.f64 (hypot.f64 1 x) -2)
3.0ms	(*.f64 x (pow.f64 (hypot.f64 1 x) -2))

rewrite47.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

534×	`log1p-expm1-u_binary64`
534×	`expm1-log1p-u_binary64`
409×	`unpow-prod-down_binary64`
275×	`log-prod_binary64`
164×	`pow2_binary64`

Counts

2 → 53

Calls

2 calls:

46.0ms	(pow.f64 (hypot.f64 1 x) -2)
46.0ms	(*.f64 x (pow.f64 (hypot.f64 1 x) -2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	140	17
2	1418	17
3	5193	17
0	0	0
1	0	0

simplify73.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

396×	`neg-mul-1_binary64`
396×	`fma-def_binary64`
381×	`sub-neg_binary64`
375×	`distribute-rgt-neg-in_binary64`
354×	`associate-l_binary64`

Counts

77 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	384
1	118	382
2	317	382
3	894	380
4	2976	380
5	4461	380
6	5065	380

prune56.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	80	4	84

Error

Counts

84 → 4

Alt Table

Status	Error	Program
▶	14.0b	(expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x x 1))))
✓	13.1b	(*.f64 x (pow.f64 (hypot.f64 1 x) -2))
	30.5b	(/.f64 1 x)
	32.5b	(-.f64 (+.f64 (pow.f64 x 5) x) (pow.f64 x 3))

Compiler

Compiled 1110 to 850 computations (23.4% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x x 1))))
✓	0.0b	(log1p.f64 (/.f64 x (fma.f64 x x 1)))
	14.0b	(/.f64 x (fma.f64 x x 1))

series8.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(log1p.f64 (/.f64 x (fma.f64 x x 1)))
3.0ms	(expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x x 1))))

rewrite79.0ms (4.9%)

Algorithm

2×	batch-egg-rewrite

Rules

536×	`expm1-log1p-u_binary64`
535×	`log1p-expm1-u_binary64`
269×	`log-prod_binary64`
265×	`prod-diff_binary64`
146×	`pow2_binary64`

Counts

2 → 76

Calls

2 calls:

78.0ms	(expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x x 1))))
78.0ms	(log1p.f64 (/.f64 x (fma.f64 x x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	117	18
2	1376	18
3	4932	18
4	5105	18
0	0	0
1	0	0

simplify100.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-def_binary64`
464×	`times-frac_binary64`
385×	`sub-neg_binary64`
306×	`cancel-sign-sub-inv_binary64`
248×	`associate-l_binary64`

Counts

100 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	372
1	139	372
2	372	368
3	1017	364
4	3284	364
5	4873	364
6	4993	364

prune100.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	179	4	183

Error

Counts

183 → 4

Alt Table

Status	Error	Program
✓	14.0b	(expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x x 1))))
✓	13.1b	(*.f64 x (pow.f64 (hypot.f64 1 x) -2))
▶	30.5b	(/.f64 1 x)
	32.5b	(-.f64 (+.f64 (pow.f64 x 5) x) (pow.f64 x 3))

Compiler

Compiled 2557 to 1785 computations (30.2% saved)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
✓	14.0b	(expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x x 1))))
✓	13.1b	(*.f64 x (pow.f64 (hypot.f64 1 x) -2))
✓	30.5b	(/.f64 1 x)
	32.5b	(-.f64 (+.f64 (pow.f64 x 5) x) (pow.f64 x 3))

Compiler

Compiled 31 to 22 computations (29% saved)

regimes62.0ms (3.8%)

Accuracy

Total 0.0b remaining (63.2%)

Threshold costs 0.0b (63.2%)

Counts

15 → 3

Compiler

Compiled 242 to 170 computations (29.8% saved)

bsearch6.0ms (0.4%)

Steps

Iters	Range		Point
2	5112.250034017074	1243949739305.8826	9969059349.580149
2	-4.048954377670537e+26	-23220579454305052.0	-8.27254731064536e+18

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	17	32
2	16	32

end65.0ms (4%)

Compiler: Compiled 77 to 54 computations (29.9% saved)

Details

analyze1.0ms (0.1%)

sample746.0ms (46.1%)

simplify6.0ms (0.4%)

prune2.0ms (0.2%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite89.0ms (5.5%)

simplify83.0ms (5.1%)

prune65.0ms (4%)

localize4.0ms (0.3%)

series8.0ms (0.5%)

rewrite47.0ms (2.9%)

simplify73.0ms (4.5%)

prune56.0ms (3.5%)

localize5.0ms (0.3%)

series8.0ms (0.5%)

rewrite79.0ms (4.9%)

simplify100.0ms (6.2%)

prune100.0ms (6.2%)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

regimes62.0ms (3.8%)

bsearch6.0ms (0.4%)

simplify2.0ms (0.1%)

end65.0ms (4%)

Profiling