Details

analyze465.0ms (15%)

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
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
37.4%	49.9%	12.6%	10
43.7%	43.7%	12.6%	11
49.1%	38.2%	12.6%	12
54.6%	26.5%	18.9%	13
58.5%	22.6%	18.9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample936.0ms (30.2%)

Results

841.0ms	8256×	body	128	valid
66.0ms	715×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	8
2	16	8
3	17	8
4	17	8

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (*.f64 y z) x)
	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 54 to 29 computations (46.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (*.f64 y z) x)

series9.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(fma.f64 z (*.f64 y z) x)

rewrite40.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

522×	`log1p-expm1-u_binary64`
522×	`expm1-log1p-u_binary64`
351×	`unpow-prod-down_binary64`
296×	`log-prod_binary64`
160×	`pow2_binary64`

Counts

1 → 36

Calls

1 calls:

39.0ms

(fma.f64 z (*.f64 y z) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	118	8
2	1371	8
3	5179	8
0	0	0
1	0	0

simplify164.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

72 → 41

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	255
1	16	255
2	27	255
3	48	255
4	97	255
5	234	255
6	714	255
7	1139	255
8	1141	255
9	1289	255
10	1459	255
11	1641	255
12	1864	255
13	2149	255
14	2568	255
15	3133	255
16	3819	255
17	4037	255
18	4281	255
19	4363	255
20	4396	255
21	4417	255
22	4986	255

prune29.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	38	5	43

Error

0.0b

Counts

43 → 5

Alt Table

Status	Error	Program
	30.8b	(pow.f64 (sqrt.f64 (fma.f64 z (*.f64 z y) x)) 2)
	35.1b	(/.f64 (-.f64 (pow.f64 (.f64 z (.f64 z y)) 2) (.f64 x x)) (-.f64 (.f64 z (*.f64 z y)) x))
▶	1.3b	(.f64 (cbrt.f64 (fma.f64 z (.f64 z y) x)) (pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 2))
✓	0.1b	(fma.f64 z (*.f64 y z) x)
	7.1b	(+.f64 (*.f64 y (pow.f64 z 2)) x)

Compiler

Compiled 640 to 229 computations (64.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (*.f64 z y) x)
✓	0.3b	(.f64 (cbrt.f64 (fma.f64 z (.f64 z y) x)) (pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 2)
✓	0.6b	(cbrt.f64 (fma.f64 z (*.f64 z y) x))

series172.0ms (5.5%)

Counts

4 → 144

Calls

4 calls:

96.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 2)
57.0ms	(cbrt.f64 (fma.f64 z (*.f64 z y) x))
10.0ms	(.f64 (cbrt.f64 (fma.f64 z (.f64 z y) x)) (pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 2))
9.0ms	(fma.f64 z (*.f64 z y) x)

rewrite108.0ms (3.5%)

Algorithm

2×	batch-egg-rewrite

Rules

712×	`log1p-expm1-u_binary64`
712×	`expm1-log1p-u_binary64`
149×	`expm1-udef_binary64`
149×	`log1p-udef_binary64`
110×	`fma-neg_binary64`

Counts

4 → 89

Calls

4 calls:

106.0ms	(fma.f64 z (*.f64 z y) x)
106.0ms	(.f64 (cbrt.f64 (fma.f64 z (.f64 z y) x)) (pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 2))
106.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 2)
106.0ms	(cbrt.f64 (fma.f64 z (*.f64 z y) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	181	37
2	1882	37
3	4961	37
4	5000	37
5	4970	37
0	0	0
1	0	0

simplify118.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

444×	`cancel-sign-sub-inv_binary64`
415×	`unswap-sqr_binary64`
314×	`associate-r_binary64`
291×	`times-frac_binary64`
258×	`associate-/r*_binary64`

Counts

233 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	4916
1	1051	4730
2	3681	4428
3	5119	4428

prune178.0ms (5.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	266	0	266
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	266	5	271

Error

0.0b

Counts

271 → 5

Alt Table

Status	Error	Program
	30.8b	(pow.f64 (sqrt.f64 (fma.f64 z (*.f64 z y) x)) 2)
	35.1b	(/.f64 (-.f64 (pow.f64 (.f64 z (.f64 z y)) 2) (.f64 x x)) (-.f64 (.f64 z (*.f64 z y)) x))
✓	1.3b	(.f64 (cbrt.f64 (fma.f64 z (.f64 z y) x)) (pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 2))
✓	0.1b	(fma.f64 z (*.f64 y z) x)
▶	7.1b	(+.f64 (*.f64 y (pow.f64 z 2)) x)

Compiler

Compiled 10351 to 5588 computations (46% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
✓	10.8b	(*.f64 y (pow.f64 z 2))

series21.0ms (0.7%)

Counts

2 → 9

Calls

2 calls:

13.0ms	(+.f64 (*.f64 y (pow.f64 z 2)) x)
8.0ms	(*.f64 y (pow.f64 z 2))

rewrite47.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

811×	`prod-diff_binary64`
778×	`log1p-expm1-u_binary64`
778×	`expm1-log1p-u_binary64`
84×	`add-sqr-sqrt_binary64`
79×	`add-log-exp_binary64`

Counts

2 → 50

Calls

2 calls:

46.0ms	(+.f64 (*.f64 y (pow.f64 z 2)) x)
46.0ms	(*.f64 y (pow.f64 z 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	172	15
2	1984	15
3	6248	15
0	0	0
1	0	0

simplify146.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

59 → 53

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	39
1	13	39
2	23	39
3	42	39
4	89	39
5	222	39
6	694	39
7	1099	39
8	1101	39
9	1249	39
10	1419	39
11	1601	39
12	1826	39
13	2111	39
14	2530	39
15	3095	39
16	3781	39
17	3999	39
18	4243	39
19	4325	39
20	4358	39
21	4379	39
22	4948	39

prune25.0ms (0.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	53	5	58

Error

0.0b

Counts

58 → 5

Alt Table

Status	Error	Program
▶	30.8b	(pow.f64 (sqrt.f64 (fma.f64 z (*.f64 z y) x)) 2)
	35.1b	(/.f64 (-.f64 (pow.f64 (.f64 z (.f64 z y)) 2) (.f64 x x)) (-.f64 (.f64 z (*.f64 z y)) x))
✓	1.3b	(.f64 (cbrt.f64 (fma.f64 z (.f64 z y) x)) (pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 2))
✓	0.1b	(fma.f64 z (*.f64 y z) x)
✓	7.1b	(+.f64 (*.f64 y (pow.f64 z 2)) x)

Compiler

Compiled 786 to 280 computations (64.4% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 z (*.f64 z y) x))
	0.1b	(fma.f64 z (*.f64 z y) x)
✓	0.2b	(pow.f64 (sqrt.f64 (fma.f64 z (*.f64 z y) x)) 2)

series230.0ms (7.4%)

Counts

2 → 40

Calls

2 calls:

188.0ms	(pow.f64 (sqrt.f64 (fma.f64 z (*.f64 z y) x)) 2)
42.0ms	(sqrt.f64 (fma.f64 z (*.f64 z y) x))

rewrite47.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

660×	`log1p-expm1-u_binary64`
660×	`expm1-log1p-u_binary64`
354×	`log-prod_binary64`
139×	`expm1-udef_binary64`
139×	`log1p-udef_binary64`

Counts

2 → 76

Calls

2 calls:

45.0ms	(sqrt.f64 (fma.f64 z (*.f64 z y) x))
45.0ms	(pow.f64 (sqrt.f64 (fma.f64 z (*.f64 z y) x)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	164	18
2	1743	18
3	5250	18
0	0	0
1	0	0

simplify63.0ms (2%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-neg_binary64`
392×	`associate-r_binary64`
347×	`associate-l_binary64`
343×	`neg-mul-1_binary64`
330×	`distribute-rgt-neg-in_binary64`

Counts

116 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	866
1	206	862
2	626	850
3	2768	850
4	4765	850
5	5168	850

prune56.0ms (1.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	114	6	120

Error

0.0b

Counts

120 → 6

Alt Table

Status	Error	Program
✓	30.8b	(pow.f64 (sqrt.f64 (fma.f64 z (*.f64 z y) x)) 2)
✓	1.3b	(.f64 (cbrt.f64 (fma.f64 z (.f64 z y) x)) (pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 2))
✓	0.1b	(fma.f64 z (*.f64 y z) x)
	0.4b	(fma.f64 (.f64 z (pow.f64 (cbrt.f64 (.f64 z y)) 2)) (cbrt.f64 (*.f64 z y)) x)
	0.5b	(fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) (.f64 z y)) x)
✓	7.1b	(+.f64 (*.f64 y (pow.f64 z 2)) x)

Compiler

Compiled 2012 to 850 computations (57.8% saved)

regimes144.0ms (4.6%)

Accuracy

Total 0.1b remaining (73.8%)

Threshold costs 0.1b (73.8%)

Counts

30 → 1

Compiler

Compiled 2047 to 1235 computations (39.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end70.0ms (2.2%)

Compiler: Compiled 101 to 57 computations (43.6% saved)

Details

analyze465.0ms (15%)

sample936.0ms (30.2%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite40.0ms (1.3%)

simplify164.0ms (5.3%)

prune29.0ms (0.9%)

localize7.0ms (0.2%)

series172.0ms (5.5%)

rewrite108.0ms (3.5%)

simplify118.0ms (3.8%)

prune178.0ms (5.7%)

localize4.0ms (0.1%)

series21.0ms (0.7%)

rewrite47.0ms (1.5%)

simplify146.0ms (4.7%)

prune25.0ms (0.8%)

localize6.0ms (0.2%)

series230.0ms (7.4%)

rewrite47.0ms (1.5%)

simplify63.0ms (2%)

prune56.0ms (1.8%)

regimes144.0ms (4.6%)

simplify4.0ms (0.1%)

end70.0ms (2.2%)

Profiling