Details

analyze121.0ms (4.7%)

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
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
87.4%	12.5%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample755.0ms (29.5%)

Infinites

21.4% of outputs are infinite.

Results

632.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify56.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

823×	`div-sub_binary64`
529×	`fma-neg_binary64`
475×	`distribute-rgt-in_binary64`
409×	`fma-def_binary64`
380×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	50	11
3	156	11
4	331	11
5	666	11
6	1744	11
7	3988	11
8	4953	11

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

5.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.0b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 y z) x)
✓	5.0b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series28.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

14.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
13.0ms	(fma.f64 x (-.f64 y z) x)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
0.0ms	(fma.f64 x (-.f64 y z) x)

simplify78.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-/l*_binary64`
629×	`fma-def_binary64`
448×	`associate-/l/_binary64`
308×	`associate-/r*_binary64`
291×	`associate-/r/_binary64`

Counts

111 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	1522
1	160	1371
2	374	1332
3	1227	1332
4	4358	1332
5	5042	1332

prune57.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Error

0.0b

Counts

74 → 5

Alt Table

Status	Error	Program
	5.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
	37.4b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))
	7.1b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
▶	2.2b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
	33.3b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))

Compiler

Compiled 1141 to 271 computations (76.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
✓	2.2b	(/.f64 (fma.f64 y x x) z)

series29.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

15.0ms	(/.f64 (fma.f64 y x x) z)
14.0ms	(-.f64 (/.f64 (fma.f64 y x x) z) x)

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

2 → 100

Calls

2 calls:

6.0ms	(-.f64 (/.f64 (fma.f64 y x x) z) x)
2.0ms	(/.f64 (fma.f64 y x x) z)

simplify117.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

502×	`fma-def_binary64`
431×	`fma-neg_binary64`
395×	`times-frac_binary64`
374×	`associate-/l*_binary64`
228×	`associate-*l/_binary64`

Counts

172 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	3072
1	267	2971
2	947	2007
3	3816	1989
4	4881	1989
5	4897	1989

prune87.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	149	5	154

Error

0.0b

Counts

154 → 5

Alt Table

Status	Error	Program
	5.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
▶	3.2b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
	7.1b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.2b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
	33.3b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))

Compiler

Compiled 3241 to 660 computations (79.6% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1)
✓	0.0b	(+.f64 (/.f64 y z) (/.f64 1 z))
✓	3.2b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)

series32.0ms (1.3%)

Counts

3 → 45

Calls

3 calls:

20.0ms	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
6.0ms	(-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1)
6.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite62.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`

Counts

3 → 137

Calls

3 calls:

21.0ms	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
15.0ms	(-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1)
13.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

simplify120.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-neg_binary64`
500×	`times-frac_binary64`
399×	`associate-l_binary64`
375×	`distribute-rgt-in_binary64`
366×	`distribute-lft-in_binary64`

Counts

182 → 184

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	2354
1	271	2128
2	775	1816
3	3167	1810
4	4715	1808
5	5115	1808

prune177.0ms (6.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	182	7	189

Error

Counts

189 → 7

Alt Table

Status	Error	Program
	5.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
✓	3.2b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
	7.1b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.2b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
	17.3b	(*.f64 (-.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 y) z) 3)) 1) x)
▶	3.2b	(*.f64 (-.f64 (fma.f64 y (/.f64 1 z) (/.f64 1 z)) 1) x)
	33.3b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))

Compiler

Compiled 3792 to 2384 computations (37.1% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 y (/.f64 1 z) (/.f64 1 z)) 1)
✓	0.2b	(fma.f64 y (/.f64 1 z) (/.f64 1 z))
✓	3.2b	(*.f64 (-.f64 (fma.f64 y (/.f64 1 z) (/.f64 1 z)) 1) x)

series35.0ms (1.4%)

Counts

3 → 84

Calls

3 calls:

19.0ms	(*.f64 (-.f64 (fma.f64 y (/.f64 1 z) (/.f64 1 z)) 1) x)
10.0ms	(-.f64 (fma.f64 y (/.f64 1 z) (/.f64 1 z)) 1)
7.0ms	(fma.f64 y (/.f64 1 z) (/.f64 1 z))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
7×	`associate-l_binary64`

Counts

3 → 70

Calls

3 calls:

5.0ms	(*.f64 (-.f64 (fma.f64 y (/.f64 1 z) (/.f64 1 z)) 1) x)
3.0ms	(-.f64 (fma.f64 y (/.f64 1 z) (/.f64 1 z)) 1)
0.0ms	(fma.f64 y (/.f64 1 z) (/.f64 1 z))

simplify133.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

381×	`*-commutative_binary64`
337×	`fma-neg_binary64`
240×	`distribute-rgt-in_binary64`
239×	`associate-l_binary64`
239×	`distribute-lft-in_binary64`

Counts

154 → 126

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	93	2282
1	171	2125
2	423	1600
3	1707	1595
4	3313	1595
5	4907	1587
6	4996	1587
7	4958	1587

prune113.0ms (4.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	126	7	133

Error

Counts

133 → 7

Alt Table

Status	Error	Program
	5.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
✓	3.2b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
	7.1b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.2b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
	17.3b	(*.f64 (-.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 y) z) 3)) 1) x)
✓	3.2b	(*.f64 (-.f64 (fma.f64 y (/.f64 1 z) (/.f64 1 z)) 1) x)
	33.3b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))

Compiler

Compiled 2549 to 1736 computations (31.9% saved)

regimes394.0ms (15.4%)

Accuracy

Total 1.2b remaining (99.2%)

Threshold costs 0b (0%)

Counts

82 → 2

Compiler

Compiled 5648 to 3286 computations (41.8% saved)

bsearch5.0ms (0.2%)

Steps

Iters	Range		Point
2	32631633.127407543	128681315.00649185	48255398.06692279

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	30
1	24	30
2	27	30
3	29	30
4	30	30
5	29	30

end98.0ms (3.8%)

Compiler: Compiled 170 to 92 computations (45.9% saved)

Details

analyze121.0ms (4.7%)

sample755.0ms (29.5%)

simplify56.0ms (2.2%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series28.0ms (1.1%)

rewrite4.0ms (0.2%)

simplify78.0ms (3.1%)

prune57.0ms (2.2%)

localize5.0ms (0.2%)

series29.0ms (1.1%)

rewrite18.0ms (0.7%)

simplify117.0ms (4.6%)

prune87.0ms (3.4%)

localize7.0ms (0.3%)

series32.0ms (1.3%)

rewrite62.0ms (2.4%)

simplify120.0ms (4.7%)

prune177.0ms (6.9%)

localize9.0ms (0.3%)

series35.0ms (1.4%)

rewrite11.0ms (0.4%)

simplify133.0ms (5.2%)

prune113.0ms (4.4%)

regimes394.0ms (15.4%)

bsearch5.0ms (0.2%)

simplify3.0ms (0.1%)

end98.0ms (3.8%)

Profiling