Details

analyze520.0ms (11%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
40.6%	56.9%	2.5%	9
46%	49.5%	4.4%	10
50.3%	44.9%	4.8%	11
60.3%	30.5%	9.2%	12
62.9%	25.7%	11.4%	13
65.2%	23.2%	11.7%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.2s (26.2%)

Results

1.0s	8256×	body	128	valid
107.0ms	974×	body	128	invalid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify121.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

724×	`div-sub_binary64`
708×	`fma-neg_binary64`
609×	`sub-neg_binary64`
598×	`times-frac_binary64`
477×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	25	17
2	55	15
3	125	15
4	274	15
5	564	11
6	1031	11
7	1668	11
8	2410	11
9	3506	11
10	4269	11
11	4538	11
12	4833	11
13	4950	11
14	4672	11

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y))
▶	0.2b	(fma.f64 (/.f64 4 y) (-.f64 x z) 4)

Compiler

Compiled 78 to 57 computations (26.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (/.f64 4 y) (-.f64 x z) 4)

series10.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

10.0ms

(fma.f64 (/.f64 4 y) (-.f64 x z) 4)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 4 y) (-.f64 x z) 4)

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

867×	`associate-*l/_binary64`
335×	`distribute-lft-in_binary64`
335×	`distribute-rgt-in_binary64`
242×	`associate-/l*_binary64`
196×	`distribute-lft-neg-out_binary64`

Counts

46 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	575
1	61	498
2	126	496
3	370	496
4	1797	496
5	5240	496

prune29.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	31	2	33

Error

0.0b

Counts

33 → 2

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 4 (.f64 4 (/.f64 x y))) (.f64 4 (/.f64 z y)))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))

Status

Error

Program

▶

0.0b

(-.f64 (+.f64 4 (*.f64 4 (/.f64 x y))) (*.f64 4 (/.f64 z y)))

1.2b

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))

Compiler

Compiled 443 to 257 computations (42% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 4 (.f64 4 (/.f64 x y))) (.f64 4 (/.f64 z y)))
✓	0.0b	(*.f64 4 (/.f64 z y))
✓	0.0b	(*.f64 4 (/.f64 x y))

series31.0ms (0.6%)

Counts

3 → 27

Calls

3 calls:

15.0ms	(-.f64 (+.f64 4 (.f64 4 (/.f64 x y))) (.f64 4 (/.f64 z y)))
8.0ms	(*.f64 4 (/.f64 z y))
7.0ms	(*.f64 4 (/.f64 x y))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
26×	`associate-r_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`

Counts

3 → 92

Calls

3 calls:

5.0ms	(*.f64 4 (/.f64 x y))
5.0ms	(*.f64 4 (/.f64 z y))
5.0ms	(-.f64 (+.f64 4 (.f64 4 (/.f64 x y))) (.f64 4 (/.f64 z y)))

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

449×	`associate-l_binary64`
387×	`associate-*r/_binary64`
376×	`times-frac_binary64`
358×	`associate-*l/_binary64`
356×	`fma-def_binary64`

Counts

119 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	1541
1	456	1467
2	1337	1423
3	4502	1423
4	5020	1423

prune139.0ms (3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	134	3	137

Error

Counts

137 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 4 (.f64 4 (/.f64 x y))) (.f64 4 (/.f64 z y)))
	18.1b	(/.f64 (fma.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16) (.f64 z -4) (.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64))) (*.f64 y (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16)))
▶	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))

Compiler

Compiled 2860 to 1613 computations (43.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))
	0.2b	(fma.f64 (/.f64 4 y) (-.f64 x z) 4)
✓	0.3b	(cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))
✓	0.8b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))

series266.0ms (5.6%)

Counts

3 → 108

Calls

3 calls:

182.0ms

(*.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))

68.0ms

(cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))

16.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))

1.0ms

(cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))

simplify234.0ms (5%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-def_binary64`
768×	`times-frac_binary64`
328×	`*-commutative_binary64`
178×	`+-commutative_binary64`
160×	`sub-neg_binary64`

Counts

201 → 243

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	841	12417
1	2791	11968
2	4990	11968
3	4963	11968

prune747.0ms (15.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	492	0	492
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	492	3	495

Error

Counts

495 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 4 (.f64 4 (/.f64 x y))) (.f64 4 (/.f64 z y)))
▶	18.1b	(/.f64 (fma.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16) (.f64 z -4) (.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64))) (*.f64 y (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16)))
✓	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))

Compiler

Compiled 34024 to 23351 computations (31.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.2b	(*.f64 y (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16))
✓	2.6b	(*.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64))
✓	5.0b	(fma.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16) (.f64 z -4) (.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64)))
✓	15.3b	(/.f64 (fma.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16) (.f64 z -4) (.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64))) (*.f64 y (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16)))

series304.0ms (6.4%)

Counts

4 → 120

Calls

4 calls:

217.0ms	(/.f64 (fma.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16) (.f64 z -4) (.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64))) (*.f64 y (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16)))
51.0ms	(fma.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16) (.f64 z -4) (.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64)))
24.0ms	(*.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64))
11.0ms	(*.f64 y (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 77

Calls

4 calls:

5.0ms	(*.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64))
3.0ms	(/.f64 (fma.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16) (.f64 z -4) (.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64))) (*.f64 y (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16)))
3.0ms	(*.f64 y (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16))
0.0ms	(fma.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16) (.f64 z -4) (.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64)))

simplify122.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

568×	`fma-def_binary64`
364×	`distribute-rgt-in_binary64`
345×	`distribute-lft-in_binary64`
265×	`cancel-sign-sub-inv_binary64`
182×	`fma-neg_binary64`

Counts

197 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	7193
1	586	6272
2	2289	5581
3	5190	5581

prune154.0ms (3.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	139	3	142

Error

Counts

142 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 4 (.f64 4 (/.f64 x y))) (.f64 4 (/.f64 z y)))
✓	18.1b	(/.f64 (fma.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16) (.f64 z -4) (.f64 y (fma.f64 64 (pow.f64 (/.f64 x y) 3) 64))) (*.f64 y (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) 16 -16) 16)))
✓	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4))) (cbrt.f64 (fma.f64 (/.f64 4 y) (-.f64 x z) 4)))

Compiler

Compiled 6492 to 3680 computations (43.3% saved)

regimes508.0ms (10.8%)

Accuracy

Total 0.0b remaining (37.9%)

Threshold costs 0.0b (37.9%)

Counts

87 → 1

Compiler

Compiled 9199 to 6498 computations (29.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	20	19
2	28	19
3	34	19
4	39	19
5	42	19
6	43	19
7	42	19

end75.0ms (1.6%)

Compiler: Compiled 122 to 82 computations (32.8% saved)

Details

analyze520.0ms (11%)

sample1.2s (26.2%)

simplify121.0ms (2.6%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series10.0ms (0.2%)

rewrite1.0ms (0%)

simplify39.0ms (0.8%)

prune29.0ms (0.6%)

localize11.0ms (0.2%)

series31.0ms (0.6%)

rewrite20.0ms (0.4%)

simplify77.0ms (1.6%)

prune139.0ms (3%)

localize10.0ms (0.2%)

series266.0ms (5.6%)

rewrite21.0ms (0.4%)

simplify234.0ms (5%)

prune747.0ms (15.8%)

localize15.0ms (0.3%)

series304.0ms (6.4%)

rewrite15.0ms (0.3%)

simplify122.0ms (2.6%)

prune154.0ms (3.3%)

regimes508.0ms (10.8%)

simplify5.0ms (0.1%)

end75.0ms (1.6%)

Profiling