Details

analyze2.1s (29.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0%	99.7%	0.3%	13
0%	99.7%	0.3%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample2.0s (28.6%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

Results

1.3s	8256×	body	128	valid
607.0ms	4052×	body	128	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify108.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1251×	`fma-neg_binary64`
530×	`fma-def_binary64`
258×	`cancel-sign-sub-inv_binary64`
148×	`distribute-rgt-in_binary64`
135×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	23
1	34	23
2	77	22
3	156	21
4	332	19
5	674	19
6	959	19
7	1365	19
8	1815	19
9	1835	19
10	1845	19
11	1846	19
12	1846	19
13	2162	19
14	2166	19
15	2166	19
16	2055	19

prune4.0ms (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	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

Compiler

Compiled 80 to 51 computations (36.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
✓	0.0b	(fma.f64 (*.f64 a b) -1/4 c)

series679.0ms (9.7%)

Counts

3 → 180

Calls

3 calls:

648.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
23.0ms	(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))
6.0ms	(fma.f64 (*.f64 a b) -1/4 c)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 30

Calls

3 calls:

0.0ms	(fma.f64 (*.f64 a b) -1/4 c)
0.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
0.0ms	(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))

simplify154.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

560×	`distribute-lft-in_binary64`
560×	`distribute-rgt-in_binary64`
420×	`fma-def_binary64`
395×	`associate-l_binary64`
366×	`associate-r_binary64`

Counts

210 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	3513
1	112	3132
2	231	2908
3	780	2908
4	3702	2908
5	4969	2908
6	5000	2908
7	4953	2908

prune57.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	2	75

Error

Counts

75 → 2

Alt Table

Status	Error	Program
	33.8b	(.f64 (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c)))) (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))
▶	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))

Status

Error

Program

33.8b

(*.f64 (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))

▶

0.0b

(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))

Compiler

Compiled 1489 to 742 computations (50.2% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))
✓	0.0b	(fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c))

series54.0ms (0.8%)

Counts

2 → 144

Calls

2 calls:

34.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))
20.0ms	(fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c))
0.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))

simplify108.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

474×	`distribute-lft-in_binary64`
474×	`distribute-rgt-in_binary64`
356×	`fma-def_binary64`
351×	`associate-*l/_binary64`
329×	`associate-*r/_binary64`

Counts

164 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	55	3077
1	103	2767
2	203	2543
3	615	2543
4	2699	2543
5	4687	2543
6	5285	2543

prune35.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	57	2	59

Error

Counts

59 → 2

Alt Table

Status	Error	Program
▶	33.8b	(.f64 (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c)))) (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))

Status

Error

Program

▶

33.8b

(*.f64 (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))

✓

0.0b

(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))

Compiler

Compiled 1123 to 577 computations (48.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
	0.0b	(fma.f64 (*.f64 a b) -1/4 c)
✓	0.1b	(sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))))
✓	0.3b	(.f64 (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c)))) (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))

series369.0ms (5.3%)

Counts

2 → 112

Calls

2 calls:

337.0ms

(sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))))

31.0ms

(*.f64 (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms

(*.f64 (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))

1.0ms

(sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))))

simplify154.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

539×	`fma-def_binary64`
451×	`*-commutative_binary64`
431×	`fma-neg_binary64`
370×	`distribute-rgt-in_binary64`
364×	`distribute-lft-in_binary64`

Counts

180 → 134

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	189	5668
1	478	5102
2	1457	4716
3	4045	4655
4	4879	4611
5	4970	4611

prune240.0ms (3.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	295	2	297

Error

Counts

297 → 2

Alt Table

Status	Error	Program
✓	33.8b	(.f64 (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c)))) (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))

Status

Error

Program

✓

33.8b

(*.f64 (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (sqrt.f64 (fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))

✓

0.0b

(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))

Compiler

Compiled 12196 to 6219 computations (49% saved)

regimes851.0ms (12.1%)

Accuracy

Total 0.0b remaining (7.8%)

Threshold costs 0.0b (7.8%)

Counts

46 → 1

Compiler

Compiled 17735 to 12090 computations (31.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	16	19
2	16	19

end96.0ms (1.4%)

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 227 to 149 computations (34.4% saved)

Details

analyze2.1s (29.2%)

sample2.0s (28.6%)

simplify108.0ms (1.5%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series679.0ms (9.7%)

rewrite2.0ms (0%)

simplify154.0ms (2.2%)

prune57.0ms (0.8%)

localize10.0ms (0.1%)

series54.0ms (0.8%)

rewrite1.0ms (0%)

simplify108.0ms (1.5%)

prune35.0ms (0.5%)

localize13.0ms (0.2%)

series369.0ms (5.3%)

rewrite13.0ms (0.2%)

simplify154.0ms (2.2%)

prune240.0ms (3.4%)

regimes851.0ms (12.1%)

simplify2.0ms (0%)

end96.0ms (1.4%)

Profiling