Details

analyze2.1s (33.6%)

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)

sample2.1s (32.9%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

Results

1.3s	8256×	body	128	valid
636.0ms	4088×	body	128	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify104.0ms (1.7%)

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

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

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 (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(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)))

series41.0ms (0.7%)

Counts

2 → 120

Calls

2 calls:

34.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
7.0ms	(fma.f64 (*.f64 a 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 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
0.0ms	(fma.f64 (*.f64 a b) -1/4 c)

simplify95.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

384×	`distribute-lft-in_binary64`
384×	`distribute-rgt-in_binary64`
363×	`fma-def_binary64`
307×	`associate-l_binary64`
285×	`associate-r_binary64`

Counts

140 → 47

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	2333
1	97	2083
2	201	1949
3	636	1949
4	2770	1949
5	4702	1949
6	5046	1949

prune38.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	4	48

Error

Counts

48 → 4

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)))
▶	0.0b	(fma.f64 a (.f64 b -1/4) (fma.f64 y x (fma.f64 1/16 (.f64 t z) c)))
	16.0b	(fma.f64 1/16 (.f64 t z) (fma.f64 (.f64 a b) -1/4 c))
	35.2b	(.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)))))

Compiler

Compiled 989 to 500 computations (49.4% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series21.0ms (0.3%)

Counts

2 → 96

Calls

2 calls:

14.0ms	(fma.f64 y x (fma.f64 1/16 (*.f64 t z) c))
7.0ms	(fma.f64 1/16 (*.f64 t z) 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 1/16 (*.f64 t z) c)
0.0ms	(fma.f64 y x (fma.f64 1/16 (*.f64 t z) c))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

946×	`distribute-lft-in_binary64`
946×	`distribute-rgt-in_binary64`
433×	`associate-l_binary64`
431×	`fma-def_binary64`
361×	`associate-r_binary64`

Counts

116 → 34

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	1177
1	50	1135
2	140	1135
3	595	1135
4	4684	1135
5	4812	1135
6	4998	1135

prune33.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	35	3	38

Error

Counts

38 → 3

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)))
▶	16.0b	(fma.f64 1/16 (.f64 t z) (fma.f64 (.f64 a b) -1/4 c))
	32.9b	(fma.f64 a (.f64 b -1/4) (fma.f64 y x (.f64 (sqrt.f64 (fma.f64 1/16 (.f64 t z) c)) (sqrt.f64 (fma.f64 1/16 (.f64 t z) c)))))

Compiler

Compiled 712 to 361 computations (49.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series21.0ms (0.3%)

Counts

1 → 60

Calls

1 calls:

21.0ms

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

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

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

822×	`associate-+r+_binary64`
791×	`associate-+l+_binary64`
352×	`distribute-lft-in_binary64`
352×	`distribute-rgt-in_binary64`
227×	`distribute-lft-neg-out_binary64`

Counts

70 → 29

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	1180
1	54	959
2	110	959
3	370	959
4	1808	959
5	6091	959

prune26.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	42	3	45

Error

Counts

45 → 3

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)))
✓	16.0b	(fma.f64 1/16 (.f64 t z) (fma.f64 (.f64 a b) -1/4 c))
▶	32.9b	(fma.f64 a (.f64 b -1/4) (fma.f64 y x (.f64 (sqrt.f64 (fma.f64 1/16 (.f64 t z) c)) (sqrt.f64 (fma.f64 1/16 (.f64 t z) c)))))

Compiler

Compiled 712 to 354 computations (50.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y x (.f64 (sqrt.f64 (fma.f64 1/16 (.f64 t z) c)) (sqrt.f64 (fma.f64 1/16 (*.f64 t z) c))))
	0.0b	(fma.f64 1/16 (*.f64 t z) c)
✓	0.0b	(sqrt.f64 (fma.f64 1/16 (*.f64 t z) c))
✓	0.2b	(.f64 (sqrt.f64 (fma.f64 1/16 (.f64 t z) c)) (sqrt.f64 (fma.f64 1/16 (*.f64 t z) c)))

series65.0ms (1%)

Counts

3 → 108

Calls

3 calls:

41.0ms

(sqrt.f64 (fma.f64 1/16 (*.f64 t z) c))

16.0ms

(fma.f64 y x (*.f64 (sqrt.f64 (fma.f64 1/16 (*.f64 t z) c)) (sqrt.f64 (fma.f64 1/16 (*.f64 t z) c))))

7.0ms

(*.f64 (sqrt.f64 (fma.f64 1/16 (*.f64 t z) c)) (sqrt.f64 (fma.f64 1/16 (*.f64 t z) c)))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

5.0ms

(*.f64 (sqrt.f64 (fma.f64 1/16 (*.f64 t z) c)) (sqrt.f64 (fma.f64 1/16 (*.f64 t z) c)))

1.0ms

(sqrt.f64 (fma.f64 1/16 (*.f64 t z) c))

0.0ms

(fma.f64 y x (*.f64 (sqrt.f64 (fma.f64 1/16 (*.f64 t z) c)) (sqrt.f64 (fma.f64 1/16 (*.f64 t z) c))))

simplify118.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

540×	`associate-l_binary64`
508×	`associate-r_binary64`
437×	`unswap-sqr_binary64`
380×	`cancel-sign-sub-inv_binary64`
266×	`fma-neg_binary64`

Counts

186 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	2460
1	273	2292
2	792	2242
3	3091	2214
4	4939	2214
5	4994	2214
6	4939	2214

prune147.0ms (2.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	178	3	181

Error

Counts

181 → 3

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)))
✓	16.0b	(fma.f64 1/16 (.f64 t z) (fma.f64 (.f64 a b) -1/4 c))
✓	32.9b	(fma.f64 a (.f64 b -1/4) (fma.f64 y x (.f64 (sqrt.f64 (fma.f64 1/16 (.f64 t z) c)) (sqrt.f64 (fma.f64 1/16 (.f64 t z) c)))))

Compiler

Compiled 5305 to 2830 computations (46.7% saved)

regimes958.0ms (15.3%)

Accuracy

Total 0.0b remaining (19%)

Threshold costs 0.0b (19%)

Counts

59 → 1

Compiler

Compiled 20391 to 14530 computations (28.7% 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

end238.0ms (3.8%)

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 237 to 158 computations (33.3% saved)

Details

analyze2.1s (33.6%)

sample2.1s (32.9%)

simplify104.0ms (1.7%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series41.0ms (0.7%)

rewrite1.0ms (0%)

simplify95.0ms (1.5%)

prune38.0ms (0.6%)

localize10.0ms (0.2%)

series21.0ms (0.3%)

rewrite1.0ms (0%)

simplify76.0ms (1.2%)

prune33.0ms (0.5%)

localize9.0ms (0.1%)

series21.0ms (0.3%)

rewrite1.0ms (0%)

simplify52.0ms (0.8%)

prune26.0ms (0.4%)

localize14.0ms (0.2%)

series65.0ms (1%)

rewrite11.0ms (0.2%)

simplify118.0ms (1.9%)

prune147.0ms (2.3%)

regimes958.0ms (15.3%)

simplify2.0ms (0%)

end238.0ms (3.8%)

Profiling