Details

analyze617.0ms (17.2%)

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
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample1.0s (28.5%)

Symmetry

(sort x y z)

Results

986.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	14
2	25	14
3	29	14
4	29	14

prune5.0ms (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

37.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	37.9b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 51 to 26 computations (49% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	35.2b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

series51.0ms (1.4%)

Counts

1 → 36

Calls

1 calls:

51.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

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

simplify119.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

704×	`cancel-sign-sub-inv_binary64`
387×	`fma-neg_binary64`
324×	`sub-neg_binary64`
203×	`fma-def_binary64`
180×	`distribute-neg-in_binary64`

Counts

51 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	2211
1	688	2064
2	2820	2062
3	4970	2062
4	5033	2062

prune119.0ms (3.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	3	93

Error

Counts

93 → 3

Alt Table

Status	Error	Program
	32.3b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 y y (.f64 x x)))) (*.f64 z z)) (hypot.f64 y x))
▶	0.4b	(hypot.f64 x z)
	32.9b	(hypot.f64 y z)

Compiler

Compiled 3151 to 1876 computations (40.5% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x z)

series12.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(hypot.f64 x z)

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

(hypot.f64 x z)

simplify52.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary64`
534×	`cancel-sign-sub-inv_binary64`
273×	`associate-/r/_binary64`
262×	`distribute-rgt-neg-in_binary64`
259×	`distribute-lft-neg-in_binary64`

Counts

34 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	550
1	178	541
2	505	525
3	2143	525
4	4483	525
5	5070	525

prune25.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	42	3	45

Error

Counts

45 → 3

Alt Table

Status	Error	Program
▶	32.3b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 y y (.f64 x x)))) (*.f64 z z)) (hypot.f64 y x))
✓	0.4b	(hypot.f64 x z)
	32.9b	(hypot.f64 y z)

Compiler

Compiled 601 to 363 computations (39.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y y (*.f64 x x))
✓	0.7b	(/.f64 1 (fma.f64 y y (*.f64 x x)))
✓	7.6b	(.f64 (sqrt.f64 (/.f64 1 (fma.f64 y y (.f64 x x)))) (*.f64 z z))
✓	27.2b	(sqrt.f64 (/.f64 1 (fma.f64 y y (*.f64 x x))))

series173.0ms (4.8%)

Counts

4 → 108

Calls

4 calls:

85.0ms	(.f64 (sqrt.f64 (/.f64 1 (fma.f64 y y (.f64 x x)))) (*.f64 z z))
67.0ms	(sqrt.f64 (/.f64 1 (fma.f64 y y (*.f64 x x))))
13.0ms	(/.f64 1 (fma.f64 y y (*.f64 x x)))
7.0ms	(fma.f64 y y (*.f64 x x))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
29×	`*-un-lft-identity_binary64`
29×	`sqrt-prod_binary64`
27×	`add-cube-cbrt_binary64`

Counts

4 → 111

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 (/.f64 1 (fma.f64 y y (.f64 x x)))) (*.f64 z z))
2.0ms	(/.f64 1 (fma.f64 y y (*.f64 x x)))
2.0ms	(sqrt.f64 (/.f64 1 (fma.f64 y y (*.f64 x x))))
0.0ms	(fma.f64 y y (*.f64 x x))

simplify185.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l*_binary64`
469×	`associate-/r*_binary64`
437×	`fma-neg_binary64`
291×	`fma-def_binary64`
257×	`cancel-sign-sub-inv_binary64`

Counts

219 → 248

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	4612
1	508	4295
2	1709	4263
3	4843	4247
4	5076	4247

prune157.0ms (4.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	248	3	251

Error

Counts

251 → 3

Alt Table

Status	Error	Program
✓	32.3b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 y y (.f64 x x)))) (*.f64 z z)) (hypot.f64 y x))
✓	0.4b	(hypot.f64 x z)
▶	32.9b	(hypot.f64 y z)

Compiler

Compiled 6716 to 3031 computations (54.9% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 y z)

series12.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(hypot.f64 y z)

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

(hypot.f64 y z)

simplify54.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

963×	`fma-neg_binary64`
527×	`cancel-sign-sub-inv_binary64`
291×	`distribute-rgt-neg-in_binary64`
290×	`distribute-lft-neg-in_binary64`
281×	`associate-/r/_binary64`

Counts

34 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	574
1	175	541
2	506	525
3	2149	525
4	4655	525
5	5014	525

prune21.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	42	3	45

Error

Counts

45 → 3

Alt Table

Status	Error	Program
✓	32.3b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 y y (.f64 x x)))) (*.f64 z z)) (hypot.f64 y x))
✓	0.4b	(hypot.f64 x z)
✓	32.9b	(hypot.f64 y z)

Compiler

Compiled 574 to 346 computations (39.7% saved)

regimes431.0ms (12%)

Accuracy

Total 0.5b remaining (95.2%)

Threshold costs 0.5b (95.2%)

Counts

48 → 1

Compiler

Compiled 6927 to 4531 computations (34.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end486.0ms (13.5%)

Compiler: Compiled 57 to 37 computations (35.1% saved)

Details

analyze617.0ms (17.2%)

sample1.0s (28.5%)

simplify6.0ms (0.2%)

prune5.0ms (0.1%)

localize6.0ms (0.2%)

series51.0ms (1.4%)

rewrite1.0ms (0%)

simplify119.0ms (3.3%)

prune119.0ms (3.3%)

localize2.0ms (0.1%)

series12.0ms (0.3%)

rewrite1.0ms (0%)

simplify52.0ms (1.4%)

prune25.0ms (0.7%)

localize11.0ms (0.3%)

series173.0ms (4.8%)

rewrite18.0ms (0.5%)

simplify185.0ms (5.1%)

prune157.0ms (4.4%)

localize2.0ms (0.1%)

series12.0ms (0.3%)

rewrite1.0ms (0%)

simplify54.0ms (1.5%)

prune21.0ms (0.6%)

regimes431.0ms (12%)

simplify2.0ms (0%)

end486.0ms (13.5%)

Profiling