Details

analyze574.0ms (19.3%)

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)

sample45.0ms (1.5%)

Algorithm

1×

intervals

Symmetry

(sort x y z)

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

simplify7.0ms (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

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

37.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	37.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

Compiler

Compiled 55 to 30 computations (45.5% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
✓	34.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series71.0ms (2.4%)

Counts

3 → 96

Calls

3 calls:

52.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
13.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
6.0ms	(+.f64 (.f64 x x) (.f64 y y))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
4×	`sum-log_binary64`

Counts

3 → 50

Calls

3 calls:

5.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
5.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify82.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

813×	`cancel-sign-sub-inv_binary64`
368×	`fma-neg_binary64`
357×	`sub-neg_binary64`
254×	`fma-def_binary64`
189×	`associate-r_binary64`

Counts

146 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	290	3374
1	842	3126
2	3648	3124
3	5589	3124

prune105.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	159	4	163

Error

Counts

163 → 4

Alt Table

Status	Error	Program
▶	0.6b	(hypot.f64 z x)
✓	37.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
	6.2b	(fma.f64 1/2 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (fma.f64 z z (*.f64 x x))))) (hypot.f64 z x))
	29.3b	(hypot.f64 z y)

Compiler

Compiled 4485 to 2174 computations (51.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(hypot.f64 z x)

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 z x)

simplify55.0ms (1.8%)

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

prune24.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	42	4	46

Error

Counts

46 → 4

Alt Table

Status	Error	Program
✓	0.6b	(hypot.f64 z x)
✓	37.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
▶	6.2b	(fma.f64 1/2 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (fma.f64 z z (*.f64 x x))))) (hypot.f64 z x))
	29.3b	(hypot.f64 z y)

Compiler

Compiled 616 to 372 computations (39.6% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z z (*.f64 x x))
✓	0.4b	(/.f64 1 (fma.f64 z z (*.f64 x x)))
✓	6.3b	(.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (fma.f64 z z (*.f64 x x)))))
✓	34.3b	(sqrt.f64 (/.f64 1 (fma.f64 z z (*.f64 x x))))

series126.0ms (4.2%)

Counts

4 → 108

Calls

4 calls:

85.0ms	(.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (fma.f64 z z (*.f64 x x)))))
18.0ms	(sqrt.f64 (/.f64 1 (fma.f64 z z (*.f64 x x))))
16.0ms	(/.f64 1 (fma.f64 z z (*.f64 x x)))
6.0ms	(fma.f64 z z (*.f64 x x))

rewrite21.0ms (0.7%)

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:

8.0ms	(.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (fma.f64 z z (*.f64 x x)))))
2.0ms	(/.f64 1 (fma.f64 z z (*.f64 x x)))
2.0ms	(sqrt.f64 (/.f64 1 (fma.f64 z z (*.f64 x x))))
0.0ms	(fma.f64 z z (*.f64 x x))

simplify120.0ms (4%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-/l*_binary64`
486×	`fma-neg_binary64`
453×	`associate-/r*_binary64`
291×	`fma-def_binary64`
257×	`cancel-sign-sub-inv_binary64`

Counts

219 → 247

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	4575
1	515	4258
2	1721	4226
3	4603	4210
4	4973	4210

prune182.0ms (6.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	247	4	251

Error

Counts

251 → 4

Alt Table

Status	Error	Program
✓	0.6b	(hypot.f64 z x)
✓	37.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
✓	6.2b	(fma.f64 1/2 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (fma.f64 z z (*.f64 x x))))) (hypot.f64 z x))
▶	29.3b	(hypot.f64 z y)

Compiler

Compiled 6676 to 3003 computations (55% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(hypot.f64 z y)

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 z y)

simplify56.0ms (1.9%)

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

prune23.0ms (0.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	42	4	46

Error

Counts

46 → 4

Alt Table

Status	Error	Program
✓	0.6b	(hypot.f64 z x)
✓	37.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
✓	6.2b	(fma.f64 1/2 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (fma.f64 z z (*.f64 x x))))) (hypot.f64 z x))
✓	29.3b	(hypot.f64 z y)

Compiler

Compiled 589 to 355 computations (39.7% saved)

regimes317.0ms (10.7%)

Accuracy

Total 0.4b remaining (72.8%)

Threshold costs 0.4b (72.8%)

Counts

37 → 1

Compiler

Compiled 4958 to 3251 computations (34.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end13.0ms (0.4%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample1.1s (36.3%)

Algorithm

1×

intervals

Results

387.0ms

8000×

body

128

valid

Compiler

Compiled 73 to 47 computations (35.6% saved)

Details

analyze574.0ms (19.3%)

sample45.0ms (1.5%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series71.0ms (2.4%)

rewrite15.0ms (0.5%)

simplify82.0ms (2.8%)

prune105.0ms (3.5%)

localize4.0ms (0.1%)

series11.0ms (0.4%)

rewrite1.0ms (0%)

simplify55.0ms (1.8%)

prune24.0ms (0.8%)

localize14.0ms (0.5%)

series126.0ms (4.2%)

rewrite21.0ms (0.7%)

simplify120.0ms (4%)

prune182.0ms (6.1%)

localize2.0ms (0.1%)

series11.0ms (0.4%)

rewrite1.0ms (0%)

simplify56.0ms (1.9%)

prune23.0ms (0.8%)

regimes317.0ms (10.7%)

simplify2.0ms (0.1%)

end13.0ms (0.4%)

sample1.1s (36.3%)

Profiling