Details

analyze568.0ms (21.4%)

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)

sample49.0ms (1.8%)

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 (0.3%)

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

39.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	39.0b	(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 (.f64 x x) (.f64 y y)) (*.f64 z z))
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	36.3b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series73.0ms (2.7%)

Counts

3 → 96

Calls

3 calls:

52.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
14.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
6.0ms	(+.f64 (.f64 x x) (.f64 y y))

rewrite16.0ms (0.6%)

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	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
4.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify83.0ms (3.1%)

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

prune104.0ms (3.9%)

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
✓	39.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
	37.2b	(neg.f64 (fma.f64 1/2 (/.f64 (.f64 z z) x) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))
	30.0b	(hypot.f64 z y)
▶	0.5b	(hypot.f64 z x)

Compiler

Compiled 4505 to 2177 computations (51.7% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series12.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(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)

simplify50.0ms (1.9%)

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

prune21.0ms (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
✓	39.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
	37.2b	(neg.f64 (fma.f64 1/2 (/.f64 (.f64 z z) x) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))
▶	30.0b	(hypot.f64 z y)
✓	0.5b	(hypot.f64 z x)

Compiler

Compiled 612 to 370 computations (39.5% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series13.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(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)

simplify49.0ms (1.8%)

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

prune22.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

Counts

46 → 4

Alt Table

Status	Error	Program
✓	39.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
▶	37.2b	(neg.f64 (fma.f64 1/2 (/.f64 (.f64 z z) x) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))
✓	30.0b	(hypot.f64 z y)
✓	0.5b	(hypot.f64 z x)

Compiler

Compiled 606 to 366 computations (39.6% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 (*.f64 y y) x) x)
✓	5.4b	(/.f64 (*.f64 z z) x)
✓	9.6b	(/.f64 (*.f64 y y) x)

series32.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

12.0ms	(fma.f64 1/2 (/.f64 (*.f64 y y) x) x)
11.0ms	(/.f64 (*.f64 z z) x)
10.0ms	(/.f64 (*.f64 y y) x)

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

5.0ms	(/.f64 (*.f64 z z) x)
3.0ms	(/.f64 (*.f64 y y) x)
0.0ms	(fma.f64 1/2 (/.f64 (*.f64 y y) x) x)

simplify79.0ms (3%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-neg_binary64`
354×	`*-commutative_binary64`
338×	`fma-def_binary64`
328×	`associate-/l*_binary64`
284×	`unswap-sqr_binary64`

Counts

128 → 81

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	98	1255
1	202	1142
2	576	1142
3	1952	1142
4	2730	1142
5	4720	1142
6	5129	1142

prune39.0ms (1.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	81	4	85

Error

Counts

85 → 4

Alt Table

Status	Error	Program
✓	39.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
✓	37.2b	(neg.f64 (fma.f64 1/2 (/.f64 (.f64 z z) x) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))
✓	30.0b	(hypot.f64 z y)
✓	0.5b	(hypot.f64 z x)

Compiler

Compiled 1699 to 657 computations (61.3% saved)

regimes291.0ms (11%)

Accuracy

Total 0.4b remaining (74%)

Threshold costs 0.4b (74%)

Counts

28 → 1

Compiler

Compiled 3367 to 2219 computations (34.1% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end11.0ms (0.4%)

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

sample1.1s (41.1%)

Algorithm

1×

intervals

Results

399.0ms

8000×

body

128

valid

Compiler

Compiled 71 to 46 computations (35.2% saved)

Details

analyze568.0ms (21.4%)

sample49.0ms (1.8%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series73.0ms (2.7%)

rewrite16.0ms (0.6%)

simplify83.0ms (3.1%)

prune104.0ms (3.9%)

localize2.0ms (0.1%)

series12.0ms (0.5%)

rewrite1.0ms (0%)

simplify50.0ms (1.9%)

prune21.0ms (0.8%)

localize2.0ms (0.1%)

series13.0ms (0.5%)

rewrite1.0ms (0%)

simplify49.0ms (1.8%)

prune22.0ms (0.8%)

localize11.0ms (0.4%)

series32.0ms (1.2%)

rewrite11.0ms (0.4%)

simplify79.0ms (3%)

prune39.0ms (1.5%)

regimes291.0ms (11%)

simplify5.0ms (0.2%)

end11.0ms (0.4%)

sample1.1s (41.1%)

Profiling