Details

analyze869.0ms (28.3%)

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)

sample41.0ms (1.3%)

Algorithm

1×

intervals

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

prune5.0ms (0.2%)

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

38.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	38.8b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 51 to 26 computations (49% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	36.0b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

series59.0ms (1.9%)

Counts

1 → 36

Calls

1 calls:

59.0ms

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

rewrite2.0ms (0.1%)

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))))

simplify83.0ms (2.7%)

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

prune75.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	2	93

Error

0.0b

Counts

93 → 2

Alt Table

Status	Error	Program
▶	0.0b	(hypot.f64 x z)
	36.9b	(neg.f64 (fma.f64 1/2 (/.f64 (.f64 z z) x) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))

Compiler

Compiled 3135 to 1866 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)

series14.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

14.0ms

(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)

simplify58.0ms (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 (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	42	2	44

Error

0.0b

Counts

44 → 2

Alt Table

Status	Error	Program
✓	0.0b	(hypot.f64 x z)
▶	36.9b	(neg.f64 (fma.f64 1/2 (/.f64 (.f64 z z) x) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))

Compiler

Compiled 585 to 353 computations (39.7% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	6.5b	(/.f64 (*.f64 y y) x)
✓	6.6b	(/.f64 (*.f64 z z) x)

series25.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(/.f64 (*.f64 z z) x)
11.0ms	(/.f64 (*.f64 y y) x)

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`
6×	`associate-/r*_binary64`
6×	`*-un-lft-identity_binary64`
6×	`times-frac_binary64`

Counts

2 → 46

Calls

2 calls:

5.0ms	(/.f64 (*.f64 y y) x)
3.0ms	(/.f64 (*.f64 z z) x)

simplify89.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary64`
564×	`fma-neg_binary64`
322×	`associate-/l*_binary64`
312×	`*-commutative_binary64`
284×	`unswap-sqr_binary64`

Counts

94 → 58

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	84	858
1	184	768
2	528	768
3	1799	768
4	2368	768
5	3656	768
6	4627	768
7	4912	768

prune34.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	58	2	60

Error

Counts

60 → 2

Alt Table

Status	Error	Program
✓	0.0b	(hypot.f64 x z)
▶	34.2b	(neg.f64 (fma.f64 1/2 (.f64 z (/.f64 z x)) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))

Compiler

Compiled 1229 to 476 computations (61.3% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 z (/.f64 z x))
	6.5b	(/.f64 (*.f64 y y) x)

series15.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

15.0ms

(*.f64 z (/.f64 z x))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

5.0ms

(*.f64 z (/.f64 z x))

simplify77.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

998×	`fma-neg_binary64`
447×	`associate-/r*_binary64`
409×	`*-commutative_binary64`
353×	`associate-/r/_binary64`
222×	`unswap-sqr_binary64`

Counts

58 → 51

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	565
1	152	499
2	491	499
3	1243	491
4	2159	491
5	3065	491
6	4488	491
7	5157	491

prune39.0ms (1.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	80	2	82

Error

Counts

82 → 2

Alt Table

Status	Error	Program
✓	0.0b	(hypot.f64 x z)
✓	34.2b	(neg.f64 (fma.f64 1/2 (.f64 z (/.f64 z x)) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))

Compiler

Compiled 1734 to 649 computations (62.6% saved)

regimes175.0ms (5.7%)

Accuracy

Total 0.1b remaining (13.3%)

Threshold costs 0.1b (13.3%)

Counts

13 → 1

Compiler

Compiled 1869 to 1240 computations (33.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end14.0ms (0.4%)

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

sample1.3s (43%)

Algorithm

1×

intervals

Results

461.0ms

8000×

body

128

valid

Compiler

Compiled 50 to 33 computations (34% saved)

Details

analyze869.0ms (28.3%)

sample41.0ms (1.3%)

simplify7.0ms (0.2%)

prune5.0ms (0.2%)

localize7.0ms (0.2%)

series59.0ms (1.9%)

rewrite2.0ms (0.1%)

simplify83.0ms (2.7%)

prune75.0ms (2.4%)

localize2.0ms (0.1%)

series14.0ms (0.5%)

rewrite1.0ms (0%)

simplify58.0ms (1.9%)

prune21.0ms (0.7%)

localize10.0ms (0.3%)

series25.0ms (0.8%)

rewrite10.0ms (0.3%)

simplify89.0ms (2.9%)

prune34.0ms (1.1%)

localize10.0ms (0.3%)

series15.0ms (0.5%)

rewrite7.0ms (0.2%)

simplify77.0ms (2.5%)

prune39.0ms (1.3%)

regimes175.0ms (5.7%)

simplify2.0ms (0.1%)

end14.0ms (0.4%)

sample1.3s (43%)

Profiling