Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample64.0ms (1.6%)

Algorithm

1×

intervals

Results

21.0ms	63×	body	2048	valid
11.0ms	140×	body	128	valid
8.0ms	37×	body	1024	valid
2.0ms	10×	body	512	valid
1.0ms	6×	body	256	valid

Compiler

Compiled 28 to 26 computations (7.1% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	35	15
4	42	15
5	52	15
6	60	15
7	69	15
8	72	15
9	53	15

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

15.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.0b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	3.0b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series18.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
4.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
24×	`sqrt-prod_binary64`
21×	`prod-diff_binary64`

Counts

4 → 110

Calls

4 calls:

8.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
0.0ms	(hypot.f64 1 x)

simplify133.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
463×	`fma-neg_binary64`
398×	`times-frac_binary64`
372×	`associate-l_binary64`
332×	`associate-r_binary64`

Counts

158 → 196

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	3244
1	653	2896
2	1805	2575
3	4560	2539
4	4860	2539
5	5266	2539

prune170.0ms (4.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	193	4	197

Error

Counts

197 → 4

Alt Table

Status	Error	Program
▶	14.5b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	15.3b	(+.f64 (fma.f64 1 1 (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
✓	15.0b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	33.0b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))

Compiler

Compiled 4534 to 4028 computations (11.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	2.5b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series29.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

26.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
3.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`add-sqr-sqrt_binary64`
109×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
58×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

2 → 138

Calls

2 calls:

15.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
6.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify198.0ms (5%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
230×	`fma-def_binary64`
191×	`associate-r_binary64`
183×	`fma-neg_binary64`
177×	`associate-/r*_binary64`

Counts

162 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	407	7612
1	1109	5376
2	3422	5334
3	4984	5334
4	4941	5334

prune370.0ms (9.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	336	1	337
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	339	2	341

Error

Counts

341 → 2

Alt Table

Status	Error	Program
	33.0b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
▶	14.5b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 11652 to 10396 computations (10.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	2.5b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series10.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64`
64×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
28×	`distribute-lft-out_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 66

Calls

1 calls:

14.0ms

(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

simplify108.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary64`
434×	`associate--l+_binary64`
397×	`fma-neg_binary64`
299×	`associate-/r*_binary64`
172×	`associate-+r+_binary64`

Counts

78 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	3489
1	548	3360
2	1834	3344
3	4893	3341
4	5158	3341

prune328.0ms (8.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	334	0	334
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	334	2	336

Error

Counts

336 → 2

Alt Table

Status	Error	Program
▶	33.0b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
✓	14.5b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 11556 to 10304 computations (10.8% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	16.1b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(fma.f64 (pow.f64 x 4) -11/128 (*.f64 1/8 (*.f64 x 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

(fma.f64 (pow.f64 x 4) -11/128 (*.f64 1/8 (*.f64 x x)))

simplify43.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

563×	`distribute-rgt-out_binary64`
508×	`associate-l_binary64`
438×	`associate-r_binary64`
278×	`exp-prod_binary64`
199×	`distribute-lft-neg-out_binary64`

Counts

22 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	364
1	42	317
2	88	317
3	337	317
4	2024	317
5	4944	317

prune14.0ms (0.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	23	2	25

Error

Counts

25 → 2

Alt Table

Status	Error	Program
✓	33.0b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
✓	14.5b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 367 to 239 computations (34.9% saved)

regimes816.0ms (20.6%)

Accuracy

Total 0.0b remaining (44.4%)

Threshold costs 0.0b (44.4%)

Counts

79 → 2

Compiler

Compiled 13403 to 12115 computations (9.6% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	30	53
2	37	53
3	39	53
4	40	53
5	38	53

end1.0ms (0%)

Compiler: Compiled 37 to 31 computations (16.2% saved)

sample1.5s (38.6%)

Algorithm

1×

intervals

Results

684.0ms	2127×	body	2048	valid
241.0ms	1001×	body	1024	valid
231.0ms	4115×	body	128	valid
90.0ms	512×	body	512	valid
26.0ms	245×	body	256	valid

Compiler

Compiled 84 to 72 computations (14.3% saved)

Details

analyze1.0ms (0%)

sample64.0ms (1.6%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series18.0ms (0.5%)

rewrite22.0ms (0.6%)

simplify133.0ms (3.4%)

prune170.0ms (4.3%)

localize8.0ms (0.2%)

series29.0ms (0.7%)

rewrite36.0ms (0.9%)

simplify198.0ms (5%)

prune370.0ms (9.3%)

localize10.0ms (0.3%)

series10.0ms (0.3%)

rewrite21.0ms (0.5%)

simplify108.0ms (2.7%)

prune328.0ms (8.3%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify43.0ms (1.1%)

prune14.0ms (0.4%)

regimes816.0ms (20.6%)

bsearch3.0ms (0.1%)

simplify6.0ms (0.2%)

end1.0ms (0%)

sample1.5s (38.6%)

Profiling