Details

analyze42.0ms (1%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample91.0ms (2.2%)

Algorithm

1×

intervals

Results

40.0ms	67×	body	2048	valid
21.0ms	35×	body	1024	valid
15.0ms	139×	body	128	valid
4.0ms	12×	body	512	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 28 to 26 computations (7.1% saved)

simplify23.0ms (0.5%)

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

prune6.0ms (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

13.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 1/2 (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))
✓	0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite141.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cube-cbrt_binary64`
24×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-log-exp_binary64`

Counts

4 → 175

Calls

4 calls:

28.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
25.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
24.0ms	(/.f64 1/2 (hypot.f64 1 x))
23.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series65.0ms (1.5%)

Counts

4 → 48

Calls

4 calls:

27.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
18.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
11.0ms	(/.f64 1/2 (hypot.f64 1 x))
9.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify176.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-def_binary64`
480×	`fma-neg_binary64`
412×	`cancel-sign-sub-inv_binary64`
235×	`sub-neg_binary64`
223×	`times-frac_binary64`

Counts

223 → 325

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	286	3473
1	725	3277
2	2200	3084
3	4509	3084
4	4787	3084

prune218.0ms (5.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	321	4	325
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	322	4	326

Error

0.0b

Counts

326 → 4

Alt Table

Status	Error	Program
	13.7b	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
	14.0b	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
	34.4b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
▶	13.1b	(/.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))))))

Compiler

Compiled 6020 to 5388 computations (10.5% 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 1/2 (hypot.f64 1 x))
✓	0.1b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cube-cbrt_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64`
5×	`flip3--_binary64`
4×	`pow1_binary64`

Counts

1 → 46

Calls

1 calls:

14.0ms

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

series5.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

simplify83.0ms (2%)

Algorithm

1×	egg-herbie

Rules

630×	`fma-neg_binary64`
293×	`neg-mul-1_binary64`
272×	`fma-def_binary64`
249×	`distribute-rgt-neg-in_binary64`
248×	`div-sub_binary64`

Counts

58 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	830
1	281	805
2	774	786
3	2375	786
4	4329	786
5	4777	786

prune253.0ms (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	411	0	411
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	411	4	415

Error

0.0b

Counts

415 → 4

Alt Table

Status	Error	Program
▶	13.7b	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
	14.0b	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
	34.4b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
✓	13.1b	(/.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))))))

Compiler

Compiled 7727 to 6827 computations (11.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.1b	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.7b	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64`

Counts

3 → 117

Calls

3 calls:

13.0ms	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
11.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
8.0ms	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))

series68.0ms (1.6%)

Counts

3 → 16

Calls

3 calls:

30.0ms	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
27.0ms	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
10.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

simplify111.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

484×	`fma-def_binary64`
452×	`sub-neg_binary64`
289×	`associate-l_binary64`
288×	`associate-r_binary64`
235×	`cancel-sign-sub-inv_binary64`

Counts

133 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	2346
1	423	2248
2	1285	2169
3	4439	2128
4	4837	2128

prune182.0ms (4.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	504	0	504
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	504	4	508

Error

0.0b

Counts

508 → 4

Alt Table

Status	Error	Program
✓	13.7b	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
▶	14.0b	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
	34.4b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
✓	13.1b	(/.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))))))

Compiler

Compiled 5303 to 4822 computations (9.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)
✓	0.5b	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
	0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cube-cbrt_binary64`
9×	`cube-div_binary64`
9×	`flip3--_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`pow1/3_binary64`

Counts

2 → 85

Calls

2 calls:

15.0ms	(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)
11.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))

series24.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

17.0ms	(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)
7.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))

simplify98.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary64`
333×	`distribute-rgt-in_binary64`
271×	`cancel-sign-sub-inv_binary64`
231×	`sub-neg_binary64`
202×	`distribute-neg-in_binary64`

Counts

109 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	2501
1	656	2200
2	2446	2174
3	4917	2174

prune254.0ms (6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	916	1	917
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	917	4	921

Error

0.0b

Counts

921 → 4

Alt Table

Status	Error	Program
	14.4b	(pow.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))) 3)
✓	13.7b	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
	34.4b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
✓	13.1b	(/.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))))))

Compiler

Compiled 7490 to 6785 computations (9.4% saved)

regimes750.0ms (17.7%)

Accuracy

Total 0.1b remaining (55%)

Threshold costs 0.1b (55%)

Compiler

Compiled 10414 to 9539 computations (8.4% saved)

bsearch2.0ms (0.1%)

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

simplify4.0ms (0.1%)

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	22	50
1	29	50
2	36	50
3	38	50
4	39	50
5	37	50

end1.0ms (0%)

Compiler: Compiled 35 to 29 computations (17.1% saved)

sample1.5s (35.6%)

Algorithm

1×

intervals

Results

689.0ms	2149×	body	2048	valid
226.0ms	1032×	body	1024	valid
212.0ms	4110×	body	128	valid
75.0ms	465×	body	512	valid
25.0ms	244×	body	256	valid

Compiler

Compiled 109 to 95 computations (12.8% saved)

Details

analyze42.0ms (1%)

sample91.0ms (2.2%)

simplify23.0ms (0.5%)

prune6.0ms (0.1%)

localize14.0ms (0.3%)

rewrite141.0ms (3.3%)

series65.0ms (1.5%)

simplify176.0ms (4.2%)

prune218.0ms (5.2%)

localize8.0ms (0.2%)

rewrite17.0ms (0.4%)

series5.0ms (0.1%)

simplify83.0ms (2%)

prune253.0ms (6%)

localize8.0ms (0.2%)

rewrite40.0ms (0.9%)

series68.0ms (1.6%)

simplify111.0ms (2.6%)

prune182.0ms (4.3%)

localize9.0ms (0.2%)

rewrite32.0ms (0.8%)

series24.0ms (0.6%)

simplify98.0ms (2.3%)

prune254.0ms (6%)

regimes750.0ms (17.7%)

bsearch2.0ms (0.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.5s (35.6%)

Profiling