Details

analyze16.0ms (0.4%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample51.0ms (1.3%)

Algorithm

1×

intervals

Results

20.0ms	70×	body	2048	valid
9.0ms	34×	body	1024	valid
6.0ms	120×	body	128	valid
4.0ms	26×	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

17.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	2.1b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series12.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

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

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`
20×	`sqrt-prod_binary64`

Counts

3 → 90

Calls

3 calls:

9.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
2.0ms	(/.f64 1/2 (hypot.f64 1 x))
0.0ms	(hypot.f64 1 x)

simplify96.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-neg_binary64`
541×	`fma-def_binary64`
371×	`associate-l_binary64`
321×	`associate-r_binary64`
223×	`cancel-sign-sub-inv_binary64`

Counts

126 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	2769
1	554	2393
2	1533	2083
3	4484	2083
4	5048	2083

prune132.0ms (3.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	3	157

Error

Counts

157 → 3

Alt Table

Status	Error	Program
▶	17.3b	(/.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))))))
	18.0b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	28.7b	(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 8) -1843/32768 (.f64 (pow.f64 x 4) -11/128))))

Compiler

Compiled 3681 to 3271 computations (11.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (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))))))
✓	1.7b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series35.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

25.0ms

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

3.0ms

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

rewrite44.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
80×	`times-frac_binary64`
60×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

3 → 157

Calls

3 calls:

17.0ms

(/.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))))))

7.0ms

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

7.0ms

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

simplify157.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

565×	`times-frac_binary64`
260×	`fma-def_binary64`
206×	`associate-r_binary64`
200×	`associate-/r*_binary64`
184×	`fma-neg_binary64`

Counts

193 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	8251
1	1249	5965
2	3887	5923
3	5050	5923

prune341.0ms (8.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	336	1	337
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	337	3	340

Error

Counts

340 → 3

Alt Table

Status	Error	Program
	28.6b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128)))
✓	17.3b	(/.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))))))
▶	18.0b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 11663 to 10409 computations (10.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	2.1b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series22.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

16.0ms

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

6.0ms

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

rewrite45.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`sqrt-prod_binary64`
84×	`add-sqr-sqrt_binary64`
62×	`*-un-lft-identity_binary64`
28×	`difference-of-squares_binary64`
23×	`swap-sqr_binary64`

Counts

2 → 114

Calls

2 calls:

22.0ms

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

9.0ms

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

simplify128.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-def_binary64`
575×	`times-frac_binary64`
462×	`fma-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
172×	`sub-neg_binary64`

Counts

138 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	236	4303
1	596	3886
2	2052	3740
3	4707	3738
4	4950	3738

prune492.0ms (12.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	441	0	441
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	441	3	444

Error

Counts

444 → 3

Alt Table

Status	Error	Program
▶	28.6b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128)))
✓	17.3b	(/.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))))))
✓	18.0b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 16840 to 15302 computations (9.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 x 4) -11/128)
✓	19.0b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128)))

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128)))
3.0ms	(*.f64 (pow.f64 x 4) -11/128)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-l_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(*.f64 (pow.f64 x 4) -11/128)
0.0ms	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128)))

simplify91.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

920×	`times-frac_binary64`
423×	`*-commutative_binary64`
397×	`exp-prod_binary64`
306×	`distribute-rgt-in_binary64`
301×	`distribute-lft-in_binary64`

Counts

61 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	868
1	145	795
2	351	777
3	1225	771
4	3296	771
5	4339	771
6	6379	771

prune45.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	60	3	63

Error

Counts

63 → 3

Alt Table

Status	Error	Program
✓	28.6b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128)))
✓	17.3b	(/.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))))))
✓	18.0b	(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 1279 to 945 computations (26.1% saved)

regimes705.0ms (17.5%)

Accuracy

Total 0.0b remaining (35.3%)

Threshold costs 0.0b (35.3%)

Counts

94 → 2

Compiler

Compiled 10352 to 9365 computations (9.5% 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`
3×	`*-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	26	57
1	34	57
2	41	57
3	43	57
4	44	57
5	42	57

end1.0ms (0%)

Compiler: Compiled 40 to 33 computations (17.5% saved)

sample1.5s (38.1%)

Algorithm

1×

intervals

Results

672.0ms	2088×	body	2048	valid
230.0ms	995×	body	1024	valid
216.0ms	4153×	body	128	valid
92.0ms	484×	body	512	valid
29.0ms	280×	body	256	valid

Compiler

Compiled 114 to 98 computations (14% saved)

Details

analyze16.0ms (0.4%)

sample51.0ms (1.3%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series12.0ms (0.3%)

rewrite19.0ms (0.5%)

simplify96.0ms (2.4%)

prune132.0ms (3.3%)

localize8.0ms (0.2%)

series35.0ms (0.9%)

rewrite44.0ms (1.1%)

simplify157.0ms (3.9%)

prune341.0ms (8.5%)

localize8.0ms (0.2%)

series22.0ms (0.6%)

rewrite45.0ms (1.1%)

simplify128.0ms (3.2%)

prune492.0ms (12.2%)

localize9.0ms (0.2%)

series8.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify91.0ms (2.2%)

prune45.0ms (1.1%)

regimes705.0ms (17.5%)

bsearch2.0ms (0.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.5s (38.1%)

Profiling