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)

sample2.1s (41.4%)

Results

1.1s	2188×	body	2048	valid
450.0ms	4257×	body	128	valid
383.0ms	1041×	body	1024	valid
135.0ms	513×	body	512	valid
45.0ms	257×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify9.0ms (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`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	29	15
3	37	15
4	44	15
5	54	15
6	65	15
7	77	15
8	80	15

Stop Event

1×

saturated

Counts

1 → 2

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

16.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.4b	(-.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 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))
✓	1.6b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series13.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
4.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
2.0ms	(hypot.f64 1 x)

rewrite54.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

406×	`log-prod_binary64`
387×	`prod-diff_binary64`
205×	`fma-def_binary64`
170×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	202	38
2	2576	38

Stop Event

1×	node limit

Counts

4 → 119

Calls

4 calls:

52.0ms	(hypot.f64 1 x)
52.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
52.0ms	(/.f64 1/2 (hypot.f64 1 x))
52.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify46.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

891×	`fma-neg_binary64`
449×	`fma-def_binary64`
232×	`associate--l+_binary64`
220×	`cancel-sign-sub-inv_binary64`
196×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	942
1	428	918
2	1343	892
3	4763	892

Stop Event

1×	node limit

Counts

167 → 202

prune201.0ms (3.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	198	5	203

Error

0.0b

Counts

203 → 5

Alt Table

Status	Error	Program
	16.7b	(fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)
▶	16.0b	(/.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))))))
	16.4b	(-.f64 1 (pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2) 1/3))
	16.7b	(/.f64 (+.f64 1 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
	29.9b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))

Compiler

Compiled 3860 to 3425 computations (11.3% 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	(/.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))))))
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	1.1b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series24.0ms (0.5%)

Counts

3 → 36

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))))))

4.0ms

(+.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)))

rewrite123.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`prod-diff_binary64`
219×	`log1p-udef_binary64`
217×	`egg-rr`
124×	`add-sqr-sqrt_binary64`
120×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	52
1	255	40
2	3616	40

Stop Event

1×	node limit

Counts

3 → 217

Calls

3 calls:

114.0ms

(/.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))))))

114.0ms

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

114.0ms

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

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary64`
455×	`distribute-rgt-in_binary64`
222×	`cancel-sign-sub-inv_binary64`
178×	`associate-/r*_binary64`
163×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	1608
1	736	1428
2	2762	1385

Stop Event

1×	node limit

Counts

253 → 281

prune603.0ms (11.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	371	2	373
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	374	4	378

Error

Counts

378 → 4

Alt Table

Status	Error	Program
	16.7b	(fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)
✓	16.0b	(/.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))))))
	29.9b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
▶	16.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))

Compiler

Compiled 19917 to 17844 computations (10.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))
✓	0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))
✓	0.4b	(/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))
	1.1b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series31.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

16.0ms

(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))

9.0ms

(/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))

6.0ms

(-.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))

rewrite73.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

294×	`log1p-udef_binary64`
163×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
160×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	338	55
2	4986	55

Stop Event

1×	node limit

Counts

3 → 127

Calls

3 calls:

71.0ms

(-.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))

71.0ms

(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))

71.0ms

(/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))

simplify35.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

587×	`associate-/r*_binary64`
253×	`distribute-rgt-in_binary64`
237×	`associate--l+_binary64`
222×	`distribute-lft-in_binary64`
168×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1336
1	501	1120
2	2009	1108

Stop Event

1×	node limit

Counts

163 → 155

prune224.0ms (4.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	217	4	221

Error

Counts

221 → 4

Alt Table

Status	Error	Program
▶	16.7b	(fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)
✓	16.0b	(/.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))))))
	29.9b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
✓	16.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))

Compiler

Compiled 6824 to 6107 computations (10.5% 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	(cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.5b	(cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	1.6b	(fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)

series17.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

8.0ms

(fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)

4.0ms

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

4.0ms

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

rewrite50.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

449×	`log-prod_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
165×	`log-pow_binary64`
164×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	57
1	249	40
2	3000	40

Stop Event

1×	node limit

Counts

3 → 99

Calls

3 calls:

48.0ms

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

48.0ms

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

48.0ms

(fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)

simplify30.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

539×	`fma-def_binary64`
433×	`cancel-sign-sub-inv_binary64`
379×	`associate-r_binary64`
292×	`associate-l_binary64`
225×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	786
1	352	671
2	1222	606

Stop Event

1×	node limit

Counts

135 → 160

prune208.0ms (4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	252	4	256

Error

Counts

256 → 4

Alt Table

Status	Error	Program
✓	16.7b	(fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)
✓	16.0b	(/.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))))))
	29.9b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
✓	16.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))

Compiler

Compiled 6369 to 5674 computations (10.9% saved)

regimes1.0s (19.8%)

Accuracy

Total 0.2b remaining (89.7%)

Threshold costs 0.2b (89.7%)

Counts

124 → 3

Compiler

Compiled 14103 to 12791 computations (9.3% saved)

bsearch45.0ms (0.9%)

Steps

Iters	Range		Point
10	2.3755431360764592e-15	16009.231964979726	0.025962973167688124
10	-12192580.02758435	-1.8071544790601476e-7	-1.1033926414358677

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`distribute-neg-frac_binary64`
3×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	93
1	54	93
2	66	93
3	75	93
4	79	93
5	80	93

Stop Event

1×

saturated

end118.0ms (2.3%)

Compiler: Compiled 209 to 176 computations (15.8% saved)

Details

analyze1.0ms (0%)

sample2.1s (41.4%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series13.0ms (0.3%)

rewrite54.0ms (1.1%)

simplify46.0ms (0.9%)

prune201.0ms (3.9%)

localize9.0ms (0.2%)

series24.0ms (0.5%)

rewrite123.0ms (2.4%)

simplify49.0ms (0.9%)

prune603.0ms (11.7%)

localize10.0ms (0.2%)

series31.0ms (0.6%)

rewrite73.0ms (1.4%)

simplify35.0ms (0.7%)

prune224.0ms (4.4%)

localize9.0ms (0.2%)

series17.0ms (0.3%)

rewrite50.0ms (1%)

simplify30.0ms (0.6%)

prune208.0ms (4%)

regimes1.0s (19.8%)

bsearch45.0ms (0.9%)

simplify4.0ms (0.1%)

end118.0ms (2.3%)

Profiling