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)

sample2.2s (36.8%)

Results

1.1s	2189×	body	2048	valid
447.0ms	4257×	body	128	valid
408.0ms	1030×	body	1024	valid
142.0ms	510×	body	512	valid
52.0ms	270×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify9.0ms (0.1%)

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%)

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

13.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.8b	(-.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	(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 (/.f64 1/2 (hypot.f64 1 x)))
✓	1.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series18.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

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

rewrite94.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 139

Calls

4 calls:

92.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
92.0ms	(/.f64 1/2 (hypot.f64 1 x))
91.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
91.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	44
1	200	44
2	2408	44
3	4933	44
4	5094	44
0	0	0
1	0	0

simplify55.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-neg_binary64`
538×	`sub-neg_binary64`
430×	`fma-def_binary64`
239×	`associate--l+_binary64`
232×	`cancel-sign-sub-inv_binary64`

Counts

187 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	934
1	399	916
2	1174	892
3	3690	892
4	4978	892

prune179.0ms (3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	216	3	219
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	217	3	220

Error

0.0b

Counts

220 → 3

Alt Table

Status	Error	Program
	35.9b	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
	13.8b	(*.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
▶	13.3b	(/.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 4136 to 3673 computations (11.2% saved)

localize9.0ms (0.2%)

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	(/.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))))
✓	0.0b	(/.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)))))
✓	1.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series39.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

25.0ms

(/.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)))))

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))))

3.0ms

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

rewrite78.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

504×	`prod-diff_binary64`
236×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`
131×	`log1p-expm1-u_binary64`
131×	`expm1-log1p-u_binary64`

Counts

3 → 126

Calls

3 calls:

75.0ms

(/.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))))

75.0ms

(/.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)))))

75.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	67
1	278	43
2	3592	43
3	4894	43
0	0	0
1	0	0

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

452×	`distribute-rgt-in_binary64`
293×	`associate-+r+_binary64`
293×	`fma-def_binary64`
238×	`cancel-sign-sub-inv_binary64`
230×	`+-commutative_binary64`

Counts

162 → 192

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	1930
1	841	1747
2	3147	1742
3	5096	1742

prune498.0ms (8.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	253	1	254
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	253	4	257

Error

Counts

257 → 4

Alt Table

Status	Error	Program
	35.9b	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
▶	13.8b	(*.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
	36.2b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
✓	13.3b	(/.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 8033 to 7166 computations (10.8% saved)

localize12.0ms (0.2%)

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	(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)
✓	0.5b	(/.f64 1 (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	1.2b	(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))

series59.0ms (1%)

Counts

3 → 36

Calls

3 calls:

49.0ms

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

5.0ms

(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))

4.0ms

(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)

rewrite72.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

348×	`fma-neg_binary64`
274×	`expm1-udef_binary64`
273×	`log1p-udef_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`

Counts

3 → 82

Calls

3 calls:

70.0ms

(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)

70.0ms

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

70.0ms

(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	59
1	334	56
2	4118	56
3	5127	56
0	0	0
1	0	0

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

299×	`fma-neg_binary64`
292×	`times-frac_binary64`
251×	`fma-def_binary64`
245×	`cancel-sign-sub-inv_binary64`
239×	`associate-+r+_binary64`

Counts

118 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	2266
1	747	1785
2	3027	1684
3	4919	1684
4	5031	1684

prune464.0ms (7.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	329	4	333

Error

Counts

333 → 4

Alt Table

Status	Error	Program
▶	35.9b	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
✓	13.8b	(*.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
	36.2b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
✓	13.3b	(/.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 14579 to 13140 computations (9.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6)))
✓	0.1b	(*.f64 69/1024 (pow.f64 x 6))
✓	20.7b	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))

series13.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

6.0ms	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
4.0ms	(fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6)))
3.0ms	(*.f64 69/1024 (pow.f64 x 6))

rewrite58.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

448×	`log-prod_binary64`
292×	`pow2_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
199×	`pow1/3_binary64`

Counts

3 → 75

Calls

3 calls:

56.0ms	(fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6)))
56.0ms	(*.f64 69/1024 (pow.f64 x 6))
56.0ms	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	273	42
2	2561	42
3	4880	42
0	0	0
1	0	0

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

678×	`distribute-rgt-neg-in_binary64`
616×	`distribute-lft-neg-in_binary64`
395×	`distribute-lft-out_binary64`
340×	`cancel-sign-sub-inv_binary64`
326×	`distribute-lft-out--_binary64`

Counts

99 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	354
1	47	336
2	93	336
3	275	336
4	963	336
5	2435	336
6	4742	336
7	4958	336

prune71.0ms (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	86	4	90

Error

Counts

90 → 4

Alt Table

Status	Error	Program
✓	35.9b	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
✓	13.8b	(*.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
	36.2b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
✓	13.3b	(/.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 1816 to 1320 computations (27.3% saved)

regimes1.7s (27.9%)

Accuracy

Total 0.0b remaining (32.6%)

Threshold costs 0.0b (32.6%)

Counts

199 → 3

Compiler

Compiled 27531 to 25026 computations (9.1% saved)

bsearch46.0ms (0.8%)

Steps

Iters	Range		Point
9	0.0003357114060053016	351.5834476539697	0.010586867664495958
9	-3.2663422632621986	-8.797170471362198e-6	-0.0108257881037984

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	116
1	55	116
2	64	116
3	68	116
4	70	116
5	68	116

end125.0ms (2.1%)

Compiler: Compiled 239 to 205 computations (14.2% saved)

Details

analyze1.0ms (0%)

sample2.2s (36.8%)

simplify9.0ms (0.1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series18.0ms (0.3%)

rewrite94.0ms (1.6%)

simplify55.0ms (0.9%)

prune179.0ms (3%)

localize9.0ms (0.2%)

series39.0ms (0.6%)

rewrite78.0ms (1.3%)

simplify64.0ms (1.1%)

prune498.0ms (8.3%)

localize12.0ms (0.2%)

series59.0ms (1%)

rewrite72.0ms (1.2%)

simplify80.0ms (1.3%)

prune464.0ms (7.7%)

localize9.0ms (0.1%)

series13.0ms (0.2%)

rewrite58.0ms (1%)

simplify65.0ms (1.1%)

prune71.0ms (1.2%)

regimes1.7s (27.9%)

bsearch46.0ms (0.8%)

simplify5.0ms (0.1%)

end125.0ms (2.1%)

Profiling