Details

analyze1.0s (17.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample1.9s (32.2%)

Results

837.0ms	6230×	body	128	valid
498.0ms	813×	body	2048	valid
223.0ms	504×	body	1024	valid
218.0ms	301×	body	4096	valid
96.0ms	271×	body	512	valid
35.0ms	137×	body	256	valid

Compiler

Compiled 75 to 54 computations (28% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	31	24
2	39	22
3	45	22
4	47	22
5	49	22
6	50	22
7	47	22

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

14.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.4b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 68 to 48 computations (29.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	0.2b	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
✓	0.3b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	15.1b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series98.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

31.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
28.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
27.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
12.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

rewrite66.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

560×	`log-prod_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
192×	`log-pow_binary64`
169×	`prod-diff_binary64`

Counts

4 → 121

Calls

4 calls:

63.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
63.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
63.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
63.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	71
1	244	67
2	2773	67
3	5005	67
0	0	0
1	0	0

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

638×	`associate-/l*_binary64`
565×	`fma-def_binary64`
497×	`fma-neg_binary64`
413×	`cancel-sign-sub-inv_binary64`
237×	`neg-mul-1_binary64`

Counts

217 → 234

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	2325
1	603	2253
2	1998	2139
3	4625	2133
4	4991	2133

prune195.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	229	5	234
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	229	6	235

Error

4.2b

Counts

235 → 6

Alt Table

Status	Error	Program
	56.1b	(sqrt.f64 (fma.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 (/.f64 p x) (/.f64 p x) (fma.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35 (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3)))))
	56.0b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
	52.7b	(neg.f64 (/.f64 p x))
✓	14.4b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	50.7b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
▶	14.9b	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2))) 3)

Compiler

Compiled 5302 to 3841 computations (27.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)
✓	0.5b	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2))) 3)
✓	0.5b	(cbrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)))
✓	30.2b	(sqrt.f64 (.f64 p (.f64 p 4)))

series124.0ms (2%)

Counts

4 → 84

Calls

4 calls:

63.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2))) 3)
38.0ms	(cbrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)))
21.0ms	(fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)
2.0ms	(sqrt.f64 (.f64 p (.f64 p 4)))

rewrite66.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

639×	`log-prod_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
217×	`log-pow_binary64`
209×	`prod-diff_binary64`

Counts

4 → 119

Calls

4 calls:

63.0ms	(fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)
63.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2))) 3)
63.0ms	(cbrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)))
63.0ms	(sqrt.f64 (.f64 p (.f64 p 4)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	72
1	294	51
2	3188	51
3	5701	51
0	0	0
1	0	0

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

627×	`associate-/l*_binary64`
560×	`associate-/r*_binary64`
489×	`fma-def_binary64`
385×	`cancel-sign-sub-inv_binary64`
190×	`fma-neg_binary64`

Counts

203 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	2238
1	527	2137
2	1802	1951
3	5239	1951

prune178.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	202	8	210

Error

2.4b

Counts

210 → 8

Alt Table

Status	Error	Program
▶	14.9b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (.f64 p 2) x)) 1/2)) 1/6) 3) (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)) 1/6) 3))
	51.6b	(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 2 (log.f64 (/.f64 -1 x))) (log.f64 (pow.f64 p 2))))) 3)
	56.1b	(sqrt.f64 (fma.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 (/.f64 p x) (/.f64 p x) (fma.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35 (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3)))))
	56.0b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
	52.7b	(neg.f64 (/.f64 p x))
✓	14.4b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	50.7b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
✓	14.9b	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2))) 3)

Compiler

Compiled 5156 to 3973 computations (22.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 x (hypot.f64 (*.f64 p 2) x))
✓	0.3b	(fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)
✓	0.5b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (.f64 p 2) x)) 1/2)) 1/6) 3) (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)) 1/6) 3))
✓	0.5b	(pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)) 1/6) 3)

series146.0ms (2.4%)

Counts

4 → 96

Calls

4 calls:

80.0ms	(pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)) 1/6) 3)
25.0ms	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (.f64 p 2) x)) 1/2)) 1/6) 3) (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)) 1/6) 3))
22.0ms	(fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)
19.0ms	(/.f64 x (hypot.f64 (*.f64 p 2) x))

rewrite66.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

597×	`log-prod_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
218×	`log-pow_binary64`
143×	`log1p-expm1-u_binary64`

Counts

4 → 122

Calls

4 calls:

64.0ms	(/.f64 x (hypot.f64 (*.f64 p 2) x))
64.0ms	(fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)
64.0ms	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (.f64 p 2) x)) 1/2)) 1/6) 3) (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)) 1/6) 3))
64.0ms	(pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)) 1/6) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	323	57
2	3160	57
3	5337	57
0	0	0
1	0	0

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
509×	`cancel-sign-sub-inv_binary64`
439×	`fma-neg_binary64`
291×	`neg-sub0_binary64`
289×	`neg-mul-1_binary64`

Counts

218 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	2861
1	707	2747
2	2422	2550
3	4494	2508
4	5081	2508

prune409.0ms (6.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	414	0	414
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	414	8	422

Error

2.4b

Counts

422 → 8

Alt Table

Status	Error	Program
✓	14.9b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (.f64 p 2) x)) 1/2)) 1/6) 3) (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)) 1/6) 3))
	51.6b	(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 2 (log.f64 (/.f64 -1 x))) (log.f64 (pow.f64 p 2))))) 3)
	56.1b	(sqrt.f64 (fma.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 (/.f64 p x) (/.f64 p x) (fma.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35 (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3)))))
	56.0b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
	52.7b	(neg.f64 (/.f64 p x))
✓	14.4b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
▶	50.7b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
✓	14.9b	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2))) 3)

Compiler

Compiled 16063 to 11291 computations (29.7% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 p (/.f64 (*.f64 x x) p))
✓	0.2b	(/.f64 (*.f64 x x) p)
✓	21.0b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

series42.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

27.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
10.0ms	(/.f64 (*.f64 x x) p)
5.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

rewrite54.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

761×	`log1p-expm1-u_binary64`
761×	`expm1-log1p-u_binary64`
132×	`egg-rr`
129×	`log1p-udef_binary64`
75×	`add-sqr-sqrt_binary64`

Counts

3 → 132

Calls

3 calls:

52.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
52.0ms	(/.f64 (*.f64 x x) p)
52.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	29
1	152	18
2	2000	18
3	5084	18
0	0	0
1	0	0

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

822×	`fma-def_binary64`
738×	`unswap-sqr_binary64`
718×	`times-frac_binary64`
333×	`associate-/l*_binary64`
325×	`fma-neg_binary64`

Counts

204 → 137

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	520
1	23	520
2	40	520
3	106	520
4	397	520
5	2323	520
6	3969	520
7	4320	520
8	5229	520

prune47.0ms (0.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	2	2	4
Picked	1	0	1
Done	0	3	3
Total	139	6	145

Error

0.0b

Counts

145 → 6

Alt Table

Status	Error	Program
	50.3b	(/.f64 p x)
✓	14.9b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (.f64 p 2) x)) 1/2)) 1/6) 3) (pow.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 (*.f64 p 2) x)) 1/2)) 1/6) 3))
	56.0b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
	52.7b	(neg.f64 (/.f64 p x))
✓	14.4b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	14.9b	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2))) 3)

Compiler

Compiled 1540 to 720 computations (53.2% saved)

regimes1.1s (18.4%)

Accuracy

Total 6.9b remaining (99.3%)

Threshold costs 0b (0%)

Counts

127 → 2

Compiler

Compiled 14155 to 11176 computations (21% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	49
1	24	49
2	24	49

end105.0ms (1.7%)

Compiler: Compiled 180 to 131 computations (27.2% saved)

Details

analyze1.0s (17.2%)

sample1.9s (32.2%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize12.0ms (0.2%)

series98.0ms (1.6%)

rewrite66.0ms (1.1%)

simplify83.0ms (1.4%)

prune195.0ms (3.2%)

localize11.0ms (0.2%)

series124.0ms (2%)

rewrite66.0ms (1.1%)

simplify57.0ms (0.9%)

prune178.0ms (2.9%)

localize10.0ms (0.2%)

series146.0ms (2.4%)

rewrite66.0ms (1.1%)

simplify94.0ms (1.6%)

prune409.0ms (6.8%)

localize5.0ms (0.1%)

series42.0ms (0.7%)

rewrite54.0ms (0.9%)

simplify66.0ms (1.1%)

prune47.0ms (0.8%)

regimes1.1s (18.4%)

bsearch3.0ms (0.1%)

simplify2.0ms (0%)

end105.0ms (1.7%)

Profiling