Details

analyze1.1s (23.7%)

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 (42.6%)

Results

840.0ms	6198×	body	128	valid
517.0ms	856×	body	2048	valid
253.0ms	546×	body	1024	valid
186.0ms	281×	body	4096	valid
95.0ms	252×	body	512	valid
28.0ms	123×	body	256	valid

Compiler

Compiled 75 to 54 computations (28% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	31	24
2	41	22
3	48	22
4	50	22
5	52	22
6	53	22

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

11.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2))

Compiler

Compiled 68 to 48 computations (29.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 4 (.f64 p p)))
✓	0.0b	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p)))))
✓	0.0b	(.f64 4 (.f64 p p))
✓	14.9b	(sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))

series40.0ms (0.9%)

Counts

4 → 84

Calls

4 calls:

21.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p)))))
9.0ms	(sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))
7.0ms	(fma.f64 x x (.f64 4 (.f64 p p)))
2.0ms	(.f64 4 (.f64 p p))

rewrite51.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

817×	`log1p-expm1-u_binary64`
817×	`expm1-log1p-u_binary64`
154×	`prod-diff_binary64`
98×	`egg-rr`
88×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	47
1	187	34
2	2276	34

Stop Event

1×	node limit

Counts

4 → 98

Calls

4 calls:

49.0ms	(fma.f64 x x (.f64 4 (.f64 p p)))
49.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p)))))
49.0ms	(.f64 4 (.f64 p p))
49.0ms	(sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))

simplify53.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

483×	`times-frac_binary64`
264×	`sub-neg_binary64`
263×	`associate-/l*_binary64`
249×	`fma-def_binary64`
211×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	1427
1	310	1401
2	1015	1369
3	4611	1342

Stop Event

1×	node limit

Counts

182 → 163

prune171.0ms (3.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	155	9	164

Error

11.5b

Counts

164 → 9

Alt Table

Status	Error	Program
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2))
	12.0b	(sqrt.f64 (fma.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 x (.f64 p 2)))) (/.f64 x (sqrt.f64 (hypot.f64 x (*.f64 p 2))))) 1/2))
	13.7b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x (*.f64 p 2))) 2) 3))) 1/2))
	13.7b	(sqrt.f64 (fma.f64 1/2 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (hypot.f64 x (*.f64 p 2))))) 1/2))
▶	11.8b	(sqrt.f64 (fma.f64 1/2 (.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2)))) 1/2))
	27.9b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (fma.f64 2 p (.f64 1/4 (.f64 (/.f64 x p) x)))) 1/2))
	13.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x (.f64 p 2))) 2) (.f64 (cbrt.f64 (hypot.f64 x (.f64 p 2))) (hypot.f64 x (*.f64 p 2)))))) 1/2))
	12.5b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (pow.f64 (sqrt.f64 (hypot.f64 x (*.f64 p 2))) 2)) 1/2))
	13.4b	(sqrt.f64 (fma.f64 1/2 (.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (hypot.f64 x (.f64 p 2)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (hypot.f64 x (*.f64 p 2))))) 1/2))

Compiler

Compiled 3471 to 2580 computations (25.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 1/2 (.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2)))) 1/2))
✓	0.0b	(/.f64 1 (hypot.f64 x (*.f64 p 2)))
✓	0.3b	(.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2))))
✓	1.2b	(fma.f64 1/2 (.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2)))) 1/2)

series61.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

18.0ms	(sqrt.f64 (fma.f64 1/2 (.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2)))) 1/2))
15.0ms	(fma.f64 1/2 (.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2)))) 1/2)
15.0ms	(.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2))))
13.0ms	(/.f64 1 (hypot.f64 x (*.f64 p 2)))

rewrite50.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

504×	`log-prod_binary64`
195×	`pow1/3_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
180×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	243	50
2	2735	50

Stop Event

1×	node limit

Counts

4 → 117

Calls

4 calls:

48.0ms	(sqrt.f64 (fma.f64 1/2 (.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2)))) 1/2))
48.0ms	(/.f64 1 (hypot.f64 x (*.f64 p 2)))
48.0ms	(.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2))))
48.0ms	(fma.f64 1/2 (.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2)))) 1/2)

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

638×	`associate-/l*_binary64`
598×	`fma-def_binary64`
446×	`cancel-sign-sub-inv_binary64`
258×	`fma-neg_binary64`
228×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2421
1	604	2351
2	2138	2237

Stop Event

1×	node limit

Counts

213 → 229

prune147.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	7	0	7
Picked	0	1	1
Done	1	0	1
Total	234	4	238

Error

1.8b

Counts

238 → 4

Alt Table

Status	Error	Program
✓	11.8b	(sqrt.f64 (fma.f64 1/2 (.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2)))) 1/2))
	53.3b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))
▶	31.0b	(fma.f64 (/.f64 x (*.f64 p (sqrt.f64 1/2))) -1/8 (sqrt.f64 1/2))
	53.2b	(/.f64 (neg.f64 p) x)

Compiler

Compiled 4659 to 2937 computations (37% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (/.f64 x (*.f64 p (sqrt.f64 1/2))) -1/8 (sqrt.f64 1/2))
✓	0.2b	(/.f64 x (*.f64 p (sqrt.f64 1/2)))
✓	0.4b	(*.f64 p (sqrt.f64 1/2))

series34.0ms (0.7%)

Counts

3 → 60

Calls

3 calls:

16.0ms	(fma.f64 (/.f64 x (*.f64 p (sqrt.f64 1/2))) -1/8 (sqrt.f64 1/2))
16.0ms	(/.f64 x (*.f64 p (sqrt.f64 1/2)))
3.0ms	(*.f64 p (sqrt.f64 1/2))

rewrite42.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

871×	`log1p-expm1-u_binary64`
871×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`
85×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	188	30
2	2324	30

Stop Event

1×	node limit

Counts

3 → 78

Calls

3 calls:

40.0ms	(fma.f64 (/.f64 x (*.f64 p (sqrt.f64 1/2))) -1/8 (sqrt.f64 1/2))
40.0ms	(/.f64 x (*.f64 p (sqrt.f64 1/2)))
40.0ms	(*.f64 p (sqrt.f64 1/2))

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-neg_binary64`
371×	`fma-def_binary64`
359×	`times-frac_binary64`
311×	`cancel-sign-sub-inv_binary64`
262×	`div-sub_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	639
1	25	639
2	69	603
3	169	603
4	336	603
5	594	603
6	939	603
7	1537	603
8	3780	603

Stop Event

1×	node limit

Counts

138 → 86

prune43.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Error

1.8b

Counts

90 → 4

Alt Table

Status	Error	Program
✓	11.8b	(sqrt.f64 (fma.f64 1/2 (.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2)))) 1/2))
	53.3b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))
✓	31.0b	(fma.f64 (/.f64 x (*.f64 p (sqrt.f64 1/2))) -1/8 (sqrt.f64 1/2))
▶	53.2b	(/.f64 (neg.f64 p) x)

Compiler

Compiled 1306 to 1040 computations (20.4% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

1.8b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	11.8b	(sqrt.f64 (fma.f64 1/2 (.f64 x (/.f64 1 (hypot.f64 x (.f64 p 2)))) 1/2))
	53.3b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))
✓	31.0b	(fma.f64 (/.f64 x (*.f64 p (sqrt.f64 1/2))) -1/8 (sqrt.f64 1/2))
✓	53.2b	(/.f64 (neg.f64 p) x)

Compiler

Compiled 43 to 31 computations (27.9% saved)

regimes644.0ms (14.1%)

Accuracy

Total 4.1b remaining (57.3%)

Threshold costs 0b (0%)

Counts

82 → 2

Compiler

Compiled 8523 to 6671 computations (21.7% saved)

bsearch2.0ms (0%)

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

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	47
1	31	47
2	35	47
3	38	47
4	39	47

Stop Event

1×

saturated

end62.0ms (1.4%)

Compiler: Compiled 109 to 75 computations (31.2% saved)

Details

analyze1.1s (23.7%)

sample1.9s (42.6%)

simplify13.0ms (0.3%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series40.0ms (0.9%)

rewrite51.0ms (1.1%)

simplify53.0ms (1.2%)

prune171.0ms (3.7%)

localize7.0ms (0.2%)

series61.0ms (1.3%)

rewrite50.0ms (1.1%)

simplify51.0ms (1.1%)

prune147.0ms (3.2%)

localize5.0ms (0.1%)

series34.0ms (0.7%)

rewrite42.0ms (0.9%)

simplify43.0ms (0.9%)

prune43.0ms (0.9%)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

regimes644.0ms (14.1%)

bsearch2.0ms (0%)

simplify2.0ms (0.1%)

end62.0ms (1.4%)

Profiling