Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25.7%	74.3%	0
25.7%	0%	74.3%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample2.4s (47.7%)

Results

1.6s	6859×	body	128	valid
302.0ms	504×	body	1024	valid
224.0ms	536×	body	512	valid
219.0ms	341×	body	256	valid
9.0ms	16×	body	2048	valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

743×	`neg-mul-1_binary64`
672×	`distribute-rgt-neg-in_binary64`
436×	`unswap-sqr_binary64`
376×	`fma-def_binary64`
296×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	37	13
3	78	13
4	204	13
5	682	13
6	1848	13
7	3102	13
8	4873	13
9	5393	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

7.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.0b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

Compiler

Compiled 33 to 24 computations (27.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x eps) 5)
✓	1.5b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

series34.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
13.0ms	(pow.f64 (+.f64 x eps) 5)

rewrite84.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

907×	`prod-diff_binary64`
400×	`fma-def_binary64`
206×	`fma-neg_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`

Counts

2 → 112

Calls

2 calls:

81.0ms	(pow.f64 (+.f64 x eps) 5)
81.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	190	20
2	2416	20
3	4786	20
4	4974	20
0	0	0
1	0	0

simplify147.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

965×	`distribute-lft-out_binary64`
836×	`unswap-sqr_binary64`
524×	`*-commutative_binary64`
428×	`sqr-pow_binary64`
400×	`distribute-rgt-out_binary64`

Counts

160 → 133

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	39	1152
1	123	1083
2	344	1062
3	1099	993
4	1638	972
5	2061	972
6	2235	960
7	2710	960
8	3005	960
9	3202	960
10	4674	960
11	4511	960
12	4901	960

prune145.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	128	5	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	5	134

Error

0.0b

Counts

134 → 5

Alt Table

Status	Error	Program
	12.6b	(.f64 eps (.f64 (pow.f64 x 3) (+.f64 (.f64 5 x) (.f64 eps 10))))
	12.5b	(.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 eps x)))))))
	13.6b	(pow.f64 (sqrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2)
▶	7.3b	(+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (pow.f64 eps 5) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
	7.5b	(.f64 (pow.f64 eps 3) (+.f64 (.f64 10 (.f64 x x)) (.f64 eps (+.f64 eps (*.f64 5 x)))))

Compiler

Compiled 3092 to 1966 computations (36.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 eps 4) x)
✓	0.0b	(.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2)))
✓	0.0b	(.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3)))
✓	0.1b	(.f64 5 (.f64 (pow.f64 eps 4) x))

series70.0ms (1.4%)

Counts

4 → 0

Calls

4 calls:

19.0ms	(.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3)))
19.0ms	(.f64 5 (.f64 (pow.f64 eps 4) x))
18.0ms	(.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2)))
13.0ms	(*.f64 (pow.f64 eps 4) x)

rewrite62.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

290×	`expm1-udef_binary64`
290×	`log1p-udef_binary64`
264×	`log-pow_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`

Counts

4 → 54

Calls

4 calls:

61.0ms	(*.f64 (pow.f64 eps 4) x)
61.0ms	(.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2)))
61.0ms	(.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3)))
61.0ms	(.f64 5 (.f64 (pow.f64 eps 4) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	43
1	398	43
2	3850	43
3	4939	43
0	0	0
1	0	0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune77.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	54	5	59

Error

0.0b

Counts

59 → 5

Alt Table

Status	Error	Program
	12.6b	(.f64 eps (.f64 (pow.f64 x 3) (+.f64 (.f64 5 x) (.f64 eps 10))))
	12.5b	(.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 eps x)))))))
	13.6b	(pow.f64 (sqrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2)
✓	7.3b	(+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (pow.f64 eps 5) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
▶	7.5b	(.f64 (pow.f64 eps 3) (+.f64 (.f64 10 (.f64 x x)) (.f64 eps (+.f64 eps (*.f64 5 x)))))

Compiler

Compiled 1998 to 1531 computations (23.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 eps (*.f64 5 x))
✓	0.1b	(.f64 eps (+.f64 eps (.f64 5 x)))
✓	0.1b	(.f64 (pow.f64 eps 3) (+.f64 (.f64 10 (.f64 x x)) (.f64 eps (+.f64 eps (*.f64 5 x)))))
✓	0.2b	(.f64 10 (.f64 x x))

series29.0ms (0.6%)

Counts

4 → 66

Calls

4 calls:

17.0ms	(.f64 (pow.f64 eps 3) (+.f64 (.f64 10 (.f64 x x)) (.f64 eps (+.f64 eps (*.f64 5 x)))))
6.0ms	(.f64 eps (+.f64 eps (.f64 5 x)))
3.0ms	(+.f64 eps (*.f64 5 x))
3.0ms	(.f64 10 (.f64 x x))

rewrite69.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

326×	`fma-neg_binary64`
264×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`
153×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`

Counts

4 → 99

Calls

4 calls:

67.0ms	(+.f64 eps (*.f64 5 x))
67.0ms	(.f64 eps (+.f64 eps (.f64 5 x)))
67.0ms	(.f64 (pow.f64 eps 3) (+.f64 (.f64 10 (.f64 x x)) (.f64 eps (+.f64 eps (*.f64 5 x)))))
67.0ms	(.f64 10 (.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	315	41
2	3897	41
3	4886	41
0	0	0
1	0	0

simplify73.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

900×	`fma-def_binary64`
735×	`associate-l_binary64`
618×	`distribute-lft-out_binary64`
547×	`associate-r_binary64`
394×	`distribute-rgt-out_binary64`

Counts

165 → 120

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	26	846
1	72	816
2	162	795
3	471	702
4	1943	672
5	3472	663
6	4872	663
7	4991	663

prune126.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	5	125

Error

0.0b

Counts

125 → 5

Alt Table

Status	Error	Program
	12.6b	(.f64 eps (.f64 (pow.f64 x 3) (+.f64 (.f64 5 x) (.f64 eps 10))))
▶	12.5b	(.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 eps x)))))))
	13.6b	(pow.f64 (sqrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2)
✓	7.3b	(+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (pow.f64 eps 5) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
✓	7.5b	(.f64 (pow.f64 eps 3) (+.f64 (.f64 10 (.f64 x x)) (.f64 eps (+.f64 eps (*.f64 5 x)))))

Compiler

Compiled 2780 to 1736 computations (37.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 eps x)))))))
✓	0.1b	(.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 eps x)))))
✓	0.1b	(*.f64 5 (pow.f64 x 4))
✓	0.1b	(.f64 x (.f64 eps (+.f64 eps x)))

series62.0ms (1.2%)

Counts

4 → 72

Calls

4 calls:

28.0ms	(.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 eps x)))))))
20.0ms	(.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 eps x)))))
11.0ms	(.f64 x (.f64 eps (+.f64 eps x)))
3.0ms	(*.f64 5 (pow.f64 x 4))

rewrite81.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

288×	`expm1-udef_binary64`
288×	`log1p-udef_binary64`
182×	`associate-r_binary64`
163×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`

Counts

4 → 75

Calls

4 calls:

79.0ms	(.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 eps x)))))))
79.0ms	(.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 eps x)))))
79.0ms	(*.f64 5 (pow.f64 x 4))
79.0ms	(.f64 x (.f64 eps (+.f64 eps x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	341	59
2	4272	59
3	4992	59
0	0	0
1	0	0

simplify303.0ms (6%)

Algorithm

1×	egg-herbie

Rules

1983×	`fma-def_binary64`
874×	`unswap-sqr_binary64`
711×	`*-commutative_binary64`
604×	`sqr-pow_binary64`
255×	`pow-sqr_binary64`

Counts

147 → 95

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	30	1392
1	87	1326
2	237	1176
3	803	1119
4	1605	1098
5	2838	1098
6	2928	1098
7	3038	1098
8	3183	1098
9	3328	1098
10	3520	1068
11	3811	1068
12	4061	1068
13	4456	1068
14	4972	1068
15	4886	1068

prune385.0ms (7.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	93	7	100

Error

0.0b

Counts

100 → 7

Alt Table

Status	Error	Program
	59.5b	(/.f64 (.f64 (+.f64 (.f64 125 (pow.f64 (pow.f64 x 4) 3)) (.f64 1000 (pow.f64 (.f64 x (.f64 x (.f64 eps (+.f64 x eps)))) 3))) eps) (+.f64 (.f64 25 (pow.f64 x 8)) (.f64 (.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 x eps))))) (-.f64 (.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 x eps))))) (*.f64 5 (pow.f64 x 4))))))
✓	7.3b	(+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (pow.f64 eps 5) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
✓	12.5b	(.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 eps x)))))))
	13.6b	(pow.f64 (sqrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2)
	50.9b	(/.f64 (.f64 (-.f64 (.f64 25 (pow.f64 x 8)) (.f64 100 (.f64 (pow.f64 x 4) (pow.f64 (.f64 eps (+.f64 x eps)) 2)))) eps) (-.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 x (.f64 x (.f64 eps (+.f64 x eps)))))))
✓	7.5b	(.f64 (pow.f64 eps 3) (+.f64 (.f64 10 (.f64 x x)) (.f64 eps (+.f64 eps (*.f64 5 x)))))
	12.6b	(.f64 eps (+.f64 (pow.f64 (.f64 (.f64 x x) (sqrt.f64 5)) 2) (.f64 10 (.f64 x (.f64 x (*.f64 eps (+.f64 eps x)))))))

Compiler

Compiled 2423 to 1313 computations (45.8% saved)

regimes584.0ms (11.6%)

Accuracy

Total 0.5b remaining (81.6%)

Threshold costs 0.5b (81.6%)

Counts

117 → 3

Compiler

Compiled 7186 to 5126 computations (28.7% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
7×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	121
1	61	121
2	64	121
3	66	121
4	67	121
5	67	121

end179.0ms (3.5%)

Compiler: Compiled 381 to 263 computations (31% saved)

Details

analyze2.0ms (0%)

sample2.4s (47.7%)

simplify62.0ms (1.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series34.0ms (0.7%)

rewrite84.0ms (1.7%)

simplify147.0ms (2.9%)

prune145.0ms (2.9%)

localize18.0ms (0.4%)

series70.0ms (1.4%)

rewrite62.0ms (1.2%)

simplify7.0ms (0.1%)

prune77.0ms (1.5%)

localize10.0ms (0.2%)

series29.0ms (0.6%)

rewrite69.0ms (1.4%)

simplify73.0ms (1.4%)

prune126.0ms (2.5%)

localize12.0ms (0.2%)

series62.0ms (1.2%)

rewrite81.0ms (1.6%)

simplify303.0ms (6%)

prune385.0ms (7.6%)

regimes584.0ms (11.6%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.1%)

end179.0ms (3.5%)

Profiling