Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample28.0ms (1.5%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	11	9
3	11	9

prune1.0ms (0.1%)

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

29.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.4b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize95.0ms (5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(sqrt.f64 (*.f64 2 (*.f64 x x)))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64`
3×	`sqrt-pow1_binary64`
3×	`pow-prod-down_binary64`
1×	`*-un-lft-identity_binary64`
1×	`sqrt-prod_binary64`

Counts

1 → 14

Calls

1 calls:

3.0ms

(sqrt.f64 (*.f64 2 (*.f64 x x)))

simplify97.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

1178×	`fma-def_binary64`
437×	`sqr-pow_binary64`
362×	`unswap-sqr_binary64`
342×	`distribute-rgt-neg-in_binary64`
306×	`distribute-lft-neg-in_binary64`

Counts

26 → 17

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	208
1	35	202
2	63	202
3	80	202
4	87	202
5	114	202
6	145	202
7	203	202
8	415	202
9	774	202
10	787	202
11	955	202
12	1220	202
13	1628	202
14	2596	202
15	3178	202
16	4810	202
17	4912	202

prune13.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	13	4	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	5	18

Error

0.2b

Counts

18 → 5

Alt Table

Status	Error	Program
	32.1b	(*.f64 (sqrt.f64 2) x)
✓	29.4b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	29.6b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
	30.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))))

Compiler

Compiled 269 to 180 computations (33.1% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
✓	0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
	28.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

series14.0ms (0.8%)

Counts

2 → 12

Calls

2 calls:

10.0ms	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
4.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))

rewrite33.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`sqrt-pow1_binary64`
144×	`pow1_binary64`
76×	`pow-prod-down_binary64`
31×	`sqrt-prod_binary64`
28×	`add-sqr-sqrt_binary64`

Counts

2 → 112

Calls

2 calls:

16.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
4.0ms	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))

simplify136.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

471×	`associate-*l/_binary64`
383×	`associate-*r/_binary64`
327×	`*-commutative_binary64`
318×	`associate-l_binary64`
259×	`associate-/l*_binary64`

Counts

124 → 98

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	68	1215
1	107	1155
2	308	1105
3	881	1005
4	1392	1005
5	1877	1005
6	3750	991
7	4989	991

prune97.0ms (5.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	153	6	159

Error

0.2b

Counts

159 → 6

Alt Table

Status	Error	Program
	31.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	29.5b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (*.f64 x x))))
	29.8b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))))) (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x))))))
	29.6b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))))
	32.1b	(*.f64 (sqrt.f64 2) x)
✓	29.4b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 3032 to 1987 computations (34.5% saved)

localize11.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))) (sqrt.f64 (sqrt.f64 2)))
✓	0.4b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (*.f64 x x))))
✓	28.1b	(sqrt.f64 (*.f64 x x))
	28.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

series16.0ms (0.8%)

Counts

3 → 24

Calls

3 calls:

8.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))) (sqrt.f64 (sqrt.f64 2)))

6.0ms

(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (*.f64 x x))))

2.0ms

(sqrt.f64 (*.f64 x x))

rewrite42.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`sqrt-pow1_binary64`
59×	`pow1_binary64`
41×	`pow-prod-down_binary64`
36×	`add-sqr-sqrt_binary64`
34×	`sqrt-prod_binary64`

Counts

3 → 100

Calls

3 calls:

18.0ms

(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (*.f64 x x))))

12.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))) (sqrt.f64 (sqrt.f64 2)))

2.0ms

(sqrt.f64 (*.f64 x x))

simplify129.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

601×	`associate-/l/_binary64`
489×	`associate-/l*_binary64`
478×	`times-frac_binary64`
336×	`*-commutative_binary64`
267×	`fma-def_binary64`

Counts

124 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	2070
1	204	1954
2	631	1954
3	825	1926
4	1033	1926
5	1336	1926
6	2208	1926
7	4736	1926
8	4893	1926

prune87.0ms (4.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	140	6	146

Error

0.2b

Counts

146 → 6

Alt Table

Status	Error	Program
▶	29.6b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))))
	29.7b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (.f64 x x))))
	32.1b	(*.f64 (sqrt.f64 2) x)
✓	29.4b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	29.8b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fabs.f64 x)) (cbrt.f64 (fabs.f64 x))) (cbrt.f64 (fabs.f64 x)))))

Compiler

Compiled 3153 to 1910 computations (39.4% saved)

localize13.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x)))
✓	0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))))
	28.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

series25.0ms (1.3%)

Counts

2 → 12

Calls

2 calls:

18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))))
7.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x)))

rewrite31.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`add-sqr-sqrt_binary64`
48×	`sqrt-prod_binary64`
30×	`rem-sqrt-square_binary64`
18×	`mul-fabs_binary64`
16×	`associate-l_binary64`

Counts

2 → 86

Calls

2 calls:

15.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))))
8.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x)))

simplify118.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

480×	`associate-/l*_binary64`
464×	`associate-/l/_binary64`
390×	`cube-div_binary64`
390×	`log-div_binary64`
302×	`*-commutative_binary64`

Counts

98 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	1898
1	187	1816
2	516	1744
3	668	1744
4	828	1744
5	1055	1744
6	1825	1744
7	4148	1744
8	5240	1744

prune76.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	141	6	147

Error

0.0b

Counts

147 → 6

Alt Table

Status	Error	Program
✓	29.4b	(sqrt.f64 (.f64 2 (.f64 x x)))
	0.7b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))))
	32.1b	(*.f64 (sqrt.f64 2) x)
	0.4b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (fabs.f64 x))) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))))
	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))
	31.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 2962 to 1940 computations (34.5% saved)

regimes301.0ms (15.9%)

Accuracy

Total 0.5b remaining (96.7%)

Threshold costs 0.5b (96.7%)

Counts

59 → 1

Compiler

Compiled 6336 to 4548 computations (28.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	14	24
2	14	24

end1.0ms (0%)

Compiler: Compiled 15 to 12 computations (20% saved)

sample506.0ms (26.7%)

Algorithm

1×

intervals

Results

253.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 84 to 67 computations (20.2% saved)

Details

analyze5.0ms (0.2%)

sample28.0ms (1.5%)

simplify6.0ms (0.3%)

prune1.0ms (0.1%)

localize95.0ms (5%)

series3.0ms (0.2%)

rewrite4.0ms (0.2%)

simplify97.0ms (5.1%)

prune13.0ms (0.7%)

localize6.0ms (0.3%)

series14.0ms (0.8%)

rewrite33.0ms (1.7%)

simplify136.0ms (7.2%)

prune97.0ms (5.1%)

localize11.0ms (0.6%)

series16.0ms (0.8%)

rewrite42.0ms (2.2%)

simplify129.0ms (6.8%)

prune87.0ms (4.6%)

localize13.0ms (0.7%)

series25.0ms (1.3%)

rewrite31.0ms (1.6%)

simplify118.0ms (6.2%)

prune76.0ms (4%)

regimes301.0ms (15.9%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample506.0ms (26.7%)

Profiling