Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	0%	50%	2

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample980.0ms (35.5%)

Infinites

6% of outputs are infinite.

Results

719.0ms

8256×

body

128

valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify36.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-neg_binary64`
309×	`fma-def_binary64`
228×	`cancel-sign-sub-inv_binary64`
83×	`associate-/l*_binary64`
72×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.5b	(/.f64 1 (*.f64 x 9))

series34.0ms (1.2%)

Counts

3 → 24

Calls

3 calls:

25.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
7.0ms	(*.f64 3 (sqrt.f64 x))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64`
15×	`add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 77

Calls

3 calls:

7.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
3.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify99.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
498×	`times-frac_binary64`
486×	`div-sub_binary64`
415×	`associate-l_binary64`
367×	`associate-/l*_binary64`

Counts

101 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	976
1	229	818
2	663	817
3	3063	817
4	3462	817
5	4071	817
6	4866	817
7	5395	817

prune105.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	6	97
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Error

0.0b

Counts

99 → 7

Alt Table

Status	Error	Program
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	16.5b	(-.f64 (-.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 1 (.f64 x 9)) (/.f64 1 (.f64 x 9))) (/.f64 1 (.f64 x 9))))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x)))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
▶	0.1b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (sqrt.f64 (/.f64 1/9 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 2020 to 1479 computations (26.8% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1/9 x))
✓	0.2b	(*.f64 y (sqrt.f64 (/.f64 1/9 x)))
✓	0.4b	(/.f64 1/9 x)
	0.5b	(/.f64 1 (*.f64 x 9))

series25.0ms (0.9%)

Counts

3 → 12

Calls

3 calls:

17.0ms	(*.f64 y (sqrt.f64 (/.f64 1/9 x)))
6.0ms	(sqrt.f64 (/.f64 1/9 x))
1.0ms	(/.f64 1/9 x)

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
28×	`sqrt-prod_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`

Counts

3 → 92

Calls

3 calls:

5.0ms	(*.f64 y (sqrt.f64 (/.f64 1/9 x)))
2.0ms	(/.f64 1/9 x)
2.0ms	(sqrt.f64 (/.f64 1/9 x))

simplify123.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-/l*_binary64`
490×	`div-sub_binary64`
407×	`unswap-sqr_binary64`
368×	`fma-def_binary64`
320×	`associate-/r/_binary64`

Counts

104 → 117

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	124	1162
1	196	1093
2	429	1093
3	609	1093
4	1008	1093
5	1512	1093
6	2533	1093
7	2925	1093
8	4077	1093
9	4750	1093
10	4814	1093

prune191.0ms (6.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	159	6	165

Error

0.0b

Counts

165 → 6

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	16.5b	(-.f64 (-.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 1 (.f64 x 9)) (/.f64 1 (.f64 x 9))) (/.f64 1 (.f64 x 9))))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (*.f64 y (fabs.f64 (cbrt.f64 1/9))) (sqrt.f64 (/.f64 (cbrt.f64 1/9) x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1/9 x)) (*.f64 y (sqrt.f64 (/.f64 1/9 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 3275 to 2552 computations (22.1% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (/.f64 y 3) (sqrt.f64 x))
	0.5b	(/.f64 1 (*.f64 x 9))

series26.0ms (0.9%)

Counts

1 → 12

Calls

1 calls:

26.0ms

(/.f64 (/.f64 y 3) (sqrt.f64 x))

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
78×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
42×	`sqrt-prod_binary64`

Counts

1 → 114

Calls

1 calls:

5.0ms

(/.f64 (/.f64 y 3) (sqrt.f64 x))

simplify154.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

651×	`fma-neg_binary64`
474×	`distribute-rgt-in_binary64`
457×	`associate-/r/_binary64`
436×	`associate-*l/_binary64`
435×	`div-sub_binary64`

Counts

126 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	2622
1	381	2565
2	870	2564
3	1820	2562
4	2867	2562
5	2998	2562
6	3559	2562
7	4612	2562
8	4750	2562

prune194.0ms (7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	195	6	201

Error

0.0b

Counts

201 → 6

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	16.5b	(-.f64 (-.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 1 (.f64 x 9)) (/.f64 1 (.f64 x 9))) (/.f64 1 (.f64 x 9))))) (/.f64 y (.f64 3 (sqrt.f64 x))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (*.f64 y (fabs.f64 (cbrt.f64 1/9))) (sqrt.f64 (/.f64 (cbrt.f64 1/9) x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1/9 x)) (*.f64 y (sqrt.f64 (/.f64 1/9 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 4608 to 3079 computations (33.2% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (cbrt.f64 1/9) x)
✓	0.1b	(sqrt.f64 (/.f64 (cbrt.f64 1/9) x))
✓	0.3b	(.f64 (.f64 y (fabs.f64 (cbrt.f64 1/9))) (sqrt.f64 (/.f64 (cbrt.f64 1/9) x)))
	0.5b	(/.f64 1 (*.f64 x 9))

series59.0ms (2.1%)

Counts

3 → 12

Calls

3 calls:

40.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 1/9))) (sqrt.f64 (/.f64 (cbrt.f64 1/9) x)))
15.0ms	(sqrt.f64 (/.f64 (cbrt.f64 1/9) x))
5.0ms	(/.f64 (cbrt.f64 1/9) x)

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
44×	`sqrt-prod_binary64`

Counts

3 → 121

Calls

3 calls:

8.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 1/9))) (sqrt.f64 (/.f64 (cbrt.f64 1/9) x)))
3.0ms	(sqrt.f64 (/.f64 (cbrt.f64 1/9) x))
3.0ms	(/.f64 (cbrt.f64 1/9) x)

simplify140.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

704×	`associate-/l*_binary64`
688×	`fma-neg_binary64`
374×	`associate-*l/_binary64`
343×	`*-commutative_binary64`
285×	`times-frac_binary64`

Counts

133 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2272
1	293	2140
2	855	2140
3	1293	2136
4	3360	2136
5	3582	2136
6	4373	2136
7	5007	2136

prune245.0ms (8.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	193	6	199

Error

0.0b

Counts

199 → 6

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	16.5b	(-.f64 (-.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 1 (.f64 x 9)) (/.f64 1 (.f64 x 9))) (/.f64 1 (.f64 x 9))))) (/.f64 y (.f64 3 (sqrt.f64 x))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (*.f64 y (fabs.f64 (cbrt.f64 1/9))) (sqrt.f64 (/.f64 (cbrt.f64 1/9) x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1/9 x)) (*.f64 y (sqrt.f64 (/.f64 1/9 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 5066 to 4200 computations (17.1% saved)

regimes137.0ms (5%)

Accuracy

Total 0.2b remaining (88.3%)

Threshold costs 0.2b (88.3%)

Counts

43 → 1

Compiler

Compiled 2588 to 2068 computations (20.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	24	21
2	38	21
3	46	21
4	51	21
5	52	21
6	50	21

end99.0ms (3.6%)

Compiler: Compiled 146 to 120 computations (17.8% saved)

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

Details

analyze1.0ms (0.1%)

sample980.0ms (35.5%)

simplify36.0ms (1.3%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series34.0ms (1.2%)

rewrite16.0ms (0.6%)

simplify99.0ms (3.6%)

prune105.0ms (3.8%)

localize8.0ms (0.3%)

series25.0ms (0.9%)

rewrite16.0ms (0.6%)

simplify123.0ms (4.4%)

prune191.0ms (6.9%)

localize8.0ms (0.3%)

series26.0ms (0.9%)

rewrite17.0ms (0.6%)

simplify154.0ms (5.6%)

prune194.0ms (7%)

localize13.0ms (0.5%)

series59.0ms (2.1%)

rewrite21.0ms (0.8%)

simplify140.0ms (5.1%)

prune245.0ms (8.9%)

regimes137.0ms (5%)

simplify3.0ms (0.1%)

end99.0ms (3.6%)

Profiling

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16