Details

analyze21.0ms (0.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample550.0ms (15.1%)

Infinites

12.5% of outputs are infinite.

Results

500.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-neg_binary64`
17×	`sub-neg_binary64`
17×	`fma-def_binary64`
16×	`cancel-sign-sub-inv_binary64`
9×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	11	11
2	18	11
3	27	11
4	43	11
5	77	11
6	89	11
7	112	11
8	136	11
9	159	11
10	167	11
11	161	11
12	144	11

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))

series19.0ms (0.5%)

Counts

1 → 0

Calls

1 calls:

19.0ms

(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64`
70×	`fabs-mul_binary64`
63×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`

Counts

1 → 96

Calls

1 calls:

6.0ms

(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))

simplify85.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

901×	`div-sub_binary64`
444×	`associate-/l/_binary64`
439×	`times-frac_binary64`
383×	`associate-/l*_binary64`
382×	`fma-def_binary64`

Counts

96 → 112

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	147	2173
1	222	2127
2	491	2127
3	1085	2127
4	2714	2127
5	5167	2127

prune52.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	109	4	113

Error

Counts

113 → 4

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))
▶	0.1b	(/.f64 1 (/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y))))
	0.4b	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y)))
	2.2b	(expm1.f64 (log1p.f64 (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))))

Compiler

Compiled 2060 to 417 computations (79.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y)))
✓	0.1b	(/.f64 1 (/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y))))

series45.0ms (1.2%)

Counts

2 → 24

Calls

2 calls:

24.0ms	(/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y)))
20.0ms	(/.f64 1 (/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y))))

rewrite71.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

522×	`times-frac_binary64`
394×	`add-sqr-sqrt_binary64`
318×	`fabs-mul_binary64`
312×	`*-un-lft-identity_binary64`
240×	`add-cube-cbrt_binary64`

Counts

2 → 398

Calls

2 calls:

15.0ms	(/.f64 1 (/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y))))
6.0ms	(/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y)))

simplify308.0ms (8.5%)

Algorithm

1×	egg-herbie

Rules

882×	`fma-def_binary64`
447×	`times-frac_binary64`
356×	`associate-/r/_binary64`
302×	`associate-/r*_binary64`
275×	`associate-/l*_binary64`

Counts

422 → 482

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	10334
1	447	9455
2	1175	9242
3	2996	9242
4	4165	9242
5	5440	9242

prune226.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	482	0	482
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	482	4	486

Error

Counts

486 → 4

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))
✓	0.1b	(/.f64 1 (/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y))))
▶	0.4b	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y)))
	2.2b	(expm1.f64 (log1p.f64 (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))))

Compiler

Compiled 10444 to 2831 computations (72.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))
✓	0.2b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y))
✓	0.2b	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y)))

series44.0ms (1.2%)

Counts

3 → 48

Calls

3 calls:

20.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y))
17.0ms	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y)))
7.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))

rewrite86.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

356×	`add-sqr-sqrt_binary64`
228×	`sqrt-prod_binary64`
216×	`times-frac_binary64`
209×	`fabs-mul_binary64`
138×	`*-un-lft-identity_binary64`

Counts

3 → 328

Calls

3 calls:

30.0ms	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y)))
7.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y))
3.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))

simplify334.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

628×	`fma-def_binary64`
595×	`times-frac_binary64`
380×	`associate-/r/_binary64`
282×	`*-commutative_binary64`
250×	`unswap-sqr_binary64`

Counts

376 → 417

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	10082
1	633	8256
2	1944	7024
3	2101	7024
4	3290	7024
5	4622	7024
6	4986	7024
7	4924	7024

prune251.0ms (6.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	451	0	451
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	451	4	455

Error

Counts

455 → 4

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))
✓	0.1b	(/.f64 1 (/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y))))
✓	0.4b	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y)))
▶	2.2b	(expm1.f64 (log1p.f64 (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))))

Compiler

Compiled 10843 to 1555 computations (85.7% saved)

localize14.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))
✓	2.2b	(expm1.f64 (log1p.f64 (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))))
✓	9.0b	(log1p.f64 (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y)))

series1.1s (30.5%)

Counts

2 → 48

Calls

2 calls:

1.1s	(log1p.f64 (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y)))
16.0ms	(expm1.f64 (log1p.f64 (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y)))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))))

simplify143.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

752×	`times-frac_binary64`
720×	`unsub-neg_binary64`
625×	`distribute-frac-neg_binary64`
439×	`distribute-rgt-in_binary64`
378×	`distribute-lft-in_binary64`

Counts

70 → 31

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	935
1	37	885
2	57	885
3	91	885
4	152	885
5	334	885
6	1169	885
7	4234	885
8	4938	885
9	3920	885
10	4985	885
11	4997	885
12	4788	885

prune94.0ms (2.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	143	4	147

Error

Counts

147 → 4

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))
✓	0.1b	(/.f64 1 (/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y))))
✓	0.4b	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y)))
✓	2.2b	(expm1.f64 (log1p.f64 (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))))

Compiler

Compiled 2689 to 676 computations (74.9% saved)

regimes67.0ms (1.8%)

Accuracy

Total 0.0b remaining (62.6%)

Threshold costs 0.0b (62.6%)

Counts

20 → 1

Compiler

Compiled 759 to 485 computations (36.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	11	11
2	18	11
3	23	11
4	26	11
5	27	11
6	27	11

end67.0ms (1.8%)

Compiler: Compiled 65 to 42 computations (35.4% saved)

Iter	Nodes	Cost
0	7	11
1	11	11
2	18	11
3	27	11
4	43	11
5	77	11
6	89	11
7	112	11
8	136	11
9	159	11
10	167	11
11	161	11
12	144	11

Iter	Nodes	Cost
0	7	11
1	11	11
2	18	11
3	27	11
4	43	11
5	77	11
6	89	11
7	112	11
8	136	11
9	159	11
10	167	11
11	161	11
12	144	11

Details

analyze21.0ms (0.6%)

sample550.0ms (15.1%)

simplify12.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series19.0ms (0.5%)

rewrite14.0ms (0.4%)

simplify85.0ms (2.3%)

prune52.0ms (1.4%)

localize6.0ms (0.2%)

series45.0ms (1.2%)

rewrite71.0ms (1.9%)

simplify308.0ms (8.5%)

prune226.0ms (6.2%)

localize7.0ms (0.2%)

series44.0ms (1.2%)

rewrite86.0ms (2.4%)

simplify334.0ms (9.2%)

prune251.0ms (6.9%)

localize14.0ms (0.4%)

series1.1s (30.5%)

rewrite2.0ms (0%)

simplify143.0ms (3.9%)

prune94.0ms (2.6%)

regimes67.0ms (1.8%)

simplify3.0ms (0.1%)

end67.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	7	11
1	11	11
2	18	11
3	27	11
4	43	11
5	77	11
6	89	11
7	112	11
8	136	11
9	159	11
10	167	11
11	161	11
12	144	11