Details

analyze33.0ms (1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample1.0s (30.9%)

Results

934.0ms	8256×	body	128	valid
50.0ms	421×	body	128	invalid

Compiler

Compiled 67 to 38 computations (43.3% saved)

simplify46.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

13.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.8b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 55 to 29 computations (47.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 a a) (.f64 b b))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	13.3b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

series53.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

23.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
23.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
6.0ms	(-.f64 (.f64 a a) (.f64 b b))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
11×	`times-frac_binary64`
10×	`fabs-mul_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 75

Calls

3 calls:

5.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
5.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
3.0ms	(-.f64 (.f64 a a) (.f64 b b))

simplify104.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

653×	`times-frac_binary64`
330×	`associate-l_binary64`
306×	`associate-/l*_binary64`
296×	`fma-neg_binary64`
282×	`associate-r_binary64`

Counts

147 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	2391
1	285	2222
2	879	2113
3	3871	2101
4	4888	2101
5	4981	2101

prune70.0ms (2.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	2	126

Error

Counts

126 → 2

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
	13.8b	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))

Compiler

Compiled 2462 to 692 computations (71.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
✓	0.0b	(/.f64 a (/.f64 (-.f64 a b) a))
✓	0.0b	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
✓	0.0b	(/.f64 (-.f64 a b) a)

series53.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

23.0ms	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
15.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
11.0ms	(/.f64 a (/.f64 (-.f64 a b) a))
5.0ms	(/.f64 (-.f64 a b) a)

rewrite227.0ms (6.7%)

Algorithm

1×	rewrite-expression-head

Rules

1564×	`times-frac_binary64`
1064×	`*-un-lft-identity_binary64`
845×	`add-sqr-sqrt_binary64`
620×	`add-cube-cbrt_binary64`
260×	`sqrt-prod_binary64`

Counts

4 → 752

Calls

4 calls:

38.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
17.0ms	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
6.0ms	(/.f64 a (/.f64 (-.f64 a b) a))
4.0ms	(/.f64 (-.f64 a b) a)

simplify629.0ms (18.5%)

Algorithm

1×	egg-herbie

Rules

749×	`associate-/r/_binary64`
667×	`associate-/l/_binary64`
471×	`fabs-div_binary64`
360×	`fabs-mul_binary64`
298×	`fma-def_binary64`

Counts

848 → 1026

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1212	29087
1	2348	28371
2	4838	28331
3	5077	28331

prune498.0ms (14.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	1026	0	1026
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	1026	2	1028

Error

Counts

1028 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
▶	13.8b	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))

Compiler

Compiled 29948 to 6880 computations (77% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a))))
✓	0.0b	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))
✓	0.0b	(expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
✓	32.5b	(/.f64 (.f64 b b) (.f64 a a))

series99.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

31.0ms	(/.f64 (.f64 b b) (.f64 a a))
27.0ms	(log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a))))
21.0ms	(expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
19.0ms	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64`

Counts

4 → 66

Calls

4 calls:

5.0ms	(/.f64 (.f64 b b) (.f64 a a))
1.0ms	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))
0.0ms	(log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a))))
0.0ms	(expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

simplify170.0ms (5%)

Algorithm

1×	egg-herbie

Rules

867×	`times-frac_binary64`
439×	`associate-/l*_binary64`
402×	`fma-def_binary64`
346×	`associate-/r*_binary64`
306×	`associate-*l/_binary64`

Counts

162 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	2889
1	387	2565
2	1223	2527
3	4685	2527
4	4961	2527

prune79.0ms (2.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	130	2	132

Error

Counts

132 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
✓	13.8b	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))

Compiler

Compiled 2721 to 1530 computations (43.8% saved)

regimes181.0ms (5.3%)

Accuracy

Total 0.0b remaining (40.2%)

Threshold costs 0.0b (40.2%)

Counts

30 → 1

Compiler

Compiled 3252 to 2150 computations (33.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`fabs-div_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	16	20
2	24	20
3	28	20
4	31	20
5	33	20
6	36	20
7	38	20
8	39	20
9	39	20

end46.0ms (1.4%)

Compiler: Compiled 60 to 38 computations (36.7% saved)

Details

analyze33.0ms (1%)

sample1.0s (30.9%)

simplify46.0ms (1.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series53.0ms (1.5%)

rewrite17.0ms (0.5%)

simplify104.0ms (3.1%)

prune70.0ms (2.1%)

localize9.0ms (0.3%)

series53.0ms (1.6%)

rewrite227.0ms (6.7%)

simplify629.0ms (18.5%)

prune498.0ms (14.7%)

localize11.0ms (0.3%)

series99.0ms (2.9%)

rewrite10.0ms (0.3%)

simplify170.0ms (5%)

prune79.0ms (2.3%)

regimes181.0ms (5.3%)

simplify3.0ms (0.1%)

end46.0ms (1.4%)

Profiling