Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
12.5%	0%	87.5%	1

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample989.0ms (19.4%)

Infinites

57.2% of outputs are infinite.

Results

669.0ms

8256×

body

128

valid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify121.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

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
	0.1b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series27.0ms (0.5%)

Counts

3 → 56

Calls

3 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 102

Calls

3 calls:

8.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
6.0ms	(*.f64 m (-.f64 1 m))
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
423×	`distribute-rgt-in_binary64`
385×	`distribute-lft-in_binary64`
346×	`associate-/l/_binary64`
288×	`fma-neg_binary64`

Counts

158 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	2119
1	364	1923
2	1597	1729
3	4495	1728
4	4950	1728

prune154.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	165	6	171

Error

0.0b

Counts

171 → 6

Alt Table

Status	Error	Program
	30.4b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))) (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	0.7b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
	0.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
▶	0.2b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)

Compiler

Compiled 3420 to 1914 computations (44% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.2b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
✓	0.2b	(/.f64 m (sqrt.f64 v))
✓	0.2b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

series111.0ms (2.2%)

Counts

4 → 64

Calls

4 calls:

43.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
25.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
22.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
20.0ms	(/.f64 m (sqrt.f64 v))

rewrite58.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
113×	`*-un-lft-identity_binary64`
74×	`add-cube-cbrt_binary64`
66×	`sqrt-prod_binary64`

Counts

4 → 221

Calls

4 calls:

21.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
10.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
6.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
3.0ms	(/.f64 m (sqrt.f64 v))

simplify140.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

481×	`associate-/l/_binary64`
442×	`distribute-rgt-in_binary64`
429×	`distribute-lft-in_binary64`
194×	`fma-def_binary64`
178×	`associate-l_binary64`

Counts

285 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	5114
1	598	4634
2	1976	4496
3	4784	4496
4	4984	4496

prune323.0ms (6.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	292	6	298

Error

0.0b

Counts

298 → 6

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))) (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	0.7b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
▶	0.2b	(.f64 (-.f64 (.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 1 (sqrt.f64 (sqrt.f64 v)))) (/.f64 (-.f64 1 m) (sqrt.f64 (sqrt.f64 v)))) 1) m)
	0.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 6918 to 3372 computations (51.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 1 (sqrt.f64 (sqrt.f64 v)))) (/.f64 (-.f64 1 m) (sqrt.f64 (sqrt.f64 v))))
✓	0.3b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 1 (sqrt.f64 (sqrt.f64 v))))
✓	0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 (sqrt.f64 v)))
✓	0.3b	(/.f64 1 (sqrt.f64 (sqrt.f64 v)))

series524.0ms (10.3%)

Counts

4 → 68

Calls

4 calls:

403.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 1 (sqrt.f64 (sqrt.f64 v))))
76.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 (sqrt.f64 v)))
23.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 v)))
22.0ms	(.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 1 (sqrt.f64 (sqrt.f64 v)))) (/.f64 (-.f64 1 m) (sqrt.f64 (sqrt.f64 v))))

rewrite90.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

239×	`add-sqr-sqrt_binary64`
214×	`sqrt-prod_binary64`
212×	`times-frac_binary64`
183×	`*-un-lft-identity_binary64`
117×	`add-cube-cbrt_binary64`

Counts

4 → 356

Calls

4 calls:

21.0ms	(.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 1 (sqrt.f64 (sqrt.f64 v)))) (/.f64 (-.f64 1 m) (sqrt.f64 (sqrt.f64 v))))
17.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 1 (sqrt.f64 (sqrt.f64 v))))
6.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 (sqrt.f64 v)))
5.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 v)))

simplify212.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/r*_binary64`
402×	`associate-/r/_binary64`
312×	`associate-l_binary64`
283×	`associate-*l/_binary64`
244×	`associate-*r/_binary64`

Counts

424 → 409

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	9075
1	730	7283
2	2549	7164
3	4867	7164
4	5021	7164

prune490.0ms (9.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	409	0	409
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	409	6	415

Error

0.0b

Counts

415 → 6

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))) (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	0.7b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.2b	(.f64 (-.f64 (.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 1 (sqrt.f64 (sqrt.f64 v)))) (/.f64 (-.f64 1 m) (sqrt.f64 (sqrt.f64 v)))) 1) m)
▶	0.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 12606 to 5931 computations (53% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))
✓	0.2b	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
✓	25.7b	(cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
✓	25.7b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

series205.0ms (4%)

Counts

4 → 96

Calls

4 calls:

80.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
48.0ms	(*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))
44.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
32.0ms	(cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`cbrt-prod_binary64`
53×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`

Counts

4 → 122

Calls

4 calls:

16.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
7.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
3.0ms	(*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))
1.0ms	(cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))

simplify156.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

468×	`fma-def_binary64`
355×	`associate-r_binary64`
327×	`times-frac_binary64`
276×	`associate-/l*_binary64`
255×	`associate-/r*_binary64`

Counts

218 → 280

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	534	11912
1	1634	11038
2	5201	11038

prune490.0ms (9.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	348	0	348
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	348	6	354

Error

0.0b

Counts

354 → 6

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))) (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	0.7b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.2b	(.f64 (-.f64 (.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 1 (sqrt.f64 (sqrt.f64 v)))) (/.f64 (-.f64 1 m) (sqrt.f64 (sqrt.f64 v)))) 1) m)
✓	0.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 21521 to 14924 computations (30.7% saved)

regimes710.0ms (13.9%)

Accuracy

Total 0.1b remaining (62.6%)

Threshold costs 0.1b (62.6%)

Counts

239 → 1

Compiler

Compiled 18360 to 11860 computations (35.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	22	16
3	24	16
4	25	16
5	23	16

end97.0ms (1.9%)

Compiler: Compiled 172 to 113 computations (34.3% saved)

Details

analyze1.0ms (0%)

sample989.0ms (19.4%)

simplify121.0ms (2.4%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series27.0ms (0.5%)

rewrite30.0ms (0.6%)

simplify84.0ms (1.6%)

prune154.0ms (3%)

localize8.0ms (0.2%)

series111.0ms (2.2%)

rewrite58.0ms (1.1%)

simplify140.0ms (2.7%)

prune323.0ms (6.3%)

localize12.0ms (0.2%)

series524.0ms (10.3%)

rewrite90.0ms (1.8%)

simplify212.0ms (4.2%)

prune490.0ms (9.6%)

localize13.0ms (0.3%)

series205.0ms (4%)

rewrite39.0ms (0.8%)

simplify156.0ms (3.1%)

prune490.0ms (9.6%)

regimes710.0ms (13.9%)

simplify2.0ms (0%)

end97.0ms (1.9%)

Profiling