Details

analyze64.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample1.2s (24.9%)

Results

910.0ms	8256×	body	128	valid
5.0ms	46×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify119.0ms (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
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.2b	(.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)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series26.0ms (0.5%)

Counts

3 → 56

Calls

3 calls:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
4.0ms	(*.f64 m (-.f64 1 m))

rewrite26.0ms (0.5%)

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

simplify85.0ms (1.7%)

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

prune172.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	162	7	169
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	164	7	171

Error

0.0b

Counts

171 → 7

Alt Table

Status	Error	Program
	11.0b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) m))
	0.4b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	0.8b	(.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
	12.4b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	21.1b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
▶	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 3531 to 2005 computations (43.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (-.f64 1 m))
✓	0.0b	(/.f64 m (/.f64 v (-.f64 1 m)))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)

series33.0ms (0.7%)

Counts

3 → 60

Calls

3 calls:

13.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
11.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
9.0ms	(/.f64 v (-.f64 1 m))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

171×	`times-frac_binary64`
152×	`add-sqr-sqrt_binary64`
134×	`*-un-lft-identity_binary64`
81×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`

Counts

3 → 191

Calls

3 calls:

24.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
7.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
4.0ms	(/.f64 v (-.f64 1 m))

simplify143.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

722×	`times-frac_binary64`
435×	`fma-def_binary64`
416×	`distribute-rgt-in_binary64`
379×	`distribute-lft-in_binary64`
227×	`fma-neg_binary64`

Counts

251 → 298

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	4706
1	638	4431
2	2332	4350
3	4797	4350
4	4981	4350

prune319.0ms (6.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	296	2	298
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	297	8	305

Error

Counts

305 → 8

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m))) (/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m))))) 1) m)
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	36.5b	(/.f64 (-.f64 (/.f64 (pow.f64 m 3) (*.f64 (/.f64 v (-.f64 1 m)) (/.f64 v (-.f64 1 m)))) m) (+.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1))
	11.0b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) m))
	0.8b	(.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
	12.4b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	21.1b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 6496 to 3788 computations (41.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m)))
✓	0.1b	(/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m)))
✓	0.2b	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m))) (/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m))))) 1) m)
✓	0.5b	(*.f64 (/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m))) (/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m))))

series159.0ms (3.3%)

Counts

4 → 27

Calls

4 calls:

47.0ms	(*.f64 (/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m))) (/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m))))
46.0ms	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m))) (/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m))))) 1) m)
34.0ms	(/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m)))
33.0ms	(/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m)))

rewrite99.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`add-sqr-sqrt_binary64`
201×	`*-un-lft-identity_binary64`
180×	`times-frac_binary64`
148×	`sqrt-prod_binary64`
94×	`add-cube-cbrt_binary64`

Counts

4 → 295

Calls

4 calls:

36.0ms	(*.f64 (/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m))) (/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m))))
20.0ms	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m))) (/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m))))) 1) m)
6.0ms	(/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m)))
5.0ms	(/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m)))

simplify197.0ms (4%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
575×	`associate-/l/_binary64`
456×	`associate-/r*_binary64`
361×	`associate-/r/_binary64`
209×	`fma-neg_binary64`

Counts

322 → 327

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	256	7578
1	645	7183
2	2001	7066
3	4810	7066
4	5572	7066

prune383.0ms (7.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	327	0	327
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	327	8	335

Error

Counts

335 → 8

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m))) (/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m))))) 1) m)
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	36.5b	(/.f64 (-.f64 (/.f64 (pow.f64 m 3) (*.f64 (/.f64 v (-.f64 1 m)) (/.f64 v (-.f64 1 m)))) m) (+.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1))
	11.0b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) m))
▶	0.8b	(.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
	12.4b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	21.1b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 10431 to 5640 computations (45.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m)
✓	0.2b	(.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
✓	0.3b	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
✓	0.4b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

series218.0ms (4.5%)

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)))
67.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m)
48.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
22.0ms	(.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))

rewrite87.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`cbrt-div_binary64`
56×	`add-sqr-sqrt_binary64`
55×	`cbrt-prod_binary64`
42×	`*-un-lft-identity_binary64`
36×	`associate-*l/_binary64`

Counts

4 → 165

Calls

4 calls:

26.0ms	(.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
17.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
9.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m)
6.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

simplify239.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-def_binary64`
432×	`associate-l_binary64`
280×	`times-frac_binary64`
256×	`associate-/l*_binary64`
207×	`associate-/r*_binary64`

Counts

261 → 361

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	564	13830
1	1733	13068
2	4909	12488
3	5357	12488

prune692.0ms (14.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	496	1	497
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	498	7	505

Error

Counts

505 → 7

Alt Table

Status	Error	Program
	11.9b	(.f64 (cbrt.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
✓	0.3b	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (+.f64 1 (sqrt.f64 m))) (/.f64 (sqrt.f64 v) (-.f64 1 (sqrt.f64 m))))) 1) m)
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
✓	0.8b	(.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
	12.4b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	21.1b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 30617 to 21625 computations (29.4% saved)

regimes397.0ms (8.1%)

Accuracy

Total 0.1b remaining (82.6%)

Threshold costs 0.1b (82.6%)

Counts

131 → 1

Compiler

Compiled 8489 to 5706 computations (32.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	20	16
2	24	16
3	26	16
4	27	16
5	25	16

end121.0ms (2.5%)

Compiler: Compiled 226 to 157 computations (30.5% saved)

Details

analyze64.0ms (1.3%)

sample1.2s (24.9%)

simplify119.0ms (2.4%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series26.0ms (0.5%)

rewrite26.0ms (0.5%)

simplify85.0ms (1.7%)

prune172.0ms (3.5%)

localize6.0ms (0.1%)

series33.0ms (0.7%)

rewrite50.0ms (1%)

simplify143.0ms (2.9%)

prune319.0ms (6.5%)

localize11.0ms (0.2%)

series159.0ms (3.3%)

rewrite99.0ms (2%)

simplify197.0ms (4%)

prune383.0ms (7.9%)

localize10.0ms (0.2%)

series218.0ms (4.5%)

rewrite87.0ms (1.8%)

simplify239.0ms (4.9%)

prune692.0ms (14.2%)

regimes397.0ms (8.1%)

simplify2.0ms (0%)

end121.0ms (2.5%)

Profiling