Details

analyze58.0ms (1.6%)

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)

sample316.0ms (8.8%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
5.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify118.0ms (3.3%)

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
	0.7b	(*.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 (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series27.0ms (0.7%)

Counts

3 → 56

Calls

3 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite30.0ms (0.8%)

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:

11.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify89.0ms (2.5%)

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

prune147.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	164	7	171

Error

0.0b

Counts

171 → 7

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
	0.7b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
▶	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	34.4b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	8.3b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m))) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)))

Compiler

Compiled 3424 to 1920 computations (43.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
✓	0.1b	(/.f64 v (*.f64 m (-.f64 1 m)))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
✓	0.3b	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))

series52.0ms (1.5%)

Counts

3 → 68

Calls

3 calls:

28.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))
14.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
11.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))

rewrite39.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
31×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`

Counts

3 → 124

Calls

3 calls:

17.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
7.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
6.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))

simplify107.0ms (3%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
359×	`distribute-rgt-in_binary64`
334×	`fma-neg_binary64`
327×	`distribute-lft-in_binary64`
273×	`associate-/r/_binary64`

Counts

192 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	3188
1	412	2804
2	1397	2683
3	4268	2683
4	5165	2683

prune240.0ms (6.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	270	7	277

Error

Counts

277 → 7

Alt Table

Status	Error	Program
▶	0.7b	(.f64 (-.f64 (/.f64 (/.f64 1 v) (/.f64 1 (.f64 m (-.f64 1 m)))) 1) m)
	8.3b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	1.4b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
	1.0b	(.f64 (-.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 v (.f64 m (-.f64 1 m)))) (cbrt.f64 (/.f64 v (.f64 m (-.f64 1 m)))))) (cbrt.f64 (/.f64 v (*.f64 m (-.f64 1 m))))) 1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	34.4b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))

Compiler

Compiled 5834 to 3758 computations (35.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(/.f64 1 (*.f64 m (-.f64 1 m)))
✓	0.2b	(.f64 (-.f64 (/.f64 (/.f64 1 v) (/.f64 1 (.f64 m (-.f64 1 m)))) 1) m)
✓	0.8b	(/.f64 (/.f64 1 v) (/.f64 1 (*.f64 m (-.f64 1 m))))

series28.0ms (0.8%)

Counts

3 → 60

Calls

3 calls:

14.0ms	(.f64 (-.f64 (/.f64 (/.f64 1 v) (/.f64 1 (.f64 m (-.f64 1 m)))) 1) m)
11.0ms	(/.f64 (/.f64 1 v) (/.f64 1 (*.f64 m (-.f64 1 m))))
3.0ms	(/.f64 1 (*.f64 m (-.f64 1 m)))

rewrite84.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

267×	`times-frac_binary64`
135×	`add-sqr-sqrt_binary64`
114×	`*-un-lft-identity_binary64`
105×	`add-cube-cbrt_binary64`
99×	`add-exp-log_binary64`

Counts

3 → 254

Calls

3 calls:

38.0ms	(.f64 (-.f64 (/.f64 (/.f64 1 v) (/.f64 1 (.f64 m (-.f64 1 m)))) 1) m)
13.0ms	(/.f64 (/.f64 1 v) (/.f64 1 (*.f64 m (-.f64 1 m))))
7.0ms	(/.f64 1 (*.f64 m (-.f64 1 m)))

simplify179.0ms (5%)

Algorithm

1×	egg-herbie

Rules

470×	`associate-/l*_binary64`
467×	`distribute-rgt-in_binary64`
437×	`associate-/r/_binary64`
423×	`distribute-lft-in_binary64`
217×	`fma-def_binary64`

Counts

314 → 331

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	6407
1	608	5715
2	1850	5486
3	4670	5486
4	5002	5486

prune410.0ms (11.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	401	1	402
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	402	7	409

Error

Counts

409 → 7

Alt Table

Status	Error	Program
✓	0.7b	(.f64 (-.f64 (/.f64 (/.f64 1 v) (/.f64 1 (.f64 m (-.f64 1 m)))) 1) m)
	8.3b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
▶	1.4b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	34.4b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	17.7b	(.f64 (-.f64 (/.f64 (/.f64 1 v) (/.f64 1 (cbrt.f64 (pow.f64 (-.f64 m (.f64 m m)) 3)))) 1) m)

Compiler

Compiled 10020 to 7035 computations (29.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (.f64 (cbrt.f64 m) (cbrt.f64 m)))
✓	0.3b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.5b	(*.f64 (cbrt.f64 m) (cbrt.f64 m))
✓	0.6b	(cbrt.f64 m)

series204.0ms (5.7%)

Counts

4 → 72

Calls

4 calls:

109.0ms	(.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (.f64 (cbrt.f64 m) (cbrt.f64 m)))
39.0ms	(*.f64 (cbrt.f64 m) (cbrt.f64 m))
37.0ms	(cbrt.f64 m)
19.0ms	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 102

Calls

4 calls:

9.0ms	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
5.0ms	(.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (.f64 (cbrt.f64 m) (cbrt.f64 m)))
5.0ms	(*.f64 (cbrt.f64 m) (cbrt.f64 m))
1.0ms	(cbrt.f64 m)

simplify97.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-def_binary64`
731×	`unswap-sqr_binary64`
428×	`*-commutative_binary64`
304×	`fma-neg_binary64`
199×	`associate-l_binary64`

Counts

174 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2923
1	334	2349
2	1169	2180
3	2901	2152
4	5054	2152

prune105.0ms (2.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	210	7	217

Error

Counts

217 → 7

Alt Table

Status	Error	Program
✓	0.7b	(.f64 (-.f64 (/.f64 (/.f64 1 v) (/.f64 1 (.f64 m (-.f64 1 m)))) 1) m)
	8.3b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	1.4b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	34.4b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	17.7b	(.f64 (-.f64 (/.f64 (/.f64 1 v) (/.f64 1 (cbrt.f64 (pow.f64 (-.f64 m (.f64 m m)) 3)))) 1) m)

Compiler

Compiled 4599 to 2122 computations (53.9% saved)

regimes310.0ms (8.7%)

Accuracy

Total 0.1b remaining (79.9%)

Threshold costs 0.1b (79.9%)

Counts

98 → 1

Compiler

Compiled 5567 to 3906 computations (29.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	19	19
2	25	19
3	29	19
4	32	19
5	33	19
6	31	19

end1.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

sample873.0ms (24.4%)

Algorithm

1×

intervals

Results

324.0ms	8000×	body	128	valid
175.0ms	8075×	pre	128	true
3.0ms	75×	body	128	invalid

Compiler

Compiled 165 to 114 computations (30.9% saved)

Details

analyze58.0ms (1.6%)

sample316.0ms (8.8%)

simplify118.0ms (3.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series27.0ms (0.7%)

rewrite30.0ms (0.8%)

simplify89.0ms (2.5%)

prune147.0ms (4.1%)

localize8.0ms (0.2%)

series52.0ms (1.5%)

rewrite39.0ms (1.1%)

simplify107.0ms (3%)

prune240.0ms (6.7%)

localize10.0ms (0.3%)

series28.0ms (0.8%)

rewrite84.0ms (2.4%)

simplify179.0ms (5%)

prune410.0ms (11.5%)

localize10.0ms (0.3%)

series204.0ms (5.7%)

rewrite25.0ms (0.7%)

simplify97.0ms (2.7%)

prune105.0ms (2.9%)

regimes310.0ms (8.7%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample873.0ms (24.4%)

Profiling