Details

analyze350.0ms (3.7%)

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)

sample29.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
6.0ms	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify120.0ms (1.3%)

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

prune6.0ms (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 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series45.0ms (0.5%)

Counts

4 → 80

Calls

4 calls:

22.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
11.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
19×	`add-exp-log_binary64`

Counts

4 → 153

Calls

4 calls:

9.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
8.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
482×	`distribute-rgt-in_binary64`
447×	`distribute-lft-in_binary64`
328×	`fma-neg_binary64`
240×	`associate-l_binary64`

Counts

233 → 245

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3371
1	413	2852
2	1688	2595
3	4507	2594
4	4922	2594

prune406.0ms (4.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	238	7	245
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	239	8	247

Error

Counts

247 → 8

Alt Table

Status	Error	Program
	0.7b	(.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 m (/.f64 (-.f64 1 m) v) -1))))
▶	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	8.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	34.6b	(.f64 (sqrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	7.1b	(.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))
	0.2b	(*.f64 (-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1) m)
	10.2b	(.f64 (/.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m)

Compiler

Compiled 5189 to 3180 computations (38.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series54.0ms (0.6%)

Counts

3 → 64

Calls

3 calls:

34.0ms	(/.f64 (-.f64 1 m) v)
12.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
8.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`

Counts

3 → 76

Calls

3 calls:

5.0ms	(/.f64 (-.f64 1 m) v)
3.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
0.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
332×	`distribute-rgt-neg-out_binary64`
307×	`associate-l_binary64`
305×	`div-sub_binary64`
264×	`exp-prod_binary64`

Counts

140 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2018
1	285	1760
2	745	1726
3	2553	1726
4	4478	1726
5	4976	1726

prune118.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	129	6	135

Error

Counts

135 → 6

Alt Table

Status	Error	Program
	8.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	34.6b	(.f64 (sqrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
▶	0.2b	(+.f64 (.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m) (*.f64 -1 m))
	7.1b	(.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))
	0.2b	(*.f64 (-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1) m)
	0.7b	(.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 m (/.f64 (-.f64 1 m) v) -1))))

Compiler

Compiled 2236 to 1373 computations (38.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series43.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

17.0ms	(.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m)
16.0ms	(+.f64 (.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m) (*.f64 -1 m))
10.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
25×	`associate-r_binary64`
24×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 82

Calls

3 calls:

9.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
8.0ms	(+.f64 (.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m) (*.f64 -1 m))
8.0ms	(.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m)

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

504×	`associate-*l/_binary64`
374×	`fma-def_binary64`
362×	`associate-/l*_binary64`
275×	`distribute-rgt-in_binary64`
246×	`distribute-lft-in_binary64`

Counts

154 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	2143
1	391	2007
2	1293	1980
3	5156	1980

prune182.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	193	6	199

Error

Counts

199 → 6

Alt Table

Status	Error	Program
	8.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.2b	(+.f64 (.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m) (*.f64 -1 m))
	0.4b	(+.f64 (.f64 (.f64 m (.f64 (/.f64 (-.f64 1 m) v) (sqrt.f64 m))) (sqrt.f64 m)) (.f64 -1 m))
	7.1b	(.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))
▶	0.2b	(*.f64 (-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1) m)
	0.7b	(.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 m (/.f64 (-.f64 1 m) v) -1))))

Compiler

Compiled 3967 to 2405 computations (39.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1)
✓	0.1b	(/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m))
✓	0.1b	(/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v)
✓	0.2b	(*.f64 (-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1) m)

series81.0ms (0.8%)

Counts

4 → 84

Calls

4 calls:

30.0ms	(*.f64 (-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1) m)
24.0ms	(/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v)
23.0ms	(-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1)
3.0ms	(/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m))

rewrite345.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

1260×	`times-frac_binary64`
1118×	`add-sqr-sqrt_binary64`
1116×	`*-un-lft-identity_binary64`
591×	`add-cube-cbrt_binary64`
390×	`prod-diff_binary64`

Counts

4 → 839

Calls

4 calls:

81.0ms	(*.f64 (-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1) m)
51.0ms	(-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1)
19.0ms	(/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v)
10.0ms	(/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m))

simplify1.4s (14.7%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-def_binary64`
310×	`associate-/l/_binary64`
259×	`div-sub_binary64`
241×	`associate-*l/_binary64`
200×	`sub-neg_binary64`

Counts

923 → 936

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	494	27652
1	1189	26642
2	3757	25499
3	4839	25499
4	5000	25499
5	4894	25499

prune2.6s (27.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	936	0	936
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	936	6	942

Error

Counts

942 → 6

Alt Table

Status	Error	Program
	8.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.2b	(+.f64 (.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m) (*.f64 -1 m))
	0.4b	(+.f64 (.f64 (.f64 m (.f64 (/.f64 (-.f64 1 m) v) (sqrt.f64 m))) (sqrt.f64 m)) (.f64 -1 m))
	7.1b	(.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))
✓	0.2b	(*.f64 (-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1) m)
	0.7b	(.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 m (/.f64 (-.f64 1 m) v) -1))))

Compiler

Compiled 32545 to 22464 computations (31% saved)

regimes1.7s (17.4%)

Accuracy

Total 0.1b remaining (86%)

Threshold costs 0.1b (86%)

Counts

261 → 1

Compiler

Compiled 15034 to 10217 computations (32% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`mul-1-neg_binary64`
1×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	19	16
2	22	16
3	23	16
4	24	16
5	23	16

end1.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

sample1.7s (18%)

Algorithm

1×

intervals

Results

655.0ms	8000×	body	128	valid
322.0ms	8055×	pre	128	true
4.0ms	55×	body	128	invalid

Compiler

Compiled 165 to 114 computations (30.9% saved)

Details

analyze350.0ms (3.7%)

sample29.0ms (0.3%)

simplify120.0ms (1.3%)

prune6.0ms (0.1%)

localize13.0ms (0.1%)

series45.0ms (0.5%)

rewrite40.0ms (0.4%)

simplify114.0ms (1.2%)

prune406.0ms (4.3%)

localize6.0ms (0.1%)

series54.0ms (0.6%)

rewrite12.0ms (0.1%)

simplify97.0ms (1%)

prune118.0ms (1.2%)

localize9.0ms (0.1%)

series43.0ms (0.5%)

rewrite31.0ms (0.3%)

simplify60.0ms (0.6%)

prune182.0ms (1.9%)

localize10.0ms (0.1%)

series81.0ms (0.8%)

rewrite345.0ms (3.6%)

simplify1.4s (14.7%)

prune2.6s (27.1%)

regimes1.7s (17.4%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.7s (18%)

Profiling