Details

analyze357.0ms (5.5%)

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 23 to 16 computations (30.4% saved)

sample25.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
5.0ms	260×	pre	128	true
0.0ms	4×	body	128	invalid

Compiler

Compiled 38 to 27 computations (28.9% saved)

simplify124.0ms (1.9%)

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)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

rewrite26.0ms (0.4%)

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:

9.0ms	(.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))

series61.0ms (0.9%)

Counts

3 → 56

Calls

3 calls:

28.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
26.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
6.0ms	(*.f64 m (-.f64 1 m))

simplify92.0ms (1.4%)

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 → 299

Iterations

Useful iterations: 3 (0.0ms)

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

prune158.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	293	6	299
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	295	6	301

Error

0.0b

Counts

301 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	38.1b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
▶	0.1b	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) m)
	34.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	11.7b	(/.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))
	17.5b	(/.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))))

Compiler

Compiled 3422 to 1932 computations (43.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64`
53×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
18×	`distribute-lft-neg-in_binary64`

Counts

3 → 133

Calls

3 calls:

20.0ms	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) m)
6.0ms	(/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v))
3.0ms	(-.f64 (*.f64 m m) m)

series85.0ms (1.3%)

Counts

3 → 60

Calls

3 calls:

42.0ms	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) m)
36.0ms	(/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v))
7.0ms	(-.f64 (*.f64 m m) m)

simplify181.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-neg_binary64`
551×	`fma-def_binary64`
350×	`distribute-rgt-in_binary64`
177×	`div-sub_binary64`
154×	`cancel-sign-sub-inv_binary64`

Counts

193 → 338

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	3330
1	504	3108
2	1987	3065
3	4671	3065
4	5058	3065

prune310.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	337	1	338
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	338	6	344

Error

0.0b

Counts

344 → 6

Alt Table

Status	Error	Program
	11.7b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1))
▶	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	38.1b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.1b	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) m)
	34.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	17.5b	(/.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))))

Compiler

Compiled 4233 to 1471 computations (65.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 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) (sqrt.f64 m))
✓	0.4b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

2 → 55

Calls

2 calls:

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

series119.0ms (1.8%)

Counts

2 → 32

Calls

2 calls:

60.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
59.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

simplify169.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-neg_binary64`
546×	`associate-/l*_binary64`
487×	`fma-def_binary64`
357×	`times-frac_binary64`
305×	`associate-/r/_binary64`

Counts

87 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	1884
1	250	1638
2	727	1451
3	1939	1448
4	4767	1448
5	5248	1448

prune331.0ms (5.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	369	1	370
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	369	7	376

Error

Counts

376 → 7

Alt Table

Status	Error	Program
	11.7b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1))
▶	0.7b	(.f64 (.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))) (sqrt.f64 (sqrt.f64 m)))
✓	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	38.1b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.1b	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) m)
	34.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	17.5b	(/.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))))

Compiler

Compiled 5072 to 2621 computations (48.3% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite65.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary64`
35×	`add-sqr-sqrt_binary64`
31×	`pow1_binary64`
20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 117

Calls

4 calls:

23.0ms	(.f64 (.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))) (sqrt.f64 (sqrt.f64 m)))
14.0ms	(.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m))))
14.0ms	(*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))
3.0ms	(sqrt.f64 (sqrt.f64 m))

series880.0ms (13.5%)

Counts

4 → 56

Calls

4 calls:

319.0ms	(*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))
297.0ms	(sqrt.f64 (sqrt.f64 m))
211.0ms	(.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m))))
51.0ms	(.f64 (.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))) (sqrt.f64 (sqrt.f64 m)))

simplify205.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-def_binary64`
557×	`fma-neg_binary64`
385×	`associate-/l*_binary64`
339×	`*-commutative_binary64`
200×	`associate-l_binary64`

Counts

173 → 296

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	3065
1	306	2592
2	992	2389
3	2345	2383
4	4598	2383
5	4937	2383

prune229.0ms (3.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	296	0	296
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	296	7	303

Error

Counts

303 → 7

Alt Table

Status	Error	Program
	11.7b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1))
✓	0.7b	(.f64 (.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))) (sqrt.f64 (sqrt.f64 m)))
✓	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	38.1b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.1b	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) m)
	34.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	17.5b	(/.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))))

Compiler

Compiled 4116 to 1771 computations (57% saved)

regimes1.4s (20.8%)

Accuracy

Total 0.1b remaining (85.5%)

Threshold costs 0.1b (85.5%)

Compiler

Compiled 13594 to 8765 computations (35.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	21	18
2	26	18
3	29	18
4	30	18
5	28	18

end3.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample1.6s (24.6%)

Algorithm

1×

intervals

Results

602.0ms	8000×	body	128	valid
297.0ms	8046×	pre	128	true
3.0ms	46×	body	128	invalid

Compiler

Compiled 204 to 132 computations (35.3% saved)

Details

analyze357.0ms (5.5%)

sample25.0ms (0.4%)

simplify124.0ms (1.9%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

rewrite26.0ms (0.4%)

series61.0ms (0.9%)

simplify92.0ms (1.4%)

prune158.0ms (2.4%)

localize7.0ms (0.1%)

rewrite35.0ms (0.5%)

series85.0ms (1.3%)

simplify181.0ms (2.8%)

prune310.0ms (4.7%)

localize17.0ms (0.3%)

rewrite51.0ms (0.8%)

series119.0ms (1.8%)

simplify169.0ms (2.6%)

prune331.0ms (5.1%)

localize21.0ms (0.3%)

rewrite65.0ms (1%)

series880.0ms (13.5%)

simplify205.0ms (3.1%)

prune229.0ms (3.5%)

regimes1.4s (20.8%)

simplify6.0ms (0.1%)

end3.0ms (0%)

sample1.6s (24.6%)

Profiling