Details

analyze55.0ms (1.4%)

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)

sample310.0ms (8.1%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
6.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify119.0ms (3.1%)

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

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize7.0ms (0.2%)

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

series36.0ms (0.9%)

Counts

4 → 80

Calls

4 calls:

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

rewrite39.0ms (1%)

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

simplify105.0ms (2.8%)

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

prune444.0ms (11.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	239	6	245
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	240	7	247

Error

0.0b

Counts

247 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	9.8b	(.f64 (fma.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (sqrt.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)
	53.0b	(neg.f64 (/.f64 (pow.f64 m 3) v))
	9.7b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	12.7b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))

Compiler

Compiled 5058 to 3077 computations (39.2% 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)))
✓	0.1b	(.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 (1.4%)

Counts

3 → 68

Calls

3 calls:

29.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))
13.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
11.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))

rewrite38.0ms (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)))

simplify103.0ms (2.7%)

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

prune246.0ms (6.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

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

Error

0.0b

Counts

277 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	9.8b	(.f64 (fma.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (sqrt.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)
	53.0b	(neg.f64 (/.f64 (pow.f64 m 3) v))
	9.7b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
▶	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	12.7b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))

Compiler

Compiled 5798 to 3724 computations (35.8% saved)

localize9.0ms (0.2%)

Local error

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

series45.0ms (1.2%)

Counts

2 → 32

Calls

2 calls:

24.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
21.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

rewrite27.0ms (0.7%)

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:

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

simplify83.0ms (2.2%)

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 → 98

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

prune208.0ms (5.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	213	2	215
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	214	8	222

Error

Counts

222 → 8

Alt Table

Status	Error	Program
	23.7b	(/.f64 (fma.f64 (/.f64 (-.f64 1 m) (/.f64 v (-.f64 1 m))) (/.f64 (pow.f64 m 3) v) (neg.f64 m)) (+.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	9.8b	(.f64 (fma.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (sqrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)) -1) m)
▶	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)))
	12.7b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	9.7b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

Compiler

Compiled 5093 to 2624 computations (48.5% saved)

localize10.0ms (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 (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)))

series159.0ms (4.2%)

Counts

4 → 56

Calls

4 calls:

98.0ms	(.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m))))
26.0ms	(*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))
18.0ms	(sqrt.f64 (sqrt.f64 m))
17.0ms	(.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)))

rewrite34.0ms (0.9%)

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:

11.0ms	(.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)))
8.0ms	(.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m))))
7.0ms	(*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))
1.0ms	(sqrt.f64 (sqrt.f64 m))

simplify111.0ms (2.9%)

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 → 168

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

prune129.0ms (3.4%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	191	8	199

Error

Counts

199 → 8

Alt Table

Status	Error	Program
	23.7b	(/.f64 (fma.f64 (/.f64 (-.f64 1 m) (/.f64 v (-.f64 1 m))) (/.f64 (pow.f64 m 3) v) (neg.f64 m)) (+.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	9.8b	(.f64 (fma.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (sqrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)) -1) m)
✓	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)))
	12.7b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	9.7b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

Compiler

Compiled 4626 to 1938 computations (58.1% saved)

regimes477.0ms (12.5%)

Accuracy

Total 0.2b remaining (90.3%)

Threshold costs 0.2b (90.3%)

Counts

134 → 1

Compiler

Compiled 7523 to 5063 computations (32.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	18	16
2	22	16
3	24	16
4	25	16
5	23	16

end1.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample949.0ms (24.9%)

Algorithm

1×

intervals

Results

371.0ms	8000×	body	128	valid
184.0ms	8060×	pre	128	true
2.0ms	60×	body	128	invalid

Compiler

Compiled 201 to 131 computations (34.8% saved)

Details

analyze55.0ms (1.4%)

sample310.0ms (8.1%)

simplify119.0ms (3.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series36.0ms (0.9%)

rewrite39.0ms (1%)

simplify105.0ms (2.8%)

prune444.0ms (11.7%)

localize8.0ms (0.2%)

series52.0ms (1.4%)

rewrite38.0ms (1%)

simplify103.0ms (2.7%)

prune246.0ms (6.5%)

localize9.0ms (0.2%)

series45.0ms (1.2%)

rewrite27.0ms (0.7%)

simplify83.0ms (2.2%)

prune208.0ms (5.5%)

localize10.0ms (0.3%)

series159.0ms (4.2%)

rewrite34.0ms (0.9%)

simplify111.0ms (2.9%)

prune129.0ms (3.4%)

regimes477.0ms (12.5%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample949.0ms (24.9%)

Profiling