Details

analyze58.0ms (1.1%)

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)

sample322.0ms (6.1%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
5.0ms	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify114.0ms (2.2%)

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

series32.0ms (0.6%)

Counts

3 → 68

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

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 102

Calls

3 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)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify93.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

892×	`times-frac_binary64`
630×	`associate-/l*_binary64`
421×	`fma-neg_binary64`
343×	`distribute-rgt-in_binary64`
333×	`distribute-lft-in_binary64`

Counts

170 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2521
1	333	2111
2	1062	2094
3	4926	2094
4	5274	2094

prune180.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	168	6	174
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	170	6	176

Error

Counts

176 → 6

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	8.7b	(-.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))
	10.3b	(.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))
	0.7b	(.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 (cbrt.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)

Compiler

Compiled 3605 to 2358 computations (34.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series42.0ms (0.8%)

Counts

4 → 84

Calls

4 calls:

14.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
10.0ms	(/.f64 v (-.f64 1 m))
9.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
9.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)

rewrite184.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

684×	`times-frac_binary64`
580×	`add-sqr-sqrt_binary64`
546×	`*-un-lft-identity_binary64`
380×	`add-cube-cbrt_binary64`
231×	`prod-diff_binary64`

Counts

4 → 528

Calls

4 calls:

30.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
23.0ms	(*.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))

simplify344.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

824×	`times-frac_binary64`
637×	`fma-def_binary64`
234×	`fma-neg_binary64`
220×	`associate-*l/_binary64`
191×	`associate-/r/_binary64`

Counts

612 → 712

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	368	13214
1	832	12612
2	3028	11485
3	4893	11485
4	5032	11485

prune811.0ms (15.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	711	1	712
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	712	6	718

Error

Counts

718 → 6

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	8.7b	(-.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))
	10.3b	(.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))
	0.7b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)) (cbrt.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1))) (*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
▶	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)

Compiler

Compiled 19761 to 12808 computations (35.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series59.0ms (1.1%)

Counts

4 → 92

Calls

4 calls:

27.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))
13.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
10.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
9.0ms	(-.f64 (/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m)))) 1)

rewrite75.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`times-frac_binary64`
155×	`add-sqr-sqrt_binary64`
141×	`*-un-lft-identity_binary64`
123×	`add-cube-cbrt_binary64`
96×	`prod-diff_binary64`

Counts

4 → 289

Calls

4 calls:

18.0ms	(-.f64 (/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m)))) 1)
16.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
7.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
5.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))

simplify185.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-/l*_binary64`
432×	`distribute-rgt-in_binary64`
403×	`distribute-lft-in_binary64`
325×	`associate-/r/_binary64`
323×	`fma-def_binary64`

Counts

381 → 411

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	6616
1	468	5888
2	1524	5517
3	4740	5517
4	5001	5517

prune476.0ms (9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	411	0	411
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	411	6	417

Error

Counts

417 → 6

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	8.7b	(-.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))
	10.3b	(.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))
	0.7b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)) (cbrt.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1))) (*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)

Compiler

Compiled 10685 to 7928 computations (25.8% saved)

localize9.0ms (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 (*.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))

series44.0ms (0.8%)

Counts

2 → 32

Calls

2 calls:

23.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
20.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

rewrite27.0ms (0.5%)

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))
11.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))

simplify88.0ms (1.7%)

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

prune185.0ms (3.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	220	6	226

Error

Counts

226 → 6

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	8.7b	(-.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))
	10.3b	(.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))
	0.7b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)) (cbrt.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1))) (*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)

Compiler

Compiled 5158 to 2966 computations (42.5% saved)

regimes1.0s (19.6%)

Accuracy

Total 0.1b remaining (86%)

Threshold costs 0.1b (86%)

Counts

284 → 1

Compiler

Compiled 17288 to 11718 computations (32.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	17	16
2	21	16
3	23	16
4	24	16
5	22	16

end0.0ms (0%)

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

sample859.0ms (16.3%)

Algorithm

1×

intervals

Results

320.0ms	8000×	body	128	valid
175.0ms	8050×	pre	128	true
2.0ms	50×	body	128	invalid

Compiler

Compiled 159 to 112 computations (29.6% saved)

Details

analyze58.0ms (1.1%)

sample322.0ms (6.1%)

simplify114.0ms (2.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series32.0ms (0.6%)

rewrite29.0ms (0.6%)

simplify93.0ms (1.8%)

prune180.0ms (3.4%)

localize7.0ms (0.1%)

series42.0ms (0.8%)

rewrite184.0ms (3.5%)

simplify344.0ms (6.5%)

prune811.0ms (15.4%)

localize8.0ms (0.1%)

series59.0ms (1.1%)

rewrite75.0ms (1.4%)

simplify185.0ms (3.5%)

prune476.0ms (9%)

localize9.0ms (0.2%)

series44.0ms (0.8%)

rewrite27.0ms (0.5%)

simplify88.0ms (1.7%)

prune185.0ms (3.5%)

regimes1.0s (19.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample859.0ms (16.3%)

Profiling