Details

analyze1.5s (20.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0.4%	99.4%	0.2%	10
4.3%	95.5%	0.2%	11
6.4%	93.3%	0.2%	12
7.9%	91.9%	0.2%	13
13.7%	86%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.2s (16.4%)

Results

1.0s	8255×	body	128	valid
67.0ms	500×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify96.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
683×	`sub-neg_binary64`
438×	`neg-mul-1_binary64`
412×	`neg-sub0_binary64`
378×	`distribute-rgt-out--_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	28	19
2	66	19
3	158	17
4	344	17
5	846	17
6	2066	17
7	3773	17
8	4182	17
9	4701	17
10	4906	17
11	4923	17

prune4.0ms (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

2.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	2.3b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 100 to 63 computations (37% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (+.f64 (-.f64 t z) 1))
✓	2.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series88.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

56.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
32.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
8×	`distribute-lft-out_binary64`

Counts

2 → 49

Calls

2 calls:

6.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))
0.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

simplify124.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

379×	`times-frac_binary64`
371×	`sub-neg_binary64`
318×	`associate-+r+_binary64`
277×	`+-commutative_binary64`
256×	`associate-/l*_binary64`

Counts

145 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	349	4823
1	1015	4738
2	4256	4723
3	4982	4723
4	5014	4723

prune122.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	144	4	148

Error

0.0b

Counts

148 → 4

Alt Table

Status	Error	Program
✓	2.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	34.3b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
	11.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
▶	2.3b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 4582 to 2225 computations (51.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
✓	8.9b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series136.0ms (1.9%)

Counts

3 → 144

Calls

3 calls:

67.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
58.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
11.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite195.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

1052×	`*-un-lft-identity_binary64`
883×	`times-frac_binary64`
649×	`add-sqr-sqrt_binary64`
448×	`add-cube-cbrt_binary64`
300×	`prod-diff_binary64`

Counts

3 → 600

Calls

3 calls:

34.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
10.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
7.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify885.0ms (12.4%)

Algorithm

1×	egg-herbie

Rules

435×	`times-frac_binary64`
336×	`sub-neg_binary64`
248×	`fma-def_binary64`
208×	`fma-udef_binary64`
196×	`neg-sub0_binary64`

Counts

744 → 670

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1050	52563
1	3195	48069
2	4814	47566
3	4994	47566

prune870.0ms (12.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	667	3	670
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	669	5	674

Error

Counts

674 → 5

Alt Table

Status	Error	Program
▶	0.5b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
✓	2.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	11.8b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	2.3b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	2.3b	(-.f64 x (/.f64 (-.f64 y z) (*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a))))

Compiler

Compiled 34666 to 14886 computations (57.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
✓	0.0b	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
✓	1.0b	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)

series166.0ms (2.3%)

Counts

3 → 144

Calls

3 calls:

68.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
59.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
38.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

rewrite75.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
29×	`add-cube-cbrt_binary64`

Counts

3 → 126

Calls

3 calls:

15.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
10.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
3.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))

simplify187.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

516×	`times-frac_binary64`
374×	`associate-/l*_binary64`
277×	`associate-/r*_binary64`
246×	`+-commutative_binary64`
207×	`sub-neg_binary64`

Counts

270 → 292

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	658	10133
1	1956	9941
2	4965	9941
3	4992	9941

prune260.0ms (3.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	292	5	297

Error

Counts

297 → 5

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
✓	2.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	11.8b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	2.3b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	2.3b	(-.f64 x (/.f64 (-.f64 y z) (*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a))))

Compiler

Compiled 10917 to 5213 computations (52.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (-.f64 y z) (*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a))))
✓	0.2b	(*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a))
✓	8.9b	(/.f64 (-.f64 y z) (*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a)))

series142.0ms (2%)

Counts

3 → 144

Calls

3 calls:

74.0ms	(-.f64 x (/.f64 (-.f64 y z) (*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a))))
53.0ms	(/.f64 (-.f64 y z) (*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a)))
15.0ms	(*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64`
57×	`*-un-lft-identity_binary64`
45×	`prod-diff_binary64`
37×	`add-cube-cbrt_binary64`
36×	`times-frac_binary64`

Counts

3 → 163

Calls

3 calls:

12.0ms	(/.f64 (-.f64 y z) (*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a)))
10.0ms	(-.f64 x (/.f64 (-.f64 y z) (*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a))))
9.0ms	(*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a))

simplify221.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

496×	`times-frac_binary64`
357×	`associate-/l*_binary64`
295×	`associate-/r*_binary64`
194×	`sub-neg_binary64`
168×	`+-commutative_binary64`

Counts

307 → 331

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	631	12392
1	1824	10286
2	4808	10280
3	4985	10280

prune298.0ms (4.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	331	0	331
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	331	5	336

Error

Counts

336 → 5

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
✓	2.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	11.8b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	2.3b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	2.3b	(-.f64 x (/.f64 (-.f64 y z) (*.f64 (+.f64 (-.f64 t z) 1) (/.f64 1 a))))

Compiler

Compiled 13007 to 6149 computations (52.7% saved)

regimes452.0ms (6.3%)

Accuracy

Total 0.3b remaining (97.4%)

Threshold costs 0.3b (97.4%)

Counts

66 → 1

Compiler

Compiled 9340 to 6148 computations (34.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`*-commutative_binary64`
7×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	25	19
2	40	19
3	54	19
4	73	19
5	81	19
6	82	19
7	78	19

end81.0ms (1.1%)

Compiler: Compiled 127 to 85 computations (33.1% saved)

Details

analyze1.5s (20.7%)

sample1.2s (16.4%)

simplify96.0ms (1.3%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series88.0ms (1.2%)

rewrite9.0ms (0.1%)

simplify124.0ms (1.7%)

prune122.0ms (1.7%)

localize9.0ms (0.1%)

series136.0ms (1.9%)

rewrite195.0ms (2.7%)

simplify885.0ms (12.4%)

prune870.0ms (12.2%)

localize8.0ms (0.1%)

series166.0ms (2.3%)

rewrite75.0ms (1%)

simplify187.0ms (2.6%)

prune260.0ms (3.6%)

localize9.0ms (0.1%)

series142.0ms (2%)

rewrite47.0ms (0.7%)

simplify221.0ms (3.1%)

prune298.0ms (4.2%)

regimes452.0ms (6.3%)

simplify3.0ms (0%)

end81.0ms (1.1%)

Profiling