Details

analyze694.0ms (11.6%)

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
12.5%	87.3%	0.2%	6
12.5%	87.3%	0.2%	7
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
28.1%	71.7%	0.2%	10
42.1%	57.7%	0.2%	11
42.1%	57.7%	0.2%	12
42.1%	57.7%	0.2%	13
49.1%	50.7%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample952.0ms (15.8%)

Infinites

6% of outputs are infinite.

Results

871.0ms	8255×	body	128	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify103.0ms (1.7%)

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

2.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.4b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	2.4b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 100 to 63 computations (37% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (+.f64 (-.f64 t z) 1))
✓	2.4b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series76.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

53.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
23.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))

rewrite8.0ms (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:

5.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))
0.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

simplify133.0ms (2.2%)

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

prune133.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	144	4	148

Error

Counts

148 → 4

Alt Table

Status	Error	Program
	12.1b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
▶	2.4b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	14.1b	(fma.f64 (*.f64 (/.f64 a (fma.f64 (-.f64 t z) (-.f64 t z) -1)) (-.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	32.5b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))

Compiler

Compiled 4617 to 2242 computations (51.4% saved)

localize10.0ms (0.2%)

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)
✓	10.6b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series138.0ms (2.3%)

Counts

3 → 144

Calls

3 calls:

68.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
60.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
10.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite181.0ms (3%)

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:

36.0ms	(-.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))
6.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify843.0ms (14%)

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

prune581.0ms (9.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	669	1	670
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	670	4	674

Error

Counts

674 → 4

Alt Table

Status	Error	Program
✓	2.4b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	0.0b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
	14.1b	(fma.f64 (*.f64 (/.f64 a (fma.f64 (-.f64 t z) (-.f64 t z) -1)) (-.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	32.5b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))

Compiler

Compiled 34669 to 14881 computations (57.1% saved)

localize9.0ms (0.2%)

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)

series151.0ms (2.5%)

Counts

3 → 144

Calls

3 calls:

66.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
53.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
31.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

rewrite39.0ms (0.6%)

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:

14.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
8.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
3.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))

simplify186.0ms (3.1%)

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

prune251.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	292	4	296

Error

Counts

296 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 x (*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a))
✓	0.0b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
✓	2.4b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	14.1b	(fma.f64 (*.f64 (/.f64 a (fma.f64 (-.f64 t z) (-.f64 t z) -1)) (-.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Compiler

Compiled 10916 to 5206 computations (52.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a))
✓	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))
✓	0.2b	(/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z)))
✓	1.0b	(*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a)

series179.0ms (3%)

Counts

4 → 180

Calls

4 calls:

65.0ms	(-.f64 x (*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a))
57.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a)
32.0ms	(/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z)))
25.0ms	(/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))

rewrite88.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

449×	`*-un-lft-identity_binary64`
392×	`times-frac_binary64`
256×	`add-sqr-sqrt_binary64`
160×	`add-cube-cbrt_binary64`
98×	`associate-l_binary64`

Counts

4 → 352

Calls

4 calls:

20.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a)
11.0ms	(/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z)))
9.0ms	(/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))
3.0ms	(-.f64 x (*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a))

simplify265.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

603×	`times-frac_binary64`
545×	`associate-/l*_binary64`
293×	`+-commutative_binary64`
253×	`sub-neg_binary64`
211×	`associate-+r+_binary64`

Counts

532 → 552

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	809	17006
1	2312	16576
2	5123	16576

prune504.0ms (8.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	552	0	552
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	552	4	556

Error

Counts

556 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 x (*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a))
✓	0.0b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
✓	2.4b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	14.1b	(fma.f64 (*.f64 (/.f64 a (fma.f64 (-.f64 t z) (-.f64 t z) -1)) (-.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Compiler

Compiled 19430 to 9757 computations (49.8% saved)

regimes390.0ms (6.5%)

Accuracy

Total 0.2b remaining (93.5%)

Threshold costs 0.2b (93.5%)

Counts

56 → 1

Compiler

Compiled 7058 to 4748 computations (32.7% saved)

simplify3.0ms (0.1%)

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

end65.0ms (1.1%)

Compiler: Compiled 118 to 76 computations (35.6% saved)

Details

analyze694.0ms (11.6%)

sample952.0ms (15.8%)

simplify103.0ms (1.7%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series76.0ms (1.3%)

rewrite8.0ms (0.1%)

simplify133.0ms (2.2%)

prune133.0ms (2.2%)

localize10.0ms (0.2%)

series138.0ms (2.3%)

rewrite181.0ms (3%)

simplify843.0ms (14%)

prune581.0ms (9.7%)

localize9.0ms (0.2%)

series151.0ms (2.5%)

rewrite39.0ms (0.6%)

simplify186.0ms (3.1%)

prune251.0ms (4.2%)

localize12.0ms (0.2%)

series179.0ms (3%)

rewrite88.0ms (1.5%)

simplify265.0ms (4.4%)

prune504.0ms (8.4%)

regimes390.0ms (6.5%)

simplify3.0ms (0.1%)

end65.0ms (1.1%)

Profiling