Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
99.7%	0%	0.3%	1

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample1.8s (38.9%)

Infinites

36.4% of outputs are infinite.

Results

1.7s	8254×	body	128	valid
1.0ms	2×	body	512	valid

Compiler

Compiled 83 to 59 computations (28.9% saved)

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

494×	`fma-neg_binary64`
474×	`distribute-neg-in_binary64`
463×	`associate--l-_binary64`
362×	`associate--r-_binary64`
354×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	49	27
2	141	25
3	466	25
4	1615	25
5	3794	25
6	4547	25
7	4966	25

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

1.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.3b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

Compiler

Compiled 93 to 60 computations (35.5% saved)

localize21.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (-.f64 1 t) x)
✓	0.5b	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))
✓	0.8b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

series89.0ms (1.9%)

Counts

3 → 168

Calls

3 calls:

52.0ms	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
27.0ms	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))
10.0ms	(fma.f64 a (-.f64 1 t) x)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`
3×	`add-exp-log_binary64`

Counts

3 → 30

Calls

3 calls:

1.0ms	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
1.0ms	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))
1.0ms	(fma.f64 a (-.f64 1 t) x)

simplify210.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-neg_binary64`
482×	`associate--l+_binary64`
437×	`sub-neg_binary64`
413×	`associate-+l+_binary64`
409×	`associate-l_binary64`

Counts

198 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	3636
1	288	3535
2	856	3328
3	3026	3326
4	4873	3326
5	5376	3326

prune154.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	4	88

Error

Counts

88 → 4

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
▶	1.3b	(+.f64 a (-.f64 (fma.f64 b (+.f64 t y) (+.f64 z x)) (fma.f64 z y (fma.f64 a t (*.f64 b 2)))))
	18.0b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))
	19.9b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

Compiler

Compiled 1813 to 902 computations (50.2% saved)

localize24.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (+.f64 t y) (+.f64 z x))
✓	0.5b	(fma.f64 z y (fma.f64 a t (*.f64 b 2)))
✓	0.9b	(-.f64 (fma.f64 b (+.f64 t y) (+.f64 z x)) (fma.f64 z y (fma.f64 a t (*.f64 b 2))))

series93.0ms (2%)

Counts

3 → 192

Calls

3 calls:

50.0ms	(-.f64 (fma.f64 b (+.f64 t y) (+.f64 z x)) (fma.f64 z y (fma.f64 a t (*.f64 b 2))))
23.0ms	(fma.f64 z y (fma.f64 a t (*.f64 b 2)))
20.0ms	(fma.f64 b (+.f64 t y) (+.f64 z x))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 52

Calls

3 calls:

5.0ms	(-.f64 (fma.f64 b (+.f64 t y) (+.f64 z x)) (fma.f64 z y (fma.f64 a t (*.f64 b 2))))
1.0ms	(fma.f64 z y (fma.f64 a t (*.f64 b 2)))
1.0ms	(fma.f64 b (+.f64 t y) (+.f64 z x))

simplify174.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

694×	`distribute-rgt-in_binary64`
663×	`distribute-lft-in_binary64`
520×	`fma-def_binary64`
434×	`associate-l_binary64`
178×	`fma-neg_binary64`

Counts

244 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	4348
1	305	4057
2	1062	3921
3	4838	3921
4	4963	3921

prune246.0ms (5.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	135	4	139

Error

Counts

139 → 4

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
✓	1.3b	(+.f64 a (-.f64 (fma.f64 b (+.f64 t y) (+.f64 z x)) (fma.f64 z y (fma.f64 a t (*.f64 b 2)))))
▶	18.0b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))
	19.9b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

Compiler

Compiled 3815 to 1419 computations (62.8% saved)

localize16.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))

series30.0ms (0.6%)

Counts

1 → 60

Calls

1 calls:

30.0ms

(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
6×	`distribute-lft-out_binary64`
6×	`sum-log_binary64`
3×	`fma-def_binary64`

Counts

1 → 22

Calls

1 calls:

10.0ms

(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

598×	`distribute-rgt-in_binary64`
559×	`distribute-lft-in_binary64`
367×	`distribute-neg-in_binary64`
271×	`sub-neg_binary64`
261×	`associate-+l+_binary64`

Counts

82 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1598
1	241	1556
2	785	1367
3	3657	1367
4	4934	1367

prune69.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	54	4	58

Error

Counts

58 → 4

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
✓	1.3b	(+.f64 a (-.f64 (fma.f64 b (+.f64 t y) (+.f64 z x)) (fma.f64 z y (fma.f64 a t (*.f64 b 2)))))
✓	18.0b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))
▶	19.9b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

Compiler

Compiled 1049 to 449 computations (57.2% saved)

localize18.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (-.f64 b z) (*.f64 b -2))
✓	0.0b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
✓	0.0b	(+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2)))

series84.0ms (1.8%)

Counts

3 → 144

Calls

3 calls:

37.0ms	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
32.0ms	(+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2)))
15.0ms	(fma.f64 y (-.f64 b z) (*.f64 b -2))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
17×	`add-log-exp_binary64`
10×	`distribute-lft-out_binary64`
9×	`sum-log_binary64`
7×	`fma-def_binary64`

Counts

3 → 54

Calls

3 calls:

12.0ms	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
9.0ms	(+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2)))
1.0ms	(fma.f64 y (-.f64 b z) (*.f64 b -2))

simplify179.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-neg_binary64`
497×	`sub-neg_binary64`
416×	`fma-def_binary64`
379×	`associate-+l+_binary64`
290×	`associate-+r+_binary64`

Counts

198 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	3321
1	341	3106
2	1030	2860
3	3480	2860
4	4883	2860

prune149.0ms (3.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	109	4	113

Error

Counts

113 → 4

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
✓	1.3b	(+.f64 a (-.f64 (fma.f64 b (+.f64 t y) (+.f64 z x)) (fma.f64 z y (fma.f64 a t (*.f64 b 2)))))
✓	18.0b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))
✓	19.9b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

Compiler

Compiled 2128 to 882 computations (58.6% saved)

regimes1.0s (21.8%)

Accuracy

Total 1.6b remaining (99.8%)

Threshold costs 0b (0%)

Counts

130 → 1

Compiler

Compiled 16091 to 10848 computations (32.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	26	25
2	34	25
3	38	25
4	40	25
5	38	25

end76.0ms (1.6%)

Compiler: Compiled 138 to 89 computations (35.5% saved)

Details

analyze6.0ms (0.1%)

sample1.8s (38.9%)

simplify68.0ms (1.4%)

prune6.0ms (0.1%)

localize21.0ms (0.4%)

series89.0ms (1.9%)

rewrite3.0ms (0.1%)

simplify210.0ms (4.4%)

prune154.0ms (3.2%)

localize24.0ms (0.5%)

series93.0ms (2%)

rewrite12.0ms (0.2%)

simplify174.0ms (3.7%)

prune246.0ms (5.2%)

localize16.0ms (0.3%)

series30.0ms (0.6%)

rewrite12.0ms (0.3%)

simplify89.0ms (1.9%)

prune69.0ms (1.5%)

localize18.0ms (0.4%)

series84.0ms (1.8%)

rewrite28.0ms (0.6%)

simplify179.0ms (3.8%)

prune149.0ms (3.2%)

regimes1.0s (21.8%)

simplify3.0ms (0.1%)

end76.0ms (1.6%)

Profiling