Details

analyze1.8s (38.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
3.1%	96.6%	0.3%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.7s (37.2%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

Results

1.1s	8256×	body	128	valid
580.0ms	4059×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	20	12
2	35	12
3	43	12
4	43	12

prune3.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))

Compiler

Compiled 56 to 31 computations (44.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series27.0ms (0.6%)

Counts

2 → 120

Calls

2 calls:

18.0ms	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
9.0ms	(fma.f64 x y (*.f64 z t))

rewrite48.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

869×	`log1p-expm1-u_binary64`
869×	`expm1-log1p-u_binary64`
240×	`prod-diff_binary64`
102×	`add-sqr-sqrt_binary64`
93×	`add-log-exp_binary64`

Counts

2 → 49

Calls

2 calls:

47.0ms	(fma.f64 x y (*.f64 z t))
47.0ms	(fma.f64 a b (fma.f64 x y (*.f64 z t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	196	20
2	2266	20
3	5837	20
0	0	0
1	0	0

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`associate-+r+_binary64`
1×	`associate-+l+_binary64`

Counts

169 → 61

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	1080
1	29	1080
2	41	1080
3	43	1080
4	43	1080

prune35.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	3	62

Error

Counts

62 → 3

Alt Table

Status	Error	Program
	34.6b	(fma.f64 a b (/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (pow.f64 (.f64 z t) 2) (.f64 (.f64 x y) (*.f64 z t))))))
✓	0.0b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
▶	19.2b	(fma.f64 y x (*.f64 a b))

Compiler

Compiled 909 to 250 computations (72.5% saved)

localize4.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
▶	34.6b	(fma.f64 a b (/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (pow.f64 (.f64 z t) 2) (.f64 (.f64 x y) (*.f64 z t))))))
✓	0.0b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
✓	19.2b	(fma.f64 y x (*.f64 a b))

Compiler

Compiled 111 to 59 computations (46.8% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.7b	(-.f64 (pow.f64 (.f64 z t) 2) (.f64 (.f64 x y) (.f64 z t)))
✓	1.8b	(+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3))
✓	3.5b	(.f64 (.f64 x y) (*.f64 z t))
✓	35.8b	(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (pow.f64 (.f64 z t) 2) (.f64 (.f64 x y) (*.f64 z t)))))

series245.0ms (5.3%)

Counts

4 → 192

Calls

4 calls:

134.0ms	(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (pow.f64 (.f64 z t) 2) (.f64 (.f64 x y) (*.f64 z t)))))
62.0ms	(+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3))
31.0ms	(-.f64 (pow.f64 (.f64 z t) 2) (.f64 (.f64 x y) (.f64 z t)))
17.0ms	(.f64 (.f64 x y) (*.f64 z t))

rewrite85.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

597×	`prod-diff_binary64`
204×	`log1p-expm1-u_binary64`
204×	`expm1-log1p-u_binary64`
198×	`add-sqr-sqrt_binary64`
192×	`add-cbrt-cube_binary64`

Counts

4 → 143

Calls

4 calls:

81.0ms	(-.f64 (pow.f64 (.f64 z t) 2) (.f64 (.f64 x y) (.f64 z t)))
81.0ms	(+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3))
81.0ms	(.f64 (.f64 x y) (*.f64 z t))
81.0ms	(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (pow.f64 (.f64 z t) 2) (.f64 (.f64 x y) (*.f64 z t)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	91
1	427	53
2	4522	53
3	5362	53
0	0	0
1	0	0

simplify151.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

958×	`fma-def_binary64`
746×	`fma-neg_binary64`
394×	`neg-sub0_binary64`
388×	`neg-mul-1_binary64`
365×	`distribute-rgt-neg-in_binary64`

Counts

335 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	2580
1	78	2580
2	212	2364
3	710	2364
4	1241	2364
5	1632	2364
6	2320	2364
7	3313	2364
8	4225	2364
9	4964	2364

prune117.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	159	3	162

Error

Counts

162 → 3

Alt Table

Status	Error	Program
✓	34.6b	(fma.f64 a b (/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (pow.f64 (.f64 z t) 2) (.f64 (.f64 x y) (*.f64 z t))))))
✓	0.0b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
✓	19.2b	(fma.f64 y x (*.f64 a b))

Compiler

Compiled 6638 to 2130 computations (67.9% saved)

regimes232.0ms (5%)

Accuracy

Total 0.0b remaining (43%)

Threshold costs 0.0b (43%)

Counts

14 → 1

Compiler

Compiled 2887 to 1888 computations (34.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12
2	11	12

end103.0ms (2.2%)

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 189 to 110 computations (41.8% saved)

Details

analyze1.8s (38.2%)

sample1.7s (37.2%)

simplify11.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series27.0ms (0.6%)

rewrite48.0ms (1%)

simplify44.0ms (0.9%)

prune35.0ms (0.8%)

localize4.0ms (0.1%)

prune3.0ms (0.1%)

localize19.0ms (0.4%)

series245.0ms (5.3%)

rewrite85.0ms (1.8%)

simplify151.0ms (3.3%)

prune117.0ms (2.5%)

regimes232.0ms (5%)

simplify2.0ms (0%)

end103.0ms (2.2%)

Profiling