Details

analyze1.9s (35.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample2.3s (44.1%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

(sort c i)

Results

1.3s	8256×	body	128	valid
881.0ms	6078×	body	128	invalid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

58×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
17×	`+-commutative_binary64`
4×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	20
1	28	16
2	61	16
3	105	16
4	121	16
5	123	16
6	123	16

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 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

Compiler

Compiled 75 to 42 computations (44% saved)

localize9.0ms (0.2%)

Local error

Found 3 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)))
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

series65.0ms (1.2%)

Counts

3 → 216

Calls

3 calls:

36.0ms	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
20.0ms	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
8.0ms	(fma.f64 x y (*.f64 z t))

rewrite2.0ms (0%)

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:

0.0ms	(fma.f64 x y (*.f64 z t))
0.0ms	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
0.0ms	(fma.f64 a b (fma.f64 x y (*.f64 z t)))

simplify104.0ms (2%)

Algorithm

1×	egg-herbie

Rules

864×	`unswap-sqr_binary64`
587×	`fma-def_binary64`
579×	`associate-+r+_binary64`
555×	`associate-+l+_binary64`
395×	`associate-l_binary64`

Counts

246 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	2908
1	95	2833
2	224	2833
3	925	2833
4	3318	2833
5	3463	2833
6	4972	2833

prune46.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	2	76

Error

Counts

76 → 2

Alt Table

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

Compiler

Compiled 1258 to 251 computations (80% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series59.0ms (1.1%)

Counts

3 → 216

Calls

3 calls:

32.0ms	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
18.0ms	(fma.f64 a b (fma.f64 t z (*.f64 c i)))
8.0ms	(fma.f64 t z (*.f64 c i))

rewrite2.0ms (0%)

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:

0.0ms	(fma.f64 t z (*.f64 c i))
0.0ms	(fma.f64 a b (fma.f64 t z (*.f64 c i)))
0.0ms	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))

simplify79.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

814×	`associate-+r+_binary64`
749×	`associate-+l+_binary64`
681×	`fma-def_binary64`
440×	`associate-l_binary64`
356×	`associate-r_binary64`

Counts

246 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	2908
1	87	2833
2	231	2833
3	1055	2833
4	5506	2833

prune46.0ms (0.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	75	2	77

Error

Counts

77 → 2

Alt Table

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

Compiler

Compiled 1258 to 231 computations (81.6% saved)

regimes512.0ms (9.8%)

Accuracy

Total 0.0b remaining (54.5%)

Threshold costs 0.0b (54.5%)

Counts

32 → 1

Compiler

Compiled 9561 to 6477 computations (32.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	14	16
2	14	16

end125.0ms (2.4%)

Remove

(sort c i)

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 240 to 144 computations (40% saved)

Details

analyze1.9s (35.5%)

sample2.3s (44.1%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series65.0ms (1.2%)

rewrite2.0ms (0%)

simplify104.0ms (2%)

prune46.0ms (0.9%)

localize9.0ms (0.2%)

series59.0ms (1.1%)

rewrite2.0ms (0%)

simplify79.0ms (1.5%)

prune46.0ms (0.9%)

regimes512.0ms (9.8%)

simplify2.0ms (0%)

end125.0ms (2.4%)

Profiling