Details

analyze2.2s (36.8%)

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)

sample2.4s (39.3%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

(sort c i)

Results

1.3s	8256×	body	128	valid
956.0ms	5837×	body	128	invalid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify8.0ms (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

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

0.0b

Counts

3 → 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	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 a b)) (.f64 c i))

Compiler

Compiled 121 to 72 computations (40.5% saved)

localize10.0ms (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))))

series59.0ms (1%)

Counts

3 → 216

Calls

3 calls:

33.0ms	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
17.0ms	(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 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
0.0ms	(fma.f64 x y (*.f64 z t))
0.0ms	(fma.f64 a b (fma.f64 x y (*.f64 z t)))

simplify111.0ms (1.9%)

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

prune52.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	75	2	77

Error

0.0b

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 251 computations (80% saved)

localize10.0ms (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%)

Counts

3 → 216

Calls

3 calls:

31.0ms	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
17.0ms	(fma.f64 a b (fma.f64 t z (*.f64 c i)))
11.0ms	(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 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
0.0ms	(fma.f64 a b (fma.f64 t z (*.f64 c i)))

simplify73.0ms (1.2%)

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 (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Error

0.0b

Counts

77 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
▶	15.1b	(fma.f64 y x (fma.f64 t z (*.f64 a b)))
✓	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))

Compiler

Compiled 1292 to 253 computations (80.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series27.0ms (0.5%)

Counts

2 → 120

Calls

2 calls:

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

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

simplify131.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

914×	`distribute-lft-in_binary64`
914×	`distribute-rgt-in_binary64`
738×	`unswap-sqr_binary64`
682×	`distribute-rgt-out_binary64`
377×	`fma-def_binary64`

Counts

140 → 46

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	1376
1	50	1334
2	136	1334
3	545	1334
4	3041	1334
5	3131	1334
6	3468	1334
7	3841	1334
8	4319	1334
9	4435	1334
10	5641	1334

prune26.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
✓	15.1b	(fma.f64 y x (fma.f64 t z (*.f64 a b)))
✓	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
▶	32.5b	(fma.f64 t z (*.f64 y x))

Compiler

Compiled 696 to 171 computations (75.4% saved)

localize5.0ms (0.1%)

prune3.0ms (0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
✓	15.1b	(fma.f64 y x (fma.f64 t z (*.f64 a b)))
✓	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
✓	32.5b	(fma.f64 t z (*.f64 y x))

Compiler

Compiled 71 to 45 computations (36.6% saved)

regimes594.0ms (9.9%)

Accuracy

Total 0.0b remaining (92.3%)

Threshold costs 0.0b (92.3%)

Counts

37 → 1

Compiler

Compiled 10860 to 7424 computations (31.6% 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

end197.0ms (3.3%)

Remove

(sort c i)

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 271 to 165 computations (39.1% saved)

Details

analyze2.2s (36.8%)

sample2.4s (39.3%)

simplify8.0ms (0.1%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series59.0ms (1%)

rewrite2.0ms (0%)

simplify111.0ms (1.9%)

prune52.0ms (0.9%)

localize10.0ms (0.2%)

series59.0ms (1%)

rewrite2.0ms (0%)

simplify73.0ms (1.2%)

prune46.0ms (0.8%)

localize8.0ms (0.1%)

series27.0ms (0.5%)

rewrite1.0ms (0%)

simplify131.0ms (2.2%)

prune26.0ms (0.4%)

localize5.0ms (0.1%)

prune3.0ms (0%)

regimes594.0ms (9.9%)

simplify2.0ms (0%)

end197.0ms (3.3%)

Profiling