Details

analyze1.9s (31.5%)

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 (38.1%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

(sort c i)

Results

1.3s	8256×	body	128	valid
957.0ms	5770×	body	128	invalid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify14.0ms (0.2%)

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

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)

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))))

series61.0ms (1%)

Counts

3 → 216

Calls

3 calls:

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

simplify114.0ms (1.8%)

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 (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	3	76

Error

Counts

76 → 3

Alt Table

Status	Error	Program
	33.4b	(fma.f64 c i (.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (.f64 z t)))) (sqrt.f64 (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))))
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

Compiler

Compiled 1322 to 279 computations (78.9% saved)

localize9.0ms (0.2%)

Local error

Found 2 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))))

series56.0ms (0.9%)

Counts

2 → 168

Calls

2 calls:

38.0ms	(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)))

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 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)))

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

742×	`associate-+r+_binary64`
693×	`associate-+l+_binary64`
597×	`fma-def_binary64`
389×	`associate-l_binary64`
318×	`associate-r_binary64`

Counts

188 → 46

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	2448
1	77	2390
2	203	2390
3	964	2390
4	5083	2390

prune27.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	46	3	49

Error

Counts

49 → 3

Alt Table

Status	Error	Program
▶	33.4b	(fma.f64 c i (.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (.f64 z t)))) (sqrt.f64 (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))))
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

Compiler

Compiled 770 to 149 computations (80.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
✓	0.0b	(fma.f64 c i (.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (.f64 z t)))) (sqrt.f64 (fma.f64 a b (fma.f64 x y (*.f64 z t))))))
✓	0.1b	(sqrt.f64 (fma.f64 a b (fma.f64 x y (*.f64 z t))))
✓	0.2b	(.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (.f64 z t)))) (sqrt.f64 (fma.f64 a b (fma.f64 x y (*.f64 z t)))))

series245.0ms (4%)

Counts

3 → 192

Calls

3 calls:

192.0ms

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

34.0ms

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

19.0ms

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

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

5.0ms

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

1.0ms

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

0.0ms

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

simplify148.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

443×	`unswap-sqr_binary64`
437×	`distribute-lft-in_binary64`
437×	`distribute-rgt-in_binary64`
434×	`fma-def_binary64`
388×	`*-commutative_binary64`

Counts

270 → 150

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	172	4873
1	402	4641
2	1243	4519
3	3489	4479
4	4952	4449
5	4991	4449

prune132.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	245	3	248

Error

Counts

248 → 3

Alt Table

Status	Error	Program
✓	33.4b	(fma.f64 c i (.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (.f64 z t)))) (sqrt.f64 (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))))
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

Compiler

Compiled 7861 to 1437 computations (81.7% saved)

regimes768.0ms (12.5%)

Accuracy

Total 0.0b remaining (59.4%)

Threshold costs 0.0b (59.4%)

Counts

48 → 1

Compiler

Compiled 16084 to 10430 computations (35.2% 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

end134.0ms (2.2%)

Remove

(sort c i)

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 272 to 158 computations (41.9% saved)

Details

analyze1.9s (31.5%)

sample2.3s (38.1%)

simplify14.0ms (0.2%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series61.0ms (1%)

rewrite2.0ms (0%)

simplify114.0ms (1.8%)

prune52.0ms (0.8%)

localize9.0ms (0.2%)

series56.0ms (0.9%)

rewrite1.0ms (0%)

simplify69.0ms (1.1%)

prune27.0ms (0.4%)

localize14.0ms (0.2%)

series245.0ms (4%)

rewrite12.0ms (0.2%)

simplify148.0ms (2.4%)

prune132.0ms (2.1%)

regimes768.0ms (12.5%)

simplify2.0ms (0%)

end134.0ms (2.2%)

Profiling