Details

analyze1.7s (1.3%)

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)

sample1.6s (1.2%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

Results

1.0s	8256×	body	128	valid
496.0ms	3900×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify6.0ms (0%)

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%)

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%)

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)))

series32.0ms (0%)

Counts

2 → 120

Calls

2 calls:

24.0ms	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
8.0ms	(fma.f64 x y (*.f64 z t))

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

simplify138.0ms (0.1%)

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 → 47

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	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

prune28.0ms (0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	3	48

Error

0.0b

Counts

48 → 3

Alt Table

Status	Error	Program
▶	20.8b	(fma.f64 t z (*.f64 a b))
✓	0.0b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
	30.2b	(.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)))))

Compiler

Compiled 700 to 162 computations (76.9% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0%)

Counts

1 → 48

Calls

1 calls:

8.0ms

(fma.f64 t z (*.f64 a b))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

4.0ms

(fma.f64 t z (*.f64 a b))

simplify124.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

572×	`associate-/r/_binary64`
527×	`fma-def_binary64`
502×	`unswap-sqr_binary64`
500×	`distribute-rgt-in_binary64`
485×	`associate-+l+_binary64`

Counts

58 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	460
1	23	443
2	47	443
3	128	443
4	401	443
5	1504	443
6	2934	443
7	3199	443
8	3454	443
9	3982	443
10	4805	443
11	4988	443
12	4867	443

prune8.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	21	3	24

Error

0.0b

Counts

24 → 3

Alt Table

Status	Error	Program
✓	20.8b	(fma.f64 t z (*.f64 a b))
✓	0.0b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
▶	30.2b	(.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)))))

Compiler

Compiled 299 to 87 computations (70.9% saved)

localize9.0ms (0%)

Local error

Found 4 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)))
✓	0.1b	(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)))))

series199.0ms (0.2%)

Counts

2 → 96

Calls

2 calls:

180.0ms	(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)))))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 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))))

simplify157.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

429×	`unswap-sqr_binary64`
387×	`fma-def_binary64`
380×	`*-commutative_binary64`
367×	`distribute-lft-in_binary64`
367×	`distribute-rgt-in_binary64`

Counts

164 → 122

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	148	3341
1	357	3142
2	1155	3020
3	3124	2976
4	4852	2946
5	4981	2946
6	4949	2946

prune105.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	262	1	263
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	262	4	266

Error

Counts

266 → 4

Alt Table

Status	Error	Program
✓	20.8b	(fma.f64 t z (*.f64 a b))
✓	0.0b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
▶	30.5b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (.f64 z t))))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))))) 3))
✓	30.2b	(.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)))))

Compiler

Compiled 7725 to 1323 computations (82.9% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z)))))
✓	0.1b	(sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (*.f64 z t)))))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (.f64 z t))))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))))) 3))
✓	0.4b	(pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))))) 3)

series2.0min (94.8%)

Counts

4 → 288

Calls

4 calls:

2.0min	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (.f64 z t))))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))))) 3))
1.1s	(pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))))) 3)
351.0ms	(sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (*.f64 z t)))))
321.0ms	(sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z)))))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`sqrt-prod_binary64`
74×	`add-sqr-sqrt_binary64`
27×	`cube-prod_binary64`
27×	`unpow-prod-down_binary64`
25×	`*-un-lft-identity_binary64`

Counts

4 → 155

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (.f64 z t))))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))))) 3))
3.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))))) 3)
1.0ms	(sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (*.f64 z t)))))
1.0ms	(sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z)))))

simplify670.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-def_binary64`
4×	`fma-udef_binary64`

Counts

443 → 428

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4564	75094
1	5433	75094

prune1.5s (1.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	428	0	428
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	428	4	432

Error

Counts

432 → 4

Alt Table

Status	Error	Program
✓	20.8b	(fma.f64 t z (*.f64 a b))
✓	0.0b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
✓	30.5b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 x y (.f64 z t))))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))))) 3))
✓	30.2b	(.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)))))

Compiler

Compiled 82293 to 48937 computations (40.5% saved)

regimes305.0ms (0.2%)

Accuracy

Total 0.0b remaining (41.4%)

Threshold costs 0.0b (41.4%)

Counts

23 → 1

Compiler

Compiled 5173 to 3368 computations (34.9% saved)

simplify6.0ms (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

end108.0ms (0.1%)

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 205 to 119 computations (42% saved)

Details

analyze1.7s (1.3%)

sample1.6s (1.2%)

simplify6.0ms (0%)

prune3.0ms (0%)

localize7.0ms (0%)

series32.0ms (0%)

rewrite1.0ms (0%)

simplify138.0ms (0.1%)

prune28.0ms (0%)

localize4.0ms (0%)

series8.0ms (0%)

rewrite4.0ms (0%)

simplify124.0ms (0.1%)

prune8.0ms (0%)

localize9.0ms (0%)

series199.0ms (0.2%)

rewrite11.0ms (0%)

simplify157.0ms (0.1%)

prune105.0ms (0.1%)

localize23.0ms (0%)

series2.0min (94.8%)

rewrite42.0ms (0%)

simplify670.0ms (0.5%)

prune1.5s (1.1%)

regimes305.0ms (0.2%)

simplify6.0ms (0%)

end108.0ms (0.1%)

Profiling