Details

analyze2.0s (28.2%)

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
0%	99.7%	0.3%	13
0%	99.7%	0.3%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample2.0s (29%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

Results

1.3s	8256×	body	128	valid
599.0ms	4101×	body	128	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify116.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1251×	`fma-neg_binary64`
530×	`fma-def_binary64`
258×	`cancel-sign-sub-inv_binary64`
148×	`distribute-rgt-in_binary64`
135×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	23
1	34	23
2	77	22
3	156	21
4	332	19
5	674	19
6	959	19
7	1365	19
8	1815	19
9	1835	19
10	1845	19
11	1846	19
12	1846	19
13	2162	19
14	2166	19
15	2166	19
16	2055	19

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 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

Compiler

Compiled 80 to 51 computations (36.3% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

series48.0ms (0.7%)

Counts

2 → 144

Calls

2 calls:

30.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
18.0ms	(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))

rewrite60.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

275×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`
243×	`log-pow_binary64`
201×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`

Counts

2 → 54

Calls

2 calls:

59.0ms	(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))
59.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	306	34
2	3464	34
3	4928	34
0	0	0
1	0	0

simplify203.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1043×	`fma-neg_binary64`
647×	`fma-def_binary64`
404×	`cancel-sign-sub-inv_binary64`
140×	`associate--r+_binary64`
121×	`sub-neg_binary64`

Counts

198 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	2610
1	69	2374
2	129	2146
3	286	2146
4	470	2146
5	668	2146
6	1074	2146
7	1350	2146
8	1707	2146
9	1812	2146
10	1788	2146
11	1788	2146
12	2006	2146
13	2006	2146
14	2006	2146
15	1923	2146

prune61.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	2	77

Error

Counts

77 → 2

Alt Table

Status	Error	Program
▶	0.9b	(fma.f64 x y (.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c))) (pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2)))
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

Status

Error

Program

▶

0.9b

(fma.f64 x y (*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2)))

✓

0.0b

(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

Compiler

Compiled 1436 to 730 computations (49.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c))) (pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2)))
✓	0.3b	(.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c))) (pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2))
✓	0.5b	(cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2)

series709.0ms (10.2%)

Counts

4 → 264

Calls

4 calls:

460.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2)
193.0ms	(cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
36.0ms	(fma.f64 x y (.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c))) (pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2)))
19.0ms	(.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c))) (pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2))

rewrite91.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

312×	`log1p-udef_binary64`
269×	`prod-diff_binary64`
177×	`add-sqr-sqrt_binary64`
167×	`log1p-expm1-u_binary64`
167×	`expm1-log1p-u_binary64`

Counts

4 → 85

Calls

4 calls:

89.0ms	(fma.f64 x y (.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c))) (pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2)))
89.0ms	(.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c))) (pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2))
89.0ms	(cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
89.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	71
1	368	69
2	3954	69
3	4891	69
0	0	0
1	0	0

simplify210.0ms (3%)

Algorithm

1×	egg-herbie

Rules

540×	`*-commutative_binary64`
291×	`+-commutative_binary64`
261×	`fma-def_binary64`
235×	`associate-r_binary64`
200×	`associate-+r+_binary64`

Counts

349 → 309

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1320	19509
1	4999	19509

prune768.0ms (11.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	433	0	433
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	433	2	435

Error

Counts

435 → 2

Alt Table

Status	Error	Program
✓	0.9b	(fma.f64 x y (.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (.f64 a b) -1/4 c))) (pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2)))
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

Status

Error

Program

✓

0.9b

(fma.f64 x y (*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (pow.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) 2)))

✓

0.0b

(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

Compiler

Compiled 40204 to 26386 computations (34.4% saved)

regimes569.0ms (8.2%)

Accuracy

Total 0.0b remaining (5.8%)

Threshold costs 0.0b (5.8%)

Counts

31 → 1

Compiler

Compiled 9697 to 7011 computations (27.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	16	19
2	16	19

end104.0ms (1.5%)

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 226 to 150 computations (33.6% saved)

Details

analyze2.0s (28.2%)

sample2.0s (29%)

simplify116.0ms (1.7%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series48.0ms (0.7%)

rewrite60.0ms (0.9%)

simplify203.0ms (2.9%)

prune61.0ms (0.9%)

localize14.0ms (0.2%)

series709.0ms (10.2%)

rewrite91.0ms (1.3%)

simplify210.0ms (3%)

prune768.0ms (11.1%)

regimes569.0ms (8.2%)

simplify3.0ms (0%)

end104.0ms (1.5%)

Profiling