Details

analyze1.6s (22.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
7.8%	92%	0.2%	11
11.7%	88.1%	0.2%	12
17.9%	81.8%	0.2%	13
22.6%	77.2%	0.2%	14

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample28.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	254×	body	128	valid
1.0ms	17×	body	128	invalid
0.0ms	2×	body	2048	valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify119.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1714×	`fma-neg_binary64`
791×	`div-sub_binary64`
702×	`fma-def_binary64`
633×	`distribute-rgt-in_binary64`
427×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	23	17
2	46	17
3	90	17
4	173	17
5	320	17
6	671	17
7	1532	17
8	2980	17
9	3024	17
10	3167	17
11	3232	17
12	3299	17
13	3318	17
14	5334	17

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
✓	0.0b	(*.f64 60 (-.f64 x y))
✓	0.3b	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

series92.0ms (1.3%)

Counts

3 → 132

Calls

3 calls:

47.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
41.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
4.0ms	(*.f64 60 (-.f64 x y))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 91

Calls

3 calls:

8.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
5.0ms	(*.f64 60 (-.f64 x y))
0.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))

simplify117.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

742×	`cancel-sign-sub-inv_binary64`
331×	`sub-neg_binary64`
233×	`fma-neg_binary64`
229×	`fma-def_binary64`
197×	`associate-/l*_binary64`

Counts

223 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	319	4894
1	845	4557
2	3320	4449
3	5001	4449

prune176.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	157	6	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	6	164

Error

Counts

164 → 6

Alt Table

Status	Error	Program
	24.9b	(fma.f64 a 120 (/.f64 (.f64 60 (-.f64 (.f64 x x) (.f64 y y))) (.f64 (-.f64 z t) (+.f64 x y))))
▶	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.1b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
	0.2b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))
	0.1b	(fma.f64 a 120 (/.f64 (*.f64 (-.f64 x y) 60) (-.f64 z t)))
	38.1b	(fma.f64 a 120 (/.f64 (.f64 60 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (-.f64 z t) (fma.f64 y (+.f64 y x) (*.f64 x x)))))

Compiler

Compiled 4459 to 2150 computations (51.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 x y))
✓	0.2b	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

series136.0ms (1.9%)

Counts

3 → 156

Calls

3 calls:

57.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))
49.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
30.0ms	(/.f64 (-.f64 z t) (-.f64 x y))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 208

Calls

3 calls:

9.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))
7.0ms	(/.f64 (-.f64 z t) (-.f64 x y))
0.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))

simplify216.0ms (3%)

Algorithm

1×	egg-herbie

Rules

273×	`fma-neg_binary64`
253×	`associate-/r/_binary64`
228×	`fma-def_binary64`
220×	`*-commutative_binary64`
191×	`+-commutative_binary64`

Counts

364 → 308

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	477	10058
1	1305	9703
2	4771	9703
3	5001	9703

prune267.0ms (3.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	305	3	308
Fresh	5	0	5
Picked	0	1	1
Done	0	0	0
Total	310	4	314

Error

Counts

314 → 4

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 a 120 (/.f64 1 (/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60)))
✓	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.2b	(fma.f64 a 120 (.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (.f64 (-.f64 x y) (sqrt.f64 60))))
	0.1b	(fma.f64 a 120 (/.f64 (/.f64 60 (-.f64 z t)) (/.f64 1 (-.f64 x y))))

Compiler

Compiled 8334 to 3409 computations (59.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 120 (/.f64 1 (/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60)))
	0.0b	(/.f64 (-.f64 z t) (-.f64 x y))
✓	0.2b	(/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60)
✓	0.2b	(/.f64 1 (/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60))

series121.0ms (1.7%)

Counts

3 → 156

Calls

3 calls:

43.0ms	(fma.f64 a 120 (/.f64 1 (/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60)))
39.0ms	(/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60)
38.0ms	(/.f64 1 (/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60))

rewrite144.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

1156×	`times-frac_binary64`
757×	`*-un-lft-identity_binary64`
757×	`add-sqr-sqrt_binary64`
437×	`add-cube-cbrt_binary64`
160×	`distribute-lft-out--_binary64`

Counts

3 → 573

Calls

3 calls:

20.0ms	(/.f64 1 (/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60))
12.0ms	(/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60)
0.0ms	(fma.f64 a 120 (/.f64 1 (/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60)))

simplify487.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

427×	`associate-/r/_binary64`
310×	`fma-def_binary64`
306×	`associate-/l/_binary64`
244×	`associate-/r*_binary64`
231×	`associate-*l/_binary64`

Counts

729 → 706

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	636	23701
1	1697	21490
2	4701	21214
3	5132	21214

prune565.0ms (7.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	773	0	773
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	773	4	777

Error

Counts

777 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 a 120 (/.f64 1 (/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60)))
✓	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.2b	(fma.f64 a 120 (.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (.f64 (-.f64 x y) (sqrt.f64 60))))
▶	0.1b	(fma.f64 a 120 (/.f64 (/.f64 60 (-.f64 z t)) (/.f64 1 (-.f64 x y))))

Compiler

Compiled 23579 to 10267 computations (56.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 120 (/.f64 (/.f64 60 (-.f64 z t)) (/.f64 1 (-.f64 x y))))
✓	0.0b	(/.f64 60 (-.f64 z t))
✓	0.0b	(/.f64 1 (-.f64 x y))
✓	0.2b	(/.f64 (/.f64 60 (-.f64 z t)) (/.f64 1 (-.f64 x y)))

series124.0ms (1.7%)

Counts

4 → 156

Calls

4 calls:

65.0ms	(fma.f64 a 120 (/.f64 (/.f64 60 (-.f64 z t)) (/.f64 1 (-.f64 x y))))
40.0ms	(/.f64 (/.f64 60 (-.f64 z t)) (/.f64 1 (-.f64 x y)))
10.0ms	(/.f64 60 (-.f64 z t))
8.0ms	(/.f64 1 (-.f64 x y))

rewrite132.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

1131×	`times-frac_binary64`
700×	`*-un-lft-identity_binary64`
700×	`add-sqr-sqrt_binary64`
420×	`add-cube-cbrt_binary64`
140×	`distribute-lft-out--_binary64`

Counts

4 → 601

Calls

4 calls:

17.0ms	(/.f64 (/.f64 60 (-.f64 z t)) (/.f64 1 (-.f64 x y)))
6.0ms	(/.f64 1 (-.f64 x y))
4.0ms	(/.f64 60 (-.f64 z t))
0.0ms	(fma.f64 a 120 (/.f64 (/.f64 60 (-.f64 z t)) (/.f64 1 (-.f64 x y))))

simplify493.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

840×	`times-frac_binary64`
498×	`associate-/l/_binary64`
336×	`associate-/r*_binary64`
298×	`associate-/r/_binary64`
272×	`fma-def_binary64`

Counts

757 → 696

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	645	23429
1	1828	22051
2	4857	22051
3	5941	22051

prune549.0ms (7.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	696	0	696
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	696	4	700

Error

Counts

700 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 a 120 (/.f64 1 (/.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 60)))
✓	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.2b	(fma.f64 a 120 (.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (.f64 (-.f64 x y) (sqrt.f64 60))))
✓	0.1b	(fma.f64 a 120 (/.f64 (/.f64 60 (-.f64 z t)) (/.f64 1 (-.f64 x y))))

Compiler

Compiled 21089 to 10370 computations (50.8% saved)

regimes843.0ms (11.7%)

Accuracy

Total 0.1b remaining (81.9%)

Threshold costs 0.1b (81.9%)

Counts

75 → 1

Compiler

Compiled 17476 to 12212 computations (30.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	17	17
2	25	17
3	29	17
4	31	17
5	31	17

end1.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

sample876.0ms (12.2%)

Algorithm

1×

intervals

Results

404.0ms	7887×	body	128	valid
39.0ms	711×	body	128	invalid
8.0ms	46×	body	1024	valid
6.0ms	27×	body	2048	valid
4.0ms	28×	body	512	valid
1.0ms	10×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 117 to 87 computations (25.6% saved)

Details

analyze1.6s (22.2%)

sample28.0ms (0.4%)

simplify119.0ms (1.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series92.0ms (1.3%)

rewrite20.0ms (0.3%)

simplify117.0ms (1.6%)

prune176.0ms (2.5%)

localize8.0ms (0.1%)

series136.0ms (1.9%)

rewrite41.0ms (0.6%)

simplify216.0ms (3%)

prune267.0ms (3.7%)

localize10.0ms (0.1%)

series121.0ms (1.7%)

rewrite144.0ms (2%)

simplify487.0ms (6.8%)

prune565.0ms (7.9%)

localize10.0ms (0.1%)

series124.0ms (1.7%)

rewrite132.0ms (1.8%)

simplify493.0ms (6.9%)

prune549.0ms (7.6%)

regimes843.0ms (11.7%)

simplify3.0ms (0%)

end1.0ms (0%)

sample876.0ms (12.2%)

Profiling