Details

analyze1.4s (21.6%)

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)

sample89.0ms (1.4%)

Algorithm

1×

intervals

Results

13.0ms	252×	body	128	valid
1.0ms	20×	body	128	invalid
0.0ms	2×	body	1024	valid
0.0ms	1×	body	4096	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify121.0ms (1.8%)

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 (0.1%)

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

0.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.9b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize9.0ms (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))
✓	1.0b	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

series94.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

46.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
44.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
4.0ms	(*.f64 60 (-.f64 x y))

rewrite22.0ms (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:

9.0ms	(*.f64 60 (-.f64 x y))
8.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
0.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))

simplify119.0ms (1.8%)

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 (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	156	7	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	7	164

Error

Counts

164 → 7

Alt Table

Status	Error	Program
	1.3b	(fma.f64 a 120 (/.f64 (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (neg.f64 (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 y) (cbrt.f64 y))))) 60) (.f64 (fma.f64 (neg.f64 (cbrt.f64 y)) (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 y) (cbrt.f64 y)))) 60)) (-.f64 z t)))
	24.1b	(fma.f64 a 120 (*.f64 -60 (/.f64 (-.f64 x y) t)))
▶	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	18.3b	(fma.f64 a 120 (.f64 (/.f64 (.f64 60 (-.f64 x y)) (-.f64 (.f64 z z) (.f64 t t))) (+.f64 z t)))
	0.9b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))
	48.3b	(fma.f64 a 120 (*.f64 (/.f64 60 (+.f64 (sqrt.f64 z) (sqrt.f64 t))) (/.f64 (-.f64 x y) (-.f64 (sqrt.f64 z) (sqrt.f64 t)))))
	0.2b	(fma.f64 a 120 (*.f64 (/.f64 60 1) (/.f64 (-.f64 x y) (-.f64 z t))))

Compiler

Compiled 4539 to 2184 computations (51.9% saved)

localize10.0ms (0.2%)

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))
✓	0.6b	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

series130.0ms (2%)

Counts

3 → 156

Calls

3 calls:

56.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
41.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))
32.0ms	(/.f64 (-.f64 z t) (-.f64 x y))

rewrite42.0ms (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)))
8.0ms	(/.f64 (-.f64 z t) (-.f64 x y))
0.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))

simplify244.0ms (3.7%)

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

prune331.0ms (5.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	304	4	308
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	309	6	315

Error

Counts

315 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
	0.3b	(fma.f64 a 120 (*.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y)))))
	0.2b	(fma.f64 a 120 (*.f64 (sqrt.f64 60) (/.f64 (sqrt.f64 60) (/.f64 (-.f64 z t) (-.f64 x y)))))
✓	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.2b	(fma.f64 a 120 (*.f64 (/.f64 60 1) (/.f64 (-.f64 x y) (-.f64 z t))))
	24.1b	(fma.f64 a 120 (/.f64 60 (neg.f64 (/.f64 t (-.f64 x y)))))

Compiler

Compiled 8408 to 3465 computations (58.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series126.0ms (1.9%)

Counts

3 → 132

Calls

3 calls:

72.0ms	(*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t)))
42.0ms	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
11.0ms	(/.f64 60 (-.f64 z t))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 97

Calls

3 calls:

12.0ms	(*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t)))
4.0ms	(/.f64 60 (-.f64 z t))
0.0ms	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))

simplify130.0ms (2%)

Algorithm

1×	egg-herbie

Rules

920×	`times-frac_binary64`
320×	`sub-neg_binary64`
259×	`fma-def_binary64`
240×	`fma-neg_binary64`
163×	`+-commutative_binary64`

Counts

229 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	314	5826
1	920	5498
2	3364	5210
3	5099	5210

prune190.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	174	6	180

Error

Counts

180 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
	0.3b	(fma.f64 a 120 (*.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y)))))
	0.2b	(fma.f64 a 120 (*.f64 (sqrt.f64 60) (/.f64 (sqrt.f64 60) (/.f64 (-.f64 z t) (-.f64 x y)))))
✓	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
▶	0.2b	(fma.f64 a 120 (*.f64 (/.f64 60 1) (/.f64 (-.f64 x y) (-.f64 z t))))
	24.1b	(fma.f64 a 120 (/.f64 60 (neg.f64 (/.f64 t (-.f64 x y)))))

Compiler

Compiled 4557 to 2322 computations (49% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 120 (*.f64 (/.f64 60 1) (/.f64 (-.f64 x y) (-.f64 z t))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z t))
✓	0.3b	(*.f64 (/.f64 60 1) (/.f64 (-.f64 x y) (-.f64 z t)))

series114.0ms (1.7%)

Counts

3 → 156

Calls

3 calls:

45.0ms	(fma.f64 a 120 (*.f64 (/.f64 60 1) (/.f64 (-.f64 x y) (-.f64 z t))))
38.0ms	(*.f64 (/.f64 60 1) (/.f64 (-.f64 x y) (-.f64 z t)))
30.0ms	(/.f64 (-.f64 x y) (-.f64 z t))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`add-sqr-sqrt_binary64`
79×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
31×	`associate-r_binary64`

Counts

3 → 138

Calls

3 calls:

16.0ms	(*.f64 (/.f64 60 1) (/.f64 (-.f64 x y) (-.f64 z t)))
7.0ms	(/.f64 (-.f64 x y) (-.f64 z t))
0.0ms	(fma.f64 a 120 (*.f64 (/.f64 60 1) (/.f64 (-.f64 x y) (-.f64 z t))))

simplify195.0ms (3%)

Algorithm

1×	egg-herbie

Rules

704×	`cancel-sign-sub-inv_binary64`
432×	`sub-neg_binary64`
312×	`fma-neg_binary64`
211×	`fma-def_binary64`
176×	`+-commutative_binary64`

Counts

294 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	336	7319
1	975	6994
2	3454	6994
3	4972	6989
4	5004	6989

prune253.0ms (3.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	237	6	243

Error

Counts

243 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
	0.3b	(fma.f64 a 120 (*.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y)))))
	0.2b	(fma.f64 a 120 (*.f64 (sqrt.f64 60) (/.f64 (sqrt.f64 60) (/.f64 (-.f64 z t) (-.f64 x y)))))
✓	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.2b	(fma.f64 a 120 (*.f64 (/.f64 60 1) (/.f64 (-.f64 x y) (-.f64 z t))))
	24.1b	(fma.f64 a 120 (/.f64 60 (neg.f64 (/.f64 t (-.f64 x y)))))

Compiler

Compiled 6521 to 2960 computations (54.6% saved)

regimes1.7s (25.4%)

Accuracy

Total 0.1b remaining (92.7%)

Threshold costs 0.1b (92.7%)

Counts

119 → 1

Compiler

Compiled 32335 to 21838 computations (32.5% saved)

simplify3.0ms (0.1%)

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)

sample991.0ms (15.1%)

Algorithm

1×

intervals

Results

479.0ms	7871×	body	128	valid
37.0ms	647×	body	128	invalid
11.0ms	49×	body	1024	valid
8.0ms	33×	body	2048	valid
5.0ms	32×	body	512	valid
1.0ms	12×	body	256	valid
1.0ms	3×	body	4096	valid

Compiler

Compiled 154 to 115 computations (25.3% saved)

Details

analyze1.4s (21.6%)

sample89.0ms (1.4%)

simplify121.0ms (1.8%)

prune3.0ms (0.1%)

localize9.0ms (0.1%)

series94.0ms (1.4%)

rewrite22.0ms (0.3%)

simplify119.0ms (1.8%)

prune176.0ms (2.7%)

localize10.0ms (0.2%)

series130.0ms (2%)

rewrite42.0ms (0.6%)

simplify244.0ms (3.7%)

prune331.0ms (5.1%)

localize9.0ms (0.1%)

series126.0ms (1.9%)

rewrite22.0ms (0.3%)

simplify130.0ms (2%)

prune190.0ms (2.9%)

localize12.0ms (0.2%)

series114.0ms (1.7%)

rewrite35.0ms (0.5%)

simplify195.0ms (3%)

prune253.0ms (3.9%)

regimes1.7s (25.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample991.0ms (15.1%)

Profiling