Details

analyze1.5s (26%)

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)

sample84.0ms (1.5%)

Algorithm

1×

intervals

Results

13.0ms	254×	body	128	valid
1.0ms	17×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify128.0ms (2.3%)

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(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	(*.f64 60 (-.f64 x y))
✓	0.0b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
✓	0.5b	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

series124.0ms (2.2%)

Counts

3 → 132

Calls

3 calls:

77.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
43.0ms	(/.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))
7.0ms	(*.f64 60 (-.f64 x y))
0.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))

simplify141.0ms (2.5%)

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

prune152.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	157	6	163
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	157	7	164

Error

Counts

164 → 7

Alt Table

Status	Error	Program
	0.7b	(fma.f64 a 120 (/.f64 (.f64 (.f64 (cbrt.f64 60) (cbrt.f64 60)) (*.f64 (cbrt.f64 60) (-.f64 x y))) (-.f64 z t)))
	19.9b	(fma.f64 a 120 (cbrt.f64 (*.f64 216000 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 3))))
	0.9b	(fma.f64 a 120 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 60 (-.f64 x y))) (cbrt.f64 (.f64 60 (-.f64 x y)))) (cbrt.f64 (*.f64 60 (-.f64 x y)))) (-.f64 z t)))
▶	0.1b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.3b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
	32.2b	(fma.f64 a 120 (*.f64 (/.f64 60 (sqrt.f64 (-.f64 z t))) (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 z t)))))

Compiler

Compiled 4492 to 2176 computations (51.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series71.0ms (1.2%)

Counts

4 → 96

Calls

4 calls:

20.0ms	(*.f64 60 (/.f64 y (-.f64 z t)))
19.0ms	(*.f64 60 (/.f64 x (-.f64 z t)))
16.0ms	(/.f64 x (-.f64 z t))
15.0ms	(/.f64 y (-.f64 z t))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
62×	`times-frac_binary64`
44×	`add-cube-cbrt_binary64`
42×	`associate-r_binary64`

Counts

4 → 162

Calls

4 calls:

8.0ms	(*.f64 60 (/.f64 y (-.f64 z t)))
7.0ms	(*.f64 60 (/.f64 x (-.f64 z t)))
4.0ms	(/.f64 x (-.f64 z t))
4.0ms	(/.f64 y (-.f64 z t))

simplify146.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

874×	`times-frac_binary64`
713×	`fma-def_binary64`
262×	`fma-neg_binary64`
162×	`associate-/l*_binary64`
140×	`*-commutative_binary64`

Counts

258 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	4922
1	793	4718
2	2412	4302
3	4841	4302
4	4982	4302

prune214.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	228	7	235

Error

Counts

235 → 7

Alt Table

Status	Error	Program
	0.2b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 (sqrt.f64 60) (*.f64 (sqrt.f64 60) (/.f64 y (-.f64 z t))))))
	16.2b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 -60 (/.f64 y t))))
✓	0.1b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
	19.9b	(fma.f64 a 120 (cbrt.f64 (*.f64 216000 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 3))))
▶	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.3b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
	32.2b	(fma.f64 a 120 (*.f64 (/.f64 60 (sqrt.f64 (-.f64 z t))) (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 z t)))))

Compiler

Compiled 6400 to 2752 computations (57% 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))
✓	0.5b	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

series130.0ms (2.3%)

Counts

3 → 156

Calls

3 calls:

51.0ms	(/.f64 (-.f64 z t) (-.f64 x y))
43.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
37.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

rewrite41.0ms (0.7%)

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))))

simplify214.0ms (3.8%)

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

prune289.0ms (5.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	305	3	308
Fresh	3	1	4
Picked	1	0	1
Done	1	1	2
Total	310	5	315

Error

Counts

315 → 5

Alt Table

Status	Error	Program
	16.2b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 -60 (/.f64 y t))))
▶	0.1b	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
	0.4b	(fma.f64 a 120 (/.f64 (sqrt.f64 60) (/.f64 (-.f64 z t) (*.f64 (-.f64 x y) (sqrt.f64 60)))))
✓	0.3b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
	0.4b	(fma.f64 a 120 (.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (.f64 (-.f64 x y) (sqrt.f64 60))))

Compiler

Compiled 8376 to 3439 computations (58.9% saved)

localize9.0ms (0.2%)

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)))

series87.0ms (1.5%)

Counts

3 → 132

Calls

3 calls:

41.0ms	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
36.0ms	(*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t)))
11.0ms	(/.f64 60 (-.f64 z t))

rewrite22.0ms (0.4%)

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:

13.0ms	(*.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))))

simplify124.0ms (2.2%)

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

prune131.0ms (2.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	174	5	179

Error

Counts

179 → 5

Alt Table

Status	Error	Program
	16.2b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 -60 (/.f64 y t))))
✓	0.1b	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
	0.4b	(fma.f64 a 120 (/.f64 (sqrt.f64 60) (/.f64 (-.f64 z t) (*.f64 (-.f64 x y) (sqrt.f64 60)))))
	0.2b	(fma.f64 a 120 (.f64 (-.f64 x y) (.f64 60 (/.f64 1 (-.f64 z t)))))
✓	0.3b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))

Compiler

Compiled 4460 to 2247 computations (49.6% saved)

regimes1.1s (19.4%)

Accuracy

Total 0.1b remaining (88.5%)

Threshold costs 0.1b (88.5%)

Counts

87 → 1

Compiler

Compiled 20608 to 14734 computations (28.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	25	26
2	36	26
3	44	26
4	50	26
5	53	26
6	54	26
7	53	26

end1.0ms (0%)

Compiler: Compiled 23 to 15 computations (34.8% saved)

sample902.0ms (15.9%)

Algorithm

1×

intervals

Results

414.0ms	7863×	body	128	valid
41.0ms	700×	body	128	invalid
10.0ms	51×	body	1024	valid
9.0ms	42×	body	2048	valid
3.0ms	25×	body	512	valid
2.0ms	17×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 142 to 103 computations (27.5% saved)

Details

analyze1.5s (26%)

sample84.0ms (1.5%)

simplify128.0ms (2.3%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series124.0ms (2.2%)

rewrite20.0ms (0.3%)

simplify141.0ms (2.5%)

prune152.0ms (2.7%)

localize10.0ms (0.2%)

series71.0ms (1.2%)

rewrite34.0ms (0.6%)

simplify146.0ms (2.6%)

prune214.0ms (3.8%)

localize8.0ms (0.1%)

series130.0ms (2.3%)

rewrite41.0ms (0.7%)

simplify214.0ms (3.8%)

prune289.0ms (5.1%)

localize9.0ms (0.2%)

series87.0ms (1.5%)

rewrite22.0ms (0.4%)

simplify124.0ms (2.2%)

prune131.0ms (2.3%)

regimes1.1s (19.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample902.0ms (15.9%)

Profiling