Details

analyze1.5s (24.5%)

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)

sample1.4s (22.1%)

Results

1.1s	8125×	body	128	valid
90.0ms	676×	body	128	invalid
20.0ms	35×	body	2048	valid
16.0ms	43×	body	1024	valid
10.0ms	34×	body	512	valid
4.0ms	18×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify117.0ms (1.9%)

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

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(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)))
✓	0.7b	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

series86.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

42.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
40.0ms	(/.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:

9.0ms	(/.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)))

simplify119.0ms (1.9%)

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

prune150.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	160	4	164

Error

Counts

164 → 4

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
	0.7b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))
	0.2b	(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)))))

Compiler

Compiled 4332 to 2066 computations (52.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series115.0ms (1.9%)

Counts

4 → 132

Calls

4 calls:

57.0ms	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
22.0ms	(*.f64 60 (/.f64 x (-.f64 z t)))
20.0ms	(*.f64 60 (/.f64 y (-.f64 z t)))
16.0ms	(/.f64 x (-.f64 z t))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
42×	`associate-r_binary64`
34×	`add-cube-cbrt_binary64`

Counts

4 → 133

Calls

4 calls:

10.0ms	(*.f64 60 (/.f64 x (-.f64 z t)))
7.0ms	(*.f64 60 (/.f64 y (-.f64 z t)))
4.0ms	(/.f64 x (-.f64 z t))
0.0ms	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))

simplify163.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

871×	`times-frac_binary64`
399×	`cancel-sign-sub-inv_binary64`
345×	`fma-neg_binary64`
212×	`sub-neg_binary64`
190×	`fma-def_binary64`

Counts

265 → 224

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	327	5853
1	909	5594
2	2931	5588
3	4988	5584
4	5129	5584

prune175.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	224	4	228

Error

Counts

228 → 4

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
	0.7b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))
▶	0.2b	(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)))))

Compiler

Compiled 6438 to 2847 computations (55.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 x y))
✓	0.0b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.6b	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

series115.0ms (1.9%)

Counts

3 → 156

Calls

3 calls:

45.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
39.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))
30.0ms	(/.f64 (-.f64 z t) (-.f64 x y))

rewrite38.0ms (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)))
6.0ms	(/.f64 (-.f64 z t) (-.f64 x y))
0.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))

simplify216.0ms (3.5%)

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

prune220.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	308	4	312

Error

Counts

312 → 4

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
▶	0.2b	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
✓	0.2b	(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)))))

Compiler

Compiled 8290 to 3372 computations (59.3% saved)

localize8.0ms (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))
✓	0.3b	(*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t)))

series88.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

42.0ms	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
36.0ms	(*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t)))
10.0ms	(/.f64 60 (-.f64 z t))

rewrite19.0ms (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:

10.0ms	(*.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))))

simplify131.0ms (2.1%)

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

prune123.0ms (2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	174	4	178

Error

Counts

178 → 4

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
✓	0.2b	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
✓	0.2b	(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)))))

Compiler

Compiled 4439 to 2229 computations (49.8% saved)

regimes1.2s (19.8%)

Accuracy

Total 0.1b remaining (92.3%)

Threshold costs 0.1b (92.3%)

Counts

87 → 1

Compiler

Compiled 20561 to 14670 computations (28.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	19	23
2	29	23
3	35	23
4	39	23
5	40	23
6	40	23

end116.0ms (1.9%)

Compiler: Compiled 116 to 77 computations (33.6% saved)

Details

analyze1.5s (24.5%)

sample1.4s (22.1%)

simplify117.0ms (1.9%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series86.0ms (1.4%)

rewrite20.0ms (0.3%)

simplify119.0ms (1.9%)

prune150.0ms (2.4%)

localize13.0ms (0.2%)

series115.0ms (1.9%)

rewrite29.0ms (0.5%)

simplify163.0ms (2.6%)

prune175.0ms (2.8%)

localize9.0ms (0.1%)

series115.0ms (1.9%)

rewrite38.0ms (0.6%)

simplify216.0ms (3.5%)

prune220.0ms (3.5%)

localize8.0ms (0.1%)

series88.0ms (1.4%)

rewrite19.0ms (0.3%)

simplify131.0ms (2.1%)

prune123.0ms (2%)

regimes1.2s (19.8%)

simplify3.0ms (0.1%)

end116.0ms (1.9%)

Profiling