Details

analyze1.9s (31.1%)

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 (22.5%)

Results

1.2s	8120×	body	128	valid
87.0ms	700×	body	128	invalid
20.0ms	50×	body	1024	valid
18.0ms	41×	body	2048	valid
7.0ms	24×	body	512	valid
3.0ms	17×	body	256	valid
2.0ms	4×	body	4096	valid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify111.0ms (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

0.6b

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))

series84.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

43.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
37.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
4.0ms	(*.f64 60 (-.f64 x y))

rewrite74.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

968×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
139×	`add-log-exp_binary64`

Counts

3 → 87

Calls

3 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	289	37
2	3833	37
3	5806	37
0	0	0
1	0	0

simplify109.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

716×	`times-frac_binary64`
660×	`cancel-sign-sub-inv_binary64`
483×	`sub-neg_binary64`
206×	`fma-neg_binary64`
205×	`fma-def_binary64`

Counts

219 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	3761
1	525	3600
2	1966	3360
3	4442	3360
4	5009	3360

prune130.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	6	137

Error

Counts

137 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
✓	0.6b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
	1.8b	(pow.f64 (cbrt.f64 (fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))) 3)
	0.1b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
	1.1b	(fma.f64 a 120 (.f64 (pow.f64 (cbrt.f64 (.f64 60 (-.f64 x y))) 2) (.f64 (cbrt.f64 (.f64 60 (-.f64 x y))) (/.f64 1 (-.f64 z t)))))
	28.8b	(fma.f64 a 120 (.f64 60 (-.f64 (.f64 (+.f64 (/.f64 t z) 1) (/.f64 x z)) (*.f64 (+.f64 (/.f64 t z) 1) (/.f64 y z)))))

Compiler

Compiled 3486 to 1907 computations (45.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.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)))

series106.0ms (1.7%)

Counts

4 → 132

Calls

4 calls:

51.0ms	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
20.0ms	(*.f64 60 (/.f64 y (-.f64 z t)))
19.0ms	(*.f64 60 (/.f64 x (-.f64 z t)))
16.0ms	(/.f64 y (-.f64 z t))

rewrite88.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

319×	`log1p-udef_binary64`
177×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`
165×	`add-log-exp_binary64`

Counts

4 → 105

Calls

4 calls:

86.0ms	(/.f64 y (-.f64 z t))
86.0ms	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
86.0ms	(*.f64 60 (/.f64 x (-.f64 z t)))
86.0ms	(*.f64 60 (/.f64 y (-.f64 z t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	345	44
2	4701	44
3	5155	44
0	0	0
1	0	0

simplify119.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-neg_binary64`
714×	`times-frac_binary64`
463×	`associate-/l*_binary64`
384×	`cancel-sign-sub-inv_binary64`
190×	`fma-def_binary64`

Counts

237 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	3839
1	546	3711
2	1932	3330
3	4899	3330
4	5497	3330

prune158.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	180	5	185

Error

Counts

185 → 5

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
	1.8b	(pow.f64 (cbrt.f64 (fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))) 3)
▶	0.1b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
	1.1b	(fma.f64 a 120 (.f64 (pow.f64 (cbrt.f64 (.f64 60 (-.f64 x y))) 2) (.f64 (cbrt.f64 (.f64 60 (-.f64 x y))) (/.f64 1 (-.f64 z t)))))
	0.1b	(fma.f64 a 120 (-.f64 (/.f64 60 (/.f64 (-.f64 z t) x)) (*.f64 60 (/.f64 y (-.f64 z t)))))

Compiler

Compiled 4766 to 2366 computations (50.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series85.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

38.0ms	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
36.0ms	(*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y))
10.0ms	(/.f64 60 (-.f64 z t))

rewrite72.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

907×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
139×	`add-log-exp_binary64`

Counts

3 → 90

Calls

3 calls:

70.0ms	(/.f64 60 (-.f64 z t))
70.0ms	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
70.0ms	(*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	290	37
2	3749	37
3	5565	37
0	0	0
1	0	0

simplify119.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

991×	`fma-neg_binary64`
807×	`times-frac_binary64`
674×	`cancel-sign-sub-inv_binary64`
293×	`sub-neg_binary64`
249×	`fma-def_binary64`

Counts

222 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	4151
1	630	3969
2	2310	3692
3	4671	3686
4	5411	3686

prune116.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	149	5	154

Error

Counts

154 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	1.1b	(fma.f64 a 120 (.f64 (pow.f64 (cbrt.f64 (.f64 60 (-.f64 x y))) 2) (.f64 (cbrt.f64 (.f64 60 (-.f64 x y))) (/.f64 1 (-.f64 z t)))))
✓	0.6b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
	1.8b	(pow.f64 (cbrt.f64 (fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))) 3)
✓	0.1b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))

Compiler

Compiled 3751 to 2028 computations (45.9% saved)

localize8.0ms (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))))
✓	0.9b	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

series100.0ms (1.6%)

Counts

3 → 156

Calls

3 calls:

40.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
35.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))
25.0ms	(/.f64 (-.f64 z t) (-.f64 x y))

rewrite77.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

279×	`expm1-udef_binary64`
279×	`log1p-udef_binary64`
214×	`fma-neg_binary64`
155×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`

Counts

3 → 104

Calls

3 calls:

74.0ms	(/.f64 (-.f64 z t) (-.f64 x y))
74.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
74.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	299	40
2	4062	40
3	5059	40
0	0	0
1	0	0

simplify159.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

829×	`cancel-sign-sub-inv_binary64`
741×	`fma-neg_binary64`
400×	`sub-neg_binary64`
203×	`fma-def_binary64`
171×	`+-commutative_binary64`

Counts

260 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	5147
1	713	4968
2	2690	4620
3	4488	4614
4	4999	4614
5	5038	4614

prune132.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	167	5	172

Error

Counts

172 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	1.1b	(fma.f64 a 120 (.f64 (pow.f64 (cbrt.f64 (.f64 60 (-.f64 x y))) 2) (.f64 (cbrt.f64 (.f64 60 (-.f64 x y))) (/.f64 1 (-.f64 z t)))))
✓	0.6b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
	1.8b	(pow.f64 (cbrt.f64 (fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))) 3)
✓	0.1b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))

Compiler

Compiled 4279 to 2118 computations (50.5% saved)

regimes876.0ms (14.3%)

Accuracy

Total 0.1b remaining (87.4%)

Threshold costs 0.1b (87.4%)

Counts

78 → 1

Compiler

Compiled 18011 to 13009 computations (27.8% saved)

simplify4.0ms (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

end83.0ms (1.4%)

Compiler: Compiled 146 to 102 computations (30.1% saved)

Details

analyze1.9s (31.1%)

sample1.4s (22.5%)

simplify111.0ms (1.8%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series84.0ms (1.4%)

rewrite74.0ms (1.2%)

simplify109.0ms (1.8%)

prune130.0ms (2.1%)

localize16.0ms (0.3%)

series106.0ms (1.7%)

rewrite88.0ms (1.4%)

simplify119.0ms (1.9%)

prune158.0ms (2.6%)

localize8.0ms (0.1%)

series85.0ms (1.4%)

rewrite72.0ms (1.2%)

simplify119.0ms (1.9%)

prune116.0ms (1.9%)

localize8.0ms (0.1%)

series100.0ms (1.6%)

rewrite77.0ms (1.2%)

simplify159.0ms (2.6%)

prune132.0ms (2.1%)

regimes876.0ms (14.3%)

simplify4.0ms (0.1%)

end83.0ms (1.4%)

Profiling