Details

analyze2.4s (26.6%)

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)

sample1.8s (19.9%)

Results

1.5s	8109×	body	128	valid
127.0ms	712×	body	128	invalid
46.0ms	45×	body	2048	valid
25.0ms	54×	body	1024	valid
10.0ms	30×	body	512	valid
3.0ms	15×	body	256	valid
2.0ms	3×	body	4096	valid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify198.0ms (2.2%)

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

prune5.0ms (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)

localize10.0ms (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)))
✓	1.0b	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

series86.0ms (1%)

Counts

3 → 132

Calls

3 calls:

44.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
38.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
4.0ms	(*.f64 60 (-.f64 x y))

rewrite85.0ms (1%)

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 → 90

Calls

3 calls:

83.0ms	(*.f64 60 (-.f64 x y))
83.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
83.0ms	(/.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

simplify123.0ms (1.4%)

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

222 → 138

Iterations

Useful iterations: 2 (0.0ms)

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

prune1.6s (18.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	128	10	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	10	139

Error

0.0b

Counts

139 → 10

Alt Table

Status	Error	Program
	0.6b	(fma.f64 a 120 (*.f64 (/.f64 (-.f64 x y) (pow.f64 (cbrt.f64 (-.f64 z t)) 2)) (/.f64 60 (cbrt.f64 (-.f64 z t)))))
	13.1b	(fma.f64 60 (/.f64 x (-.f64 z t)) (*.f64 120 a))
▶	0.2b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
	0.6b	(fma.f64 a 120 (*.f64 (/.f64 60 (pow.f64 (cbrt.f64 (-.f64 z t)) 2)) (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 z t)))))
	26.6b	(fma.f64 a 120 (*.f64 60 (/.f64 (-.f64 x y) z)))
	0.2b	(fma.f64 a 120 (.f64 60 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z t)))))
	0.2b	(fma.f64 a 120 (*.f64 60 (/.f64 1 (/.f64 (-.f64 z t) (-.f64 x y)))))
	0.9b	(fma.f64 a 120 (/.f64 (-.f64 (.f64 60 x) (.f64 60 y)) (-.f64 z t)))
	1.0b	(fma.f64 a 120 (pow.f64 (/.f64 (-.f64 z t) (*.f64 60 (-.f64 x y))) -1))
	26.7b	(fma.f64 a 120 (pow.f64 (sqrt.f64 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))) 2))

Compiler

Compiled 3643 to 2015 computations (44.7% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series87.0ms (1%)

Counts

2 → 108

Calls

2 calls:

47.0ms	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
40.0ms	(*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y))

rewrite70.0ms (0.8%)

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

2 → 68

Calls

2 calls:

68.0ms	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
68.0ms	(*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	290	30
2	3749	30
3	5565	30
0	0	0
1	0	0

simplify129.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

713×	`times-frac_binary64`
658×	`cancel-sign-sub-inv_binary64`
478×	`sub-neg_binary64`
204×	`fma-neg_binary64`
203×	`fma-def_binary64`

Counts

176 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	3611
1	517	3450
2	1952	3210
3	4440	3210
4	5008	3210

prune123.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	7	2	9
Picked	0	1	1
Done	0	0	0
Total	118	5	123

Error

0.0b

Counts

123 → 5

Alt Table

Status	Error	Program
	0.1b	(fma.f64 a 120 (/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60)))
	0.6b	(fma.f64 a 120 (*.f64 (/.f64 (-.f64 x y) (pow.f64 (cbrt.f64 (-.f64 z t)) 2)) (/.f64 60 (cbrt.f64 (-.f64 z t)))))
▶	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.2b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
	26.6b	(fma.f64 a 120 (*.f64 60 (/.f64 (-.f64 x y) z)))

Compiler

Compiled 3032 to 1624 computations (46.4% 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)))

series112.0ms (1.3%)

Counts

3 → 156

Calls

3 calls:

48.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
38.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))
26.0ms	(/.f64 (-.f64 z t) (-.f64 x y))

rewrite76.0ms (0.9%)

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 → 107

Calls

3 calls:

73.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
73.0ms	(/.f64 (-.f64 z t) (-.f64 x y))
73.0ms	(/.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

simplify192.0ms (2.2%)

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

263 → 170

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

prune166.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	170	5	175

Error

0.0b

Counts

175 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 a 120 (/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60)))
	0.6b	(fma.f64 a 120 (*.f64 (/.f64 (-.f64 x y) (pow.f64 (cbrt.f64 (-.f64 z t)) 2)) (/.f64 60 (cbrt.f64 (-.f64 z t)))))
✓	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.2b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
	26.6b	(fma.f64 a 120 (*.f64 60 (/.f64 (-.f64 x y) z)))

Compiler

Compiled 4363 to 2160 computations (50.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series130.0ms (1.5%)

Counts

3 → 132

Calls

3 calls:

89.0ms	(fma.f64 a 120 (/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60)))
37.0ms	(/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60))
3.0ms	(/.f64 (-.f64 z t) 60)

rewrite75.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

282×	`expm1-udef_binary64`
282×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`

Counts

3 → 96

Calls

3 calls:

73.0ms	(/.f64 (-.f64 z t) 60)
73.0ms	(fma.f64 a 120 (/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60)))
73.0ms	(/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	303	37
2	4180	37
3	4934	37
0	0	0
1	0	0

simplify124.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

713×	`times-frac_binary64`
660×	`cancel-sign-sub-inv_binary64`
480×	`sub-neg_binary64`
206×	`fma-neg_binary64`
205×	`fma-def_binary64`

Counts

228 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	3761
1	532	3600
2	1973	3360
3	4434	3360
4	5001	3360

prune140.0ms (1.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	146	5	151

Error

0.0b

Counts

151 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 a 120 (/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60)))
	0.6b	(fma.f64 a 120 (*.f64 (/.f64 (-.f64 x y) (pow.f64 (cbrt.f64 (-.f64 z t)) 2)) (/.f64 60 (cbrt.f64 (-.f64 z t)))))
✓	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.2b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
	26.6b	(fma.f64 a 120 (*.f64 60 (/.f64 (-.f64 x y) z)))

Compiler

Compiled 3416 to 1836 computations (46.3% saved)

regimes958.0ms (10.8%)

Accuracy

Total 0.1b remaining (89.4%)

Threshold costs 0.1b (89.4%)

Counts

69 → 1

Compiler

Compiled 14979 to 10587 computations (29.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`sub-neg_binary64`
6×	`+-commutative_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`*-commutative_binary64`
5×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	23	19
2	34	19
3	48	17
4	60	17
5	63	17
6	59	17

end166.0ms (1.9%)

Compiler: Compiled 125 to 87 computations (30.4% saved)

Details

analyze2.4s (26.6%)

sample1.8s (19.9%)

simplify198.0ms (2.2%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

series86.0ms (1%)

rewrite85.0ms (1%)

simplify123.0ms (1.4%)

prune1.6s (18.6%)

localize9.0ms (0.1%)

series87.0ms (1%)

rewrite70.0ms (0.8%)

simplify129.0ms (1.5%)

prune123.0ms (1.4%)

localize8.0ms (0.1%)

series112.0ms (1.3%)

rewrite76.0ms (0.9%)

simplify192.0ms (2.2%)

prune166.0ms (1.9%)

localize10.0ms (0.1%)

series130.0ms (1.5%)

rewrite75.0ms (0.9%)

simplify124.0ms (1.4%)

prune140.0ms (1.6%)

regimes958.0ms (10.8%)

simplify4.0ms (0%)

end166.0ms (1.9%)

Profiling