Details

analyze1.6s (27.3%)

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)

sample1.3s (23.1%)

Results

1.1s	8101×	body	128	valid
91.0ms	687×	body	128	invalid
25.0ms	68×	body	1024	valid
18.0ms	20×	body	256	valid
16.0ms	36×	body	2048	valid
10.0ms	28×	body	512	valid
2.0ms	3×	body	4096	valid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify111.0ms (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

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)

localize9.0ms (0.2%)

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))
✓	0.7b	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

series76.0ms (1.3%)

Counts

3 → 132

Calls

3 calls:

40.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
32.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
3.0ms	(*.f64 60 (-.f64 x y))

rewrite75.0ms (1.3%)

Algorithm

1×	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:

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

simplify109.0ms (1.9%)

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

prune137.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	7	139

Error

Counts

139 → 7

Alt Table

Status	Error	Program
	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)))))
	0.7b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))
	0.6b	(fma.f64 a 120 (/.f64 (-.f64 (.f64 60 x) (.f64 60 y)) (-.f64 z t)))
	24.7b	(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)))))
	0.7b	(fma.f64 a 120 (pow.f64 (/.f64 (-.f64 z t) (*.f64 60 (-.f64 x y))) -1))
	1.0b	(fma.f64 a 120 (pow.f64 (cbrt.f64 (/.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 3553 to 1949 computations (45.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series144.0ms (2.5%)

Counts

3 → 132

Calls

3 calls:

75.0ms	(*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y))
62.0ms	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
7.0ms	(/.f64 60 (-.f64 z t))

rewrite92.0ms (1.6%)

Algorithm

1×	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 → 93

Calls

3 calls:

90.0ms	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))
90.0ms	(/.f64 60 (-.f64 z t))
90.0ms	(*.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

simplify129.0ms (2.3%)

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

225 → 152

Iterations

Useful iterations: 3 (0.0ms)

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

prune123.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	154	5	159

Error

Counts

159 → 5

Alt Table

Status	Error	Program
	0.7b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))
▶	0.1b	(fma.f64 a 120 (/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60)))
	0.6b	(fma.f64 a 120 (*.f64 (pow.f64 (cbrt.f64 (/.f64 60 (-.f64 z t))) 3) (-.f64 x y)))
	0.7b	(fma.f64 a 120 (pow.f64 (/.f64 (-.f64 z t) (*.f64 60 (-.f64 x y))) -1))
✓	0.1b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))

Compiler

Compiled 3788 to 2045 computations (46% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series70.0ms (1.2%)

Counts

3 → 132

Calls

3 calls:

36.0ms	(fma.f64 a 120 (/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60)))
30.0ms	(/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60))
4.0ms	(/.f64 (-.f64 z t) 60)

rewrite68.0ms (1.2%)

Algorithm

1×	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:

67.0ms	(fma.f64 a 120 (/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60)))
67.0ms	(/.f64 (-.f64 z t) 60)
67.0ms	(/.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

simplify124.0ms (2.2%)

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

prune154.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	146	5	151

Error

Counts

151 → 5

Alt Table

Status	Error	Program
	0.7b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))
✓	0.1b	(fma.f64 a 120 (/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60)))
▶	0.1b	(fma.f64 a 120 (*.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 60))
	0.7b	(fma.f64 a 120 (pow.f64 (/.f64 (-.f64 z t) (*.f64 60 (-.f64 x y))) -1))
✓	0.1b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))

Compiler

Compiled 3469 to 1877 computations (45.9% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series95.0ms (1.7%)

Counts

3 → 156

Calls

3 calls:

39.0ms	(fma.f64 a 120 (*.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 60))
32.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 60)
25.0ms	(/.f64 (-.f64 x y) (-.f64 z t))

rewrite68.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

274×	`expm1-udef_binary64`
274×	`log1p-udef_binary64`
211×	`fma-neg_binary64`
151×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`

Counts

3 → 100

Calls

3 calls:

66.0ms	(fma.f64 a 120 (*.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 60))
66.0ms	(/.f64 (-.f64 x y) (-.f64 z t))
66.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 60)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	292	40
2	3913	40
3	4910	40

simplify140.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

726×	`fma-neg_binary64`
715×	`times-frac_binary64`
686×	`cancel-sign-sub-inv_binary64`
390×	`sub-neg_binary64`
200×	`fma-def_binary64`

Counts

256 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	5147
1	619	4965
2	2284	4521
3	4592	4507
4	5071	4507

prune200.0ms (3.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	163	5	168

Error

Counts

168 → 5

Alt Table

Status	Error	Program
	0.7b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))
✓	0.1b	(fma.f64 a 120 (/.f64 (-.f64 x y) (/.f64 (-.f64 z t) 60)))
✓	0.1b	(fma.f64 a 120 (*.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 60))
	0.7b	(fma.f64 a 120 (pow.f64 (/.f64 (-.f64 z t) (*.f64 60 (-.f64 x y))) -1))
✓	0.1b	(fma.f64 a 120 (*.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y)))

Compiler

Compiled 4134 to 1992 computations (51.8% saved)

regimes779.0ms (13.7%)

Accuracy

Total 0.1b remaining (92.6%)

Threshold costs 0.1b (92.6%)

Counts

59 → 1

Compiler

Compiled 13234 to 9417 computations (28.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	18	17
2	26	17
3	30	17
4	32	17
5	32	17

end79.0ms (1.4%)

Compiler: Compiled 123 to 88 computations (28.5% saved)

Details

analyze1.6s (27.3%)

sample1.3s (23.1%)

simplify111.0ms (2%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series76.0ms (1.3%)

rewrite75.0ms (1.3%)

simplify109.0ms (1.9%)

prune137.0ms (2.4%)

localize8.0ms (0.1%)

series144.0ms (2.5%)

rewrite92.0ms (1.6%)

simplify129.0ms (2.3%)

prune123.0ms (2.2%)

localize10.0ms (0.2%)

series70.0ms (1.2%)

rewrite68.0ms (1.2%)

simplify124.0ms (2.2%)

prune154.0ms (2.7%)

localize12.0ms (0.2%)

series95.0ms (1.7%)

rewrite68.0ms (1.2%)

simplify140.0ms (2.5%)

prune200.0ms (3.5%)

regimes779.0ms (13.7%)

simplify3.0ms (0%)

end79.0ms (1.4%)

Profiling