Details

analyze3.0s (15.7%)

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
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample2.3s (11.9%)

Results

1.8s	8110×	body	128	valid
70.0ms	84×	body	1024	invalid
68.0ms	315×	body	128	invalid
67.0ms	78×	body	512	invalid
53.0ms	58×	body	1024	valid
36.0ms	64×	body	512	valid
29.0ms	17×	body	2048	invalid
22.0ms	59×	body	256	invalid
14.0ms	24×	body	256	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1058×	`fma-neg_binary64`
716×	`fma-def_binary64`
379×	`exp-prod_binary64`
190×	`exp-diff_binary64`
108×	`rules-33_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	50	45
2	138	44
3	477	43
4	2373	43
5	4623	43
6	4992	43

prune4.0ms (0%)

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

13.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 128 to 80 computations (37.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.0b	(/.f64 (*.f64 K (+.f64 m n)) 2)
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	32.0b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series338.0ms (1.8%)

Counts

4 → 180

Calls

4 calls:

289.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
25.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
15.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
8.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)

rewrite45.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

243×	`add-sqr-sqrt_binary64`
235×	`log1p-expm1-u_binary64`
235×	`expm1-log1p-u_binary64`
225×	`add-log-exp_binary64`
224×	`add-cbrt-cube_binary64`

Counts

4 → 88

Calls

4 calls:

43.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
43.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
43.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
43.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	81
1	530	81
2	4995	81
0	0	0
1	0	0

simplify187.0ms (1%)

Algorithm

1×	egg-herbie

Rules

598×	`rules-21_binary64`
367×	`rules-20_binary64`
292×	`rules-1_binary64`
275×	`rules-1-rev_binary64`
261×	`rules-7-rev_binary64`

Counts

268 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	625	13476
1	2763	12302
2	5135	12302

prune351.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	189	5	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	5	195

Error

0.8b

Counts

195 → 5

Alt Table

Status	Error	Program
	13.0b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.1b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.0b	(.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	29.0b	(.f64 (cos.f64 (-.f64 (expm1.f64 (log1p.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.0b	(.f64 (cos.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) 3) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 17148 to 8543 computations (50.2% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series57.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

57.0ms

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

rewrite70.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

290×	`expm1-udef_binary64`
290×	`log1p-udef_binary64`
170×	`add-sqr-sqrt_binary64`
167×	`log1p-expm1-u_binary64`
167×	`expm1-log1p-u_binary64`

Counts

1 → 32

Calls

1 calls:

69.0ms

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	377	24
2	4481	24
3	5250	24
0	0	0
1	0	0

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-def_binary64`
541×	`rules-13_binary64`
344×	`rules-20_binary64`
256×	`rules-21_binary64`
147×	`rules-7-rev_binary64`

Counts

80 → 70

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	234	4963
1	975	4187
2	5027	4187

prune188.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	114	5	119

Error

0.8b

Counts

119 → 5

Alt Table

Status	Error	Program
	13.0b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	1.1b	(.f64 (cos.f64 M) (.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2)))
▶	1.1b	(*.f64 (cos.f64 M) (pow.f64 (sqrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2))
	29.0b	(.f64 (cos.f64 (-.f64 (expm1.f64 (log1p.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.0b	(.f64 (cos.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) 3) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 7105 to 3508 computations (50.6% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series59.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

58.0ms

(exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

rewrite88.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

288×	`log1p-udef_binary64`
160×	`add-sqr-sqrt_binary64`
158×	`log1p-expm1-u_binary64`
158×	`expm1-log1p-u_binary64`
149×	`add-log-exp_binary64`

Counts

1 → 33

Calls

1 calls:

87.0ms

(exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	354	24
2	4816	24
3	5215	24
0	0	0
1	0	0

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

969×	`fma-def_binary64`
799×	`rules-13_binary64`
416×	`rules-20_binary64`
388×	`rules-21_binary64`
91×	`rules-1_binary64`

Counts

81 → 68

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	270	5175
1	1244	4660
2	5141	4660

prune210.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	112	5	117

Error

0.8b

Counts

117 → 5

Alt Table

Status	Error	Program
	13.0b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.1b	(.f64 (cos.f64 M) (.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2)))
✓	1.1b	(*.f64 (cos.f64 M) (pow.f64 (sqrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2))
	29.0b	(.f64 (cos.f64 (-.f64 (expm1.f64 (log1p.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.0b	(.f64 (cos.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) 3) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 8047 to 4447 computations (44.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.0b	(cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.0b	(*.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2))
✓	0.0b	(pow.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2)

series10.0s (52.3%)

Counts

3 → 144

Calls

3 calls:

5.1s

(cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

4.8s

(pow.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2)

63.0ms

(*.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2))

rewrite93.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

631×	`prod-diff_binary64`
177×	`add-sqr-sqrt_binary64`
175×	`log1p-expm1-u_binary64`
175×	`expm1-log1p-u_binary64`
165×	`add-cbrt-cube_binary64`

Counts

3 → 87

Calls

3 calls:

90.0ms

(cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

90.0ms

(*.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2))

90.0ms

(pow.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	79
1	401	77
2	4662	77
3	5792	77
0	0	0
1	0	0

simplify221.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

416×	`rules-20_binary64`
324×	`rules-1_binary64`
303×	`rules-1-rev_binary64`
272×	`rules-11_binary64`
255×	`rules-21_binary64`

Counts

231 → 192

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	782	17370
1	3561	15843
2	5059	15843

prune846.0ms (4.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	347	0	347
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	347	5	352

Error

0.8b

Counts

352 → 5

Alt Table

Status	Error	Program
	13.0b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.1b	(.f64 (cos.f64 M) (.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2)))
✓	1.1b	(*.f64 (cos.f64 M) (pow.f64 (sqrt.f64 (exp.f64 (-.f64 (-.f64 m n) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) 2))
	29.0b	(.f64 (cos.f64 (-.f64 (expm1.f64 (log1p.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.0b	(.f64 (cos.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) 3) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 35347 to 20061 computations (43.2% saved)

regimes656.0ms (3.5%)

Accuracy

Total 0.2b remaining (15.1%)

Threshold costs 0.2b (15.1%)

Counts

91 → 1

Compiler

Compiled 17894 to 12504 computations (30.1% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	34
1	18	34

end125.0ms (0.7%)

Compiler: Compiled 233 to 164 computations (29.6% saved)

Details

analyze3.0s (15.7%)

sample2.3s (11.9%)

simplify48.0ms (0.3%)

prune4.0ms (0%)

localize20.0ms (0.1%)

series338.0ms (1.8%)

rewrite45.0ms (0.2%)

simplify187.0ms (1%)

prune351.0ms (1.8%)

localize13.0ms (0.1%)

series57.0ms (0.3%)

rewrite70.0ms (0.4%)

simplify76.0ms (0.4%)

prune188.0ms (1%)

localize14.0ms (0.1%)

series59.0ms (0.3%)

rewrite88.0ms (0.5%)

simplify78.0ms (0.4%)

prune210.0ms (1.1%)

localize19.0ms (0.1%)

series10.0s (52.3%)

rewrite93.0ms (0.5%)

simplify221.0ms (1.2%)

prune846.0ms (4.4%)

regimes656.0ms (3.5%)

simplify1.0ms (0%)

end125.0ms (0.7%)

Profiling