Details

analyze2.9s (14.7%)

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)

sample2.1s (10.4%)

Results

1.7s	8101×	body	128	valid
74.0ms	320×	body	128	invalid
66.0ms	86×	body	1024	invalid
56.0ms	66×	body	1024	valid
42.0ms	81×	body	512	invalid
30.0ms	55×	body	512	valid
28.0ms	24×	body	2048	invalid
23.0ms	54×	body	256	invalid
13.0ms	34×	body	256	valid

Compiler

Compiled 70 to 48 computations (31.4% saved)

preprocess48.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

557×	`exp-sum_binary64`
428×	`fma-neg_binary64`
310×	`exp-prod_binary64`
288×	`exp-diff_binary64`
162×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	154	495
1	429	495
2	1042	473
3	3765	473
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort m n)

Compiler

Compiled 34 to 23 computations (32.4% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

446×	`fma-neg_binary64`
251×	`times-frac_binary64`
231×	`cancel-sign-sub-inv_binary64`
219×	`exp-sum_binary64`
202×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	58	45
2	135	43
3	442	43
4	1753	43

Stop Event

1×	node limit

Counts

1 → 2

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

18.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.7b	(*.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 128 to 83 computations (35.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
✓	0.0b	(*.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	35.4b	(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M)))

series336.0ms (1.7%)

Counts

4 → 192

Calls

48 calls:

35.0ms	(*.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))	n
34.0ms	(*.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))	m
34.0ms	(*.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))	M
27.0ms	(*.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))	K
16.0ms	(-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))	M

rewrite55.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

236×	`add-sqr-sqrt_binary64`
228×	`log1p-expm1-u_binary64`
228×	`expm1-log1p-u_binary64`
226×	`add-cbrt-cube_binary64`
219×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	95
1	461	95

Stop Event

1×	node limit

Counts

4 → 75

simplify167.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

907×	`fma-def_binary64`
384×	`associate-+l+_binary64`
354×	`*-commutative_binary64`
282×	`associate-r_binary64`
233×	`associate--r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	631	14955
1	2281	13390

Stop Event

1×	node limit

Counts

267 → 215

prune346.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	210	5	215
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	211	5	216

Error

0.9b

Counts

216 → 5

Alt Table

Status	Error	Program
	25.1b	(.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) l))))
	18.7b	(log1p.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))
	18.7b	(.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (.f64 (+.f64 m n) 1/2) M) 2) l)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))))
▶	1.5b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	19.1b	(.f64 (sqrt.f64 (pow.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 18390 to 9047 computations (50.8% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series143.0ms (0.7%)

Counts

1 → 48

Calls

12 calls:

21.0ms	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))	n	-inf
18.0ms	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))	M	0
17.0ms	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))	m	0
16.0ms	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))	n	0
10.0ms	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))	l	0

rewrite28.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

204×	`add-sqr-sqrt_binary64`
199×	`log1p-expm1-u_binary64`
199×	`expm1-log1p-u_binary64`
197×	`add-cbrt-cube_binary64`
191×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	399	29

Stop Event

1×	node limit

Counts

1 → 15

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-r_binary64`
398×	`fma-def_binary64`
366×	`times-frac_binary64`
365×	`associate-l_binary64`
246×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	251	5358
1	932	4677
2	4311	4677

Stop Event

1×	node limit

Counts

63 → 51

prune234.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	153	5	158

Error

0.9b

Counts

158 → 5

Alt Table

Status	Error	Program
	25.1b	(.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) l))))
▶	18.7b	(log1p.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))
	18.7b	(.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (.f64 (+.f64 m n) 1/2) M) 2) l)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))))
✓	1.5b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	19.1b	(.f64 (sqrt.f64 (pow.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 8508 to 4144 computations (51.3% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))
✓	0.0b	(pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2)
✓	0.0b	(expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l)))))
✓	35.4b	(cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M)))

series1.5s (7.6%)

Counts

4 → 204

Calls

51 calls:

312.0ms	(expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l)))))	M
289.0ms	(expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l)))))	n
274.0ms	(expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l)))))	m
115.0ms	(expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l)))))	K
36.0ms	(log1p.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))	n

rewrite39.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`add-sqr-sqrt_binary64`
243×	`expm1-log1p-u_binary64`
242×	`log1p-expm1-u_binary64`
238×	`add-cbrt-cube_binary64`
231×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	116
1	497	116

Stop Event

1×	node limit

Counts

4 → 59

simplify469.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-def_binary64`
419×	`+-commutative_binary64`
352×	`associate-+r+_binary64`
195×	`sub-neg_binary64`
86×	`sqr-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1850	47726
1	3910	45278

Stop Event

1×	node limit

Counts

263 → 217

prune1.7s (8.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	213	4	217
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	216	6	222

Error

0.9b

Counts

222 → 6

Alt Table

Status	Error	Program
▶	18.7b	(log1p.f64 (log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l)))))))))
	33.9b	(log1p.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 l 2) (.f64 (pow.f64 (exp.f64 (-.f64 (+.f64 (.f64 m M) (+.f64 (.f64 n M) (fabs.f64 (-.f64 n m)))) (+.f64 (.f64 1/4 (pow.f64 m 2)) (+.f64 (pow.f64 M 2) (+.f64 (.f64 1/2 (.f64 n m)) (.f64 1/4 (pow.f64 n 2))))))) 2) (.f64 (exp.f64 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 m M) (+.f64 (.f64 n M) (fabs.f64 (-.f64 n m)))) (+.f64 (.f64 1/4 (pow.f64 m 2)) (+.f64 (pow.f64 M 2) (+.f64 (.f64 1/2 (.f64 n m)) (.f64 1/4 (pow.f64 n 2))))))) (cos.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 n K)) (.f64 1/2 (.f64 K m))) M)))) (pow.f64 (cos.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 n K)) (.f64 1/2 (.f64 K m))) M)) 2))))) (+.f64 (exp.f64 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 m M) (+.f64 (.f64 n M) (fabs.f64 (-.f64 n m)))) (+.f64 (.f64 1/4 (pow.f64 m 2)) (+.f64 (pow.f64 M 2) (+.f64 (.f64 1/2 (.f64 n m)) (.f64 1/4 (pow.f64 n 2))))))) (cos.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 n K)) (.f64 1/2 (.f64 K m))) M)))) (.f64 1/2 (.f64 (pow.f64 l 2) (.f64 (exp.f64 (-.f64 (+.f64 (.f64 m M) (+.f64 (.f64 n M) (fabs.f64 (-.f64 n m)))) (+.f64 (.f64 1/4 (pow.f64 m 2)) (+.f64 (pow.f64 M 2) (+.f64 (.f64 1/2 (.f64 n m)) (.f64 1/4 (pow.f64 n 2))))))) (.f64 (exp.f64 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 m M) (+.f64 (.f64 n M) (fabs.f64 (-.f64 n m)))) (+.f64 (.f64 1/4 (pow.f64 m 2)) (+.f64 (pow.f64 M 2) (+.f64 (.f64 1/2 (.f64 n m)) (.f64 1/4 (pow.f64 n 2))))))) (cos.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 n K)) (.f64 1/2 (.f64 K m))) M)))) (cos.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 n K)) (.f64 1/2 (.f64 K m))) M)))))))) (+.f64 1 (.f64 l (.f64 (exp.f64 (-.f64 (+.f64 (.f64 m M) (+.f64 (.f64 n M) (fabs.f64 (-.f64 n m)))) (+.f64 (.f64 1/4 (pow.f64 m 2)) (+.f64 (pow.f64 M 2) (+.f64 (.f64 1/2 (.f64 n m)) (.f64 1/4 (pow.f64 n 2))))))) (.f64 (exp.f64 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 m M) (+.f64 (.f64 n M) (fabs.f64 (-.f64 n m)))) (+.f64 (.f64 1/4 (pow.f64 m 2)) (+.f64 (pow.f64 M 2) (+.f64 (.f64 1/2 (.f64 n m)) (.f64 1/4 (pow.f64 n 2))))))) (cos.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 n K)) (.f64 1/2 (.f64 K m))) M)))) (cos.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 n K)) (.f64 1/2 (*.f64 K m))) M))))))))
	25.1b	(log1p.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 1/2 m) M) 2) l))))))
	18.7b	(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))) 3)))
✓	1.5b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	19.1b	(.f64 (sqrt.f64 (pow.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 61204 to 30058 computations (50.9% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))
	0.0b	(pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2)
	0.0b	(expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l)))))
	35.4b	(cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M)))

series4.7s (23.8%)

Counts

1 → 60

Calls

15 calls:

1.5s	(expm1.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))	M
1.3s	(expm1.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))	m
1.3s	(expm1.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))	n
309.0ms	(expm1.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))	K
86.0ms	(expm1.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))	l

rewrite33.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`add-sqr-sqrt_binary64`
249×	`log1p-expm1-u_binary64`
249×	`expm1-log1p-u_binary64`
245×	`add-cbrt-cube_binary64`
238×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	47
1	511	47

Stop Event

1×	node limit

Counts

1 → 14

simplify778.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

876×	`fma-def_binary64`
451×	`+-commutative_binary64`
418×	`associate-+r+_binary64`
47×	`sub-neg_binary64`
46×	`sqr-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	2643	78906
1	4787	74855

Stop Event

1×	node limit

Counts

74 → 62

prune2.9s (14.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	211	2	213
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	212	7	219

Error

0.9b

Counts

219 → 7

Alt Table

Status	Error	Program
	25.1b	(log1p.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 1/2 m) M) 2) l))))))
	33.7b	(log1p.f64 (log.f64 (+.f64 1 (+.f64 (exp.f64 (expm1.f64 (.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m))))))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))))) (-.f64 (fma.f64 1/2 (fma.f64 (exp.f64 (expm1.f64 (.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m))))))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))))) (.f64 (.f64 l l) (.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m))))))) (.f64 (pow.f64 (exp.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m)))))))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))))) (.f64 (exp.f64 (expm1.f64 (.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m))))))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))))) (.f64 (.f64 l l) (.f64 (pow.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m))))))) 2) (.f64 (pow.f64 (pow.f64 (exp.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m)))))))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))) 2) (pow.f64 (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M))) 2)))))) (.f64 1/2 (.f64 (exp.f64 (expm1.f64 (.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m))))))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))))) (.f64 (.f64 l l) (.f64 (pow.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m))))))) 2) (.f64 (pow.f64 (exp.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m)))))))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))) (pow.f64 (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M))) 2))))))) (fma.f64 (exp.f64 (expm1.f64 (.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m))))))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))))) (.f64 l (.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m))))))) (.f64 (pow.f64 (exp.f64 (exp.f64 (-.f64 (fma.f64 m M (fma.f64 n M (fabs.f64 (-.f64 n m)))) (fma.f64 1/4 (.f64 m m) (fma.f64 M M (fma.f64 1/4 (.f64 n n) (.f64 1/2 (.f64 n m)))))))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))) (cos.f64 (fma.f64 1/2 (fma.f64 n K (.f64 K m)) (neg.f64 M)))))) 1))))))
	19.2b	(log1p.f64 (log.f64 (+.f64 1 (pow.f64 (sqrt.f64 (expm1.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))))) 2))))
	18.7b	(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l))))) 3)))
✓	18.7b	(log1p.f64 (log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (*.f64 (+.f64 m n) 1/2) M) 2) l)))))))))
✓	1.5b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	19.1b	(.f64 (sqrt.f64 (pow.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 153088 to 76975 computations (49.7% saved)

regimes832.0ms (4.2%)

Accuracy

Total 0.1b remaining (11.4%)

Threshold costs 0.1b (11.4%)

Counts

93 → 1

Compiler

Compiled 28310 to 17376 computations (38.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	28	31
2	45	31
3	60	31
4	69	31
5	72	31

Stop Event

1×

saturated

end319.0ms (1.6%)

Stop Event

1×

fuel

Remove

(sort m n)

Compiler

Compiled 921 to 457 computations (50.4% saved)

Details

analyze2.9s (14.7%)

sample2.1s (10.4%)

preprocess48.0ms (0.2%)

simplify18.0ms (0.1%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series336.0ms (1.7%)

rewrite55.0ms (0.3%)

simplify167.0ms (0.8%)

prune346.0ms (1.7%)

localize13.0ms (0.1%)

series143.0ms (0.7%)

rewrite28.0ms (0.1%)

simplify99.0ms (0.5%)

prune234.0ms (1.2%)

localize27.0ms (0.1%)

series1.5s (7.6%)

rewrite39.0ms (0.2%)

simplify469.0ms (2.4%)

prune1.7s (8.6%)

localize23.0ms (0.1%)

series4.7s (23.8%)

rewrite33.0ms (0.2%)

simplify778.0ms (3.9%)

prune2.9s (14.6%)

regimes832.0ms (4.2%)

simplify3.0ms (0%)

end319.0ms (1.6%)

Profiling