Details

analyze2.9s (14.8%)

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)

sample2.0s (10.5%)

Results

1.7s	8101×	body	128	valid
67.0ms	320×	body	128	invalid
65.0ms	86×	body	1024	invalid
52.0ms	66×	body	1024	valid
47.0ms	81×	body	512	invalid
37.0ms	55×	body	512	valid
26.0ms	24×	body	2048	invalid
24.0ms	54×	body	256	invalid
13.0ms	34×	body	256	valid

Compiler

Compiled 70 to 48 computations (31.4% saved)

preprocess51.0ms (0.3%)

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)

simplify21.0ms (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)

localize16.0ms (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)))

series370.0ms (1.9%)

Counts

4 → 192

Calls

48 calls:

68.0ms	(*.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	0
38.0ms	(*.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	0
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	0
25.0ms	(*.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	0
20.0ms	(*.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	-inf

rewrite49.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

245×	`add-sqr-sqrt_binary64`
239×	`pow1_binary64`
238×	`*-un-lft-identity_binary64`
229×	`add-log-exp_binary64`
228×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	95
1	462	95

Stop Event

1×	node limit

Counts

4 → 71

simplify207.0ms (1.1%)

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

263 → 211

prune346.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	207	4	211
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	208	4	212

Error

0.9b

Counts

212 → 4

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	(.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))))))))
	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))))))
▶	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))))

Compiler

Compiled 18214 to 8942 computations (50.9% saved)

localize14.0ms (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)

series150.0ms (0.8%)

Counts

1 → 48

Calls

12 calls:

35.0ms	(*.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
19.0ms	(*.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
15.0ms	(*.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
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))))	M	-inf

rewrite26.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

213×	`add-sqr-sqrt_binary64`
209×	`pow1_binary64`
208×	`*-un-lft-identity_binary64`
200×	`add-log-exp_binary64`
199×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	400	29

Stop Event

1×	node limit

Counts

1 → 15

simplify95.0ms (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

prune213.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	153	4	157

Error

0.9b

Counts

157 → 4

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	(.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))))))))
▶	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))))))
✓	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))))

Compiler

Compiled 8460 to 4107 computations (51.5% saved)

localize19.0ms (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 (7.8%)

Counts

4 → 204

Calls

51 calls:

324.0ms	(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
291.0ms	(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
280.0ms	(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
100.0ms	(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
38.0ms	(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))))))	m

rewrite42.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

258×	`add-sqr-sqrt_binary64`
253×	`pow1_binary64`
251×	`*-un-lft-identity_binary64`
243×	`expm1-log1p-u_binary64`
242×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	116
1	498	116

Stop Event

1×	node limit

Counts

4 → 47

simplify507.0ms (2.6%)

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

251 → 205

prune957.0ms (4.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	201	4	205
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	204	5	209

Error

0.9b

Counts

209 → 5

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))))))))
	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))))
	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))))))

Compiler

Compiled 60816 to 29832 computations (50.9% saved)

localize26.0ms (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)))

series4.8s (24.9%)

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
324.0ms	(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
95.0ms	(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

rewrite28.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`add-sqr-sqrt_binary64`
260×	`pow1_binary64`
259×	`*-un-lft-identity_binary64`
249×	`log1p-expm1-u_binary64`
249×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	47
1	512	47

Stop Event

1×	node limit

Counts

1 → 10

simplify839.0ms (4.3%)

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

70 → 58

prune3.0s (15.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	201	6	207

Error

0.9b

Counts

207 → 6

Alt Table

Status	Error	Program
	19.2b	(log1p.f64 (log.f64 (+.f64 1 (.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))))))) (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)))))))))))
	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)))))))))
	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))))))
✓	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))))
	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))))))

Compiler

Compiled 152810 to 76788 computations (49.7% saved)

regimes858.0ms (4.4%)

Accuracy

Total 0.1b remaining (11.2%)

Threshold costs 0.1b (11.2%)

Counts

91 → 1

Compiler

Compiled 27842 to 17040 computations (38.8% 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

end314.0ms (1.6%)

Stop Event

1×

fuel

Remove

(sort m n)

Compiler

Compiled 915 to 447 computations (51.1% saved)

Details

analyze2.9s (14.8%)

sample2.0s (10.5%)

preprocess51.0ms (0.3%)

simplify21.0ms (0.1%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series370.0ms (1.9%)

rewrite49.0ms (0.3%)

simplify207.0ms (1.1%)

prune346.0ms (1.8%)

localize14.0ms (0.1%)

series150.0ms (0.8%)

rewrite26.0ms (0.1%)

simplify95.0ms (0.5%)

prune213.0ms (1.1%)

localize19.0ms (0.1%)

series1.5s (7.8%)

rewrite42.0ms (0.2%)

simplify507.0ms (2.6%)

prune957.0ms (4.9%)

localize26.0ms (0.1%)

series4.8s (24.9%)

rewrite28.0ms (0.1%)

simplify839.0ms (4.3%)

prune3.0s (15.3%)

regimes858.0ms (4.4%)

simplify3.0ms (0%)

end314.0ms (1.6%)

Profiling