Details

analyze2.8s (31%)

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)

sample2.7s (29.2%)

Symmetry

(sort m n)

Results

2.2s	8097×	body	128	valid
89.0ms	112×	body	1024	invalid
75.0ms	342×	body	128	invalid
59.0ms	74×	body	1024	valid
47.0ms	85×	body	512	invalid
27.0ms	50×	body	512	valid
22.0ms	20×	body	2048	invalid
19.0ms	54×	body	256	invalid
13.0ms	35×	body	256	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify18.0ms (0.2%)

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

prune7.0ms (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

13.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.7b	(*.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 (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
✓	0.0b	(fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	31.8b	(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M)))

series79.0ms (0.9%)

Counts

4 → 180

Calls

4 calls:

34.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
17.0ms	(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M)))
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))

rewrite64.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

289×	`log1p-udef_binary64`
173×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`
166×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	57
1	340	49
2	4769	49

Stop Event

1×	node limit

Counts

4 → 112

Calls

4 calls:

62.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
62.0ms	(fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))
62.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
62.0ms	(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M)))

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

569×	`cancel-sign-sub-inv_binary64`
566×	`associate--l+_binary64`
233×	`fma-def_binary64`
223×	`associate-r_binary64`
195×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	4326
1	685	3915
2	2490	3816

Stop Event

1×	node limit

Counts

292 → 206

prune306.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	200	6	206
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	201	6	207

Error

1.3b

Counts

207 → 6

Alt Table

Status	Error	Program
	13.7b	(.f64 (cos.f64 (pow.f64 (cbrt.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.7b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.4b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.7b	(.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M))) (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)) 2))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.9b	(*.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 8151 to 4125 computations (49.4% saved)

localize15.0ms (0.2%)

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 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series39.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

39.0ms

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

rewrite29.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

176×	`add-sqr-sqrt_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`
172×	`add-cbrt-cube_binary64`
165×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	343	22

Stop Event

1×	node limit

Counts

1 → 43

Calls

1 calls:

28.0ms

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

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

681×	`associate--r+_binary64`
312×	`fma-def_binary64`
265×	`associate--l+_binary64`
251×	`associate-+l+_binary64`
249×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	1639
1	250	1476
2	936	1471
3	3951	1459

Stop Event

1×	node limit

Counts

91 → 76

prune263.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	189	6	195

Error

1.3b

Counts

195 → 6

Alt Table

Status	Error	Program
	13.7b	(.f64 (cos.f64 (pow.f64 (cbrt.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.7b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	10.4b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.7b	(.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M))) (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)) 2))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.9b	(*.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 5952 to 2977 computations (50% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
✓	0.0b	(.f64 1/2 (.f64 K m))
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	28.9b	(cos.f64 (.f64 1/2 (.f64 K m)))

series8.0ms (0.1%)

Counts

2 → 8

Calls

2 calls:

4.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))
4.0ms	(.f64 1/2 (.f64 K m))

rewrite38.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

597×	`log1p-expm1-u_binary64`
597×	`expm1-log1p-u_binary64`
343×	`log-prod_binary64`
324×	`prod-diff_binary64`
126×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	140	16
2	1630	16

Stop Event

1×	node limit

Counts

2 → 38

Calls

2 calls:

37.0ms	(.f64 1/2 (.f64 K m))
37.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))

simplify25.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

599×	`distribute-rgt-neg-in_binary64`
525×	`distribute-lft-neg-in_binary64`
489×	`fma-def_binary64`
356×	`cancel-sign-sub-inv_binary64`
299×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	184
1	75	176
2	236	168
3	1161	164
4	3818	152

Stop Event

1×	node limit

Counts

46 → 45

prune240.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	158	6	164

Error

1.3b

Counts

164 → 6

Alt Table

Status	Error	Program
	13.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.7b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.7b	(.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M))) (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)) 2))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	10.3b	(.f64 (cos.f64 (pow.f64 (cbrt.f64 (.f64 K (*.f64 m 1/2))) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.4b	(.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (.f64 K (.f64 m 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (.f64 K (*.f64 m 1/2))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 5464 to 2959 computations (45.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 K (.f64 m 1/2))) 3)
✓	15.0b	(cbrt.f64 (.f64 K (.f64 m 1/2)))
✓	28.8b	(cos.f64 (pow.f64 (cbrt.f64 (.f64 K (.f64 m 1/2))) 3))

series1.0s (11.2%)

Counts

3 → 72

Calls

3 calls:

372.0ms	(cos.f64 (pow.f64 (cbrt.f64 (.f64 K (.f64 m 1/2))) 3))
346.0ms	(pow.f64 (cbrt.f64 (.f64 K (.f64 m 1/2))) 3)
304.0ms	(cbrt.f64 (.f64 K (.f64 m 1/2)))

rewrite47.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`prod-diff_binary64`
771×	`log1p-expm1-u_binary64`
771×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
84×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	203	25
2	2153	25

Stop Event

1×	node limit

Counts

3 → 83

Calls

3 calls:

45.0ms	(pow.f64 (cbrt.f64 (.f64 K (.f64 m 1/2))) 3)
45.0ms	(cbrt.f64 (.f64 K (.f64 m 1/2)))
45.0ms	(cos.f64 (pow.f64 (cbrt.f64 (.f64 K (.f64 m 1/2))) 3))

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-def_binary64`
422×	`unswap-sqr_binary64`
266×	`associate-l_binary64`
228×	`unsub-neg_binary64`
218×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1464
1	130	1464
2	310	1392
3	870	720
4	2741	720

Stop Event

1×	node limit

Counts

155 → 104

prune288.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	162	7	169

Error

1.3b

Counts

169 → 7

Alt Table

Status	Error	Program
	13.7b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.7b	(.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M))) (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)) 2))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	10.3b	(.f64 (cos.f64 (pow.f64 (cbrt.f64 (.f64 K (*.f64 m 1/2))) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.4b	(.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (.f64 K (.f64 m 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (.f64 K (*.f64 m 1/2))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.3b	(.f64 (cos.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 m (.f64 1/2 K))) 2)) 3) (cbrt.f64 (.f64 m (.f64 1/2 K))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.3b	(.f64 (cos.f64 (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 m (.f64 1/2 K)))) (pow.f64 (pow.f64 (cbrt.f64 (.f64 m (.f64 1/2 K))) 2) 1/3)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 5507 to 3312 computations (39.9% saved)

regimes759.0ms (8.3%)

Accuracy

Total 0.3b remaining (20.5%)

Threshold costs 0.3b (20.5%)

Counts

113 → 1

Compiler

Compiled 20522 to 14568 computations (29% saved)

simplify2.0ms (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	26
1	30	26
2	46	26
3	61	26
4	70	26
5	73	26

Stop Event

1×

saturated

end168.0ms (1.8%)

Remove: (sort m n)
Compiler: Compiled 355 to 259 computations (27% saved)

Details

analyze2.8s (31%)

sample2.7s (29.2%)

simplify18.0ms (0.2%)

prune7.0ms (0.1%)

localize16.0ms (0.2%)

series79.0ms (0.9%)

rewrite64.0ms (0.7%)

simplify69.0ms (0.8%)

prune306.0ms (3.4%)

localize15.0ms (0.2%)

series39.0ms (0.4%)

rewrite29.0ms (0.3%)

simplify44.0ms (0.5%)

prune263.0ms (2.9%)

localize17.0ms (0.2%)

series8.0ms (0.1%)

rewrite38.0ms (0.4%)

simplify25.0ms (0.3%)

prune240.0ms (2.6%)

localize18.0ms (0.2%)

series1.0s (11.2%)

rewrite47.0ms (0.5%)

simplify46.0ms (0.5%)

prune288.0ms (3.2%)

regimes759.0ms (8.3%)

simplify2.0ms (0%)

end168.0ms (1.8%)

Profiling