Details

analyze3.0s (33.9%)

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 (23.9%)

Symmetry

(sort m n)

Results

1.7s	8113×	body	128	valid
87.0ms	105×	body	1024	invalid
64.0ms	270×	body	128	invalid
51.0ms	62×	body	1024	valid
38.0ms	71×	body	512	invalid
37.0ms	20×	body	2048	invalid
33.0ms	57×	body	512	valid
23.0ms	63×	body	256	invalid
9.0ms	23×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify20.0ms (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

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

14.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.6b	(*.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)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.0b	(fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))
✓	32.9b	(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M)))

series53.0ms (0.6%)

Counts

4 → 168

Calls

4 calls:

19.0ms	(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M)))
15.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
12.0ms	(fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))
6.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

rewrite64.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

354×	`fma-def_binary64`
241×	`expm1-udef_binary64`
241×	`log1p-udef_binary64`
201×	`fma-neg_binary64`
173×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	51
1	291	43
2	3972	43

Stop Event

1×	node limit

Counts

4 → 173

Calls

4 calls:

61.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
61.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
61.0ms	(fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))
61.0ms	(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M)))

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

523×	`cancel-sign-sub-inv_binary64`
308×	`associate--r+_binary64`
277×	`associate--l+_binary64`
223×	`associate-r_binary64`
185×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3245
1	547	3003
2	2063	2914

Stop Event

1×	node limit

Counts

341 → 255

prune399.0ms (4.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	250	5	255
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	251	5	256

Error

1.3b

Counts

256 → 5

Alt Table

Status	Error	Program
	14.5b	(.f64 (cos.f64 (.f64 (cbrt.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)) (pow.f64 (cbrt.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))))
	10.2b	(.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))))
▶	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))))
	14.6b	(.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)))) 1) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.6b	(.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))))

Compiler

Compiled 9782 to 4871 computations (50.2% saved)

localize12.0ms (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 (/.f64 (+.f64 m n) 2) M)
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series44.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

44.0ms

(-.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

prune294.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	237	5	242

Error

1.3b

Counts

242 → 5

Alt Table

Status	Error	Program
	14.5b	(.f64 (cos.f64 (.f64 (cbrt.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)) (pow.f64 (cbrt.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))))
▶	10.2b	(.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))))
✓	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))))
	14.6b	(.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)))) 1) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.6b	(.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))))

Compiler

Compiled 7161 to 3500 computations (51.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.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))))
	0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	29.4b	(cos.f64 (.f64 1/2 (.f64 K m)))

series238.0ms (2.7%)

Counts

2 → 68

Calls

2 calls:

227.0ms	(.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))))
11.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))

rewrite29.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`add-sqr-sqrt_binary64`
235×	`log1p-expm1-u_binary64`
235×	`expm1-log1p-u_binary64`
233×	`add-cbrt-cube_binary64`
227×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	480	46

Stop Event

1×	node limit

Counts

2 → 29

Calls

2 calls:

26.0ms	(.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))))
26.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))

simplify107.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

654×	`associate-r_binary64`
441×	`associate-l_binary64`
418×	`fma-def_binary64`
326×	`fma-neg_binary64`
296×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	7332
1	1105	6596
2	4989	6592

Stop Event

1×	node limit

Counts

97 → 81

prune459.0ms (5.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	240	2	242
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	242	5	247

Error

1.3b

Counts

247 → 5

Alt Table

Status	Error	Program
✓	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))))
	14.6b	(.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)))) 1) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.5b	(.f64 (cos.f64 (.f64 (cbrt.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)) (pow.f64 (cbrt.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))))
▶	10.2b	(.f64 (log.f64 (+.f64 1 (expm1.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))))
	10.2b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (*.f64 K m)))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 13100 to 6656 computations (49.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(log.f64 (+.f64 1 (expm1.f64 (cos.f64 (.f64 1/2 (.f64 K m))))))
✓	0.6b	(expm1.f64 (cos.f64 (.f64 1/2 (.f64 K m))))
✓	0.6b	(+.f64 1 (expm1.f64 (cos.f64 (.f64 1/2 (.f64 K m)))))
	29.4b	(cos.f64 (.f64 1/2 (.f64 K m)))

series367.0ms (4.2%)

Counts

3 → 72

Calls

3 calls:

349.0ms	(log.f64 (+.f64 1 (expm1.f64 (cos.f64 (.f64 1/2 (.f64 K m))))))
9.0ms	(expm1.f64 (cos.f64 (.f64 1/2 (.f64 K m))))
9.0ms	(+.f64 1 (expm1.f64 (cos.f64 (.f64 1/2 (.f64 K m)))))

rewrite51.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

875×	`log1p-expm1-u_binary64`
875×	`expm1-log1p-u_binary64`
462×	`prod-diff_binary64`
96×	`add-sqr-sqrt_binary64`
89×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	206	31
2	2368	31

Stop Event

1×	node limit

Counts

3 → 84

Calls

3 calls:

50.0ms	(log.f64 (+.f64 1 (expm1.f64 (cos.f64 (.f64 1/2 (.f64 K m))))))
50.0ms	(expm1.f64 (cos.f64 (.f64 1/2 (.f64 K m))))
50.0ms	(+.f64 1 (expm1.f64 (cos.f64 (.f64 1/2 (.f64 K m)))))

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

493×	`distribute-rgt-neg-in_binary64`
471×	`distribute-lft-neg-in_binary64`
418×	`associate-l_binary64`
416×	`associate-r_binary64`
327×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1176
1	200	1144
2	692	1110
3	3419	1108

Stop Event

1×	node limit

Counts

156 → 110

prune205.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	132	5	137

Error

1.3b

Counts

137 → 5

Alt Table

Status	Error	Program
✓	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))))
	14.6b	(.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)))) 1) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.3b	(.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) 2))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.2b	(.f64 (log.f64 (+.f64 1 (log.f64 (exp.f64 (expm1.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))))
	14.5b	(.f64 (cos.f64 (.f64 (cbrt.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) M)) (pow.f64 (cbrt.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))))

Compiler

Compiled 4747 to 2910 computations (38.7% saved)

regimes992.0ms (11.3%)

Accuracy

Total 0.2b remaining (17.7%)

Threshold costs 0.2b (17.7%)

Counts

148 → 1

Compiler

Compiled 26546 to 18996 computations (28.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	41
1	36	41
2	53	41
3	68	41
4	77	41
5	80	41

Stop Event

1×

saturated

end135.0ms (1.5%)

Remove: (sort m n)
Compiler: Compiled 308 to 223 computations (27.6% saved)

Details

analyze3.0s (33.9%)

sample2.1s (23.9%)

simplify20.0ms (0.2%)

prune4.0ms (0%)

localize17.0ms (0.2%)

series53.0ms (0.6%)

rewrite64.0ms (0.7%)

simplify68.0ms (0.8%)

prune399.0ms (4.5%)

localize12.0ms (0.1%)

series44.0ms (0.5%)

rewrite29.0ms (0.3%)

simplify44.0ms (0.5%)

prune294.0ms (3.3%)

localize15.0ms (0.2%)

series238.0ms (2.7%)

rewrite29.0ms (0.3%)

simplify107.0ms (1.2%)

prune459.0ms (5.2%)

localize21.0ms (0.2%)

series367.0ms (4.2%)

rewrite51.0ms (0.6%)

simplify44.0ms (0.5%)

prune205.0ms (2.3%)

regimes992.0ms (11.3%)

simplify3.0ms (0%)

end135.0ms (1.5%)

Profiling