Details

analyze2.9s (26.3%)

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 (20.8%)

Results

1.9s	8085×	body	128	valid
73.0ms	71×	body	1024	valid
73.0ms	89×	body	1024	invalid
69.0ms	299×	body	128	invalid
37.0ms	70×	body	512	invalid
37.0ms	64×	body	512	valid
23.0ms	20×	body	2048	invalid
22.0ms	59×	body	256	invalid
14.0ms	36×	body	256	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1713×	`rules-43_binary64`
966×	`rules-42_binary64`
924×	`fma-neg_binary64`
499×	`rules-40_binary64`
485×	`rules-41_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	133	45
2	442	45
3	1826	43
4	3904	28
5	4343	15
6	4678	15
7	4906	15

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

18.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.3b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 112 to 73 computations (34.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.2b	(/.f64 (*.f64 K (+.f64 m n)) 2)
✓	37.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series56.0ms (0.5%)

Counts

4 → 156

Calls

4 calls:

24.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
7.0ms	(*.f64 K (+.f64 m n))

rewrite91.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

292×	`log1p-udef_binary64`
162×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`
151×	`egg-rr`

Counts

4 → 151

Calls

4 calls:

88.0ms	(*.f64 K (+.f64 m n))
88.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
88.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
88.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	45
1	353	45
2	4766	45
3	5175	45
0	0	0
1	0	0

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
429×	`fma-def_binary64`
390×	`rules-7-rev_binary64`
360×	`rules-20_binary64`
329×	`rules-13_binary64`

Counts

307 → 216

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	159	2838
1	1205	2734
2	5442	2734

prune241.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	212	4	216
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	213	4	217

Error

0.8b

Counts

217 → 4

Alt Table

Status	Error	Program
	46.0b	(.f64 (cos.f64 (-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 (.f64 K (+.f64 m n)) 2)))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	11.4b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	1.2b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	18.3b	(.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 8616 to 4245 computations (50.7% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series128.0ms (1.2%)

Counts

1 → 48

Calls

1 calls:

128.0ms

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

rewrite93.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

970×	`prod-diff_binary64`
172×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`
159×	`add-cbrt-cube_binary64`

Counts

1 → 103

Calls

1 calls:

89.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	378	24
2	4527	24
3	6316	24
0	0	0
1	0	0

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

717×	`rules-40_binary64`
717×	`rules-41_binary64`
717×	`rules-42_binary64`
717×	`rules-43_binary64`
327×	`rules-21_binary64`

Counts

151 → 137

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	1645
1	431	1514
2	2338	1514
3	4970	1514

prune327.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	199	4	203

Error

0.8b

Counts

203 → 4

Alt Table

Status	Error	Program
	46.0b	(.f64 (cos.f64 (-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 (.f64 K (+.f64 m n)) 2)))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	11.4b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	1.2b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	18.3b	(.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 7496 to 3411 computations (54.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/2 (.f64 n K)) M)
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.2b	(.f64 1/2 (.f64 n K))
✓	28.6b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series23.0ms (0.2%)

Counts

3 → 21

Calls

3 calls:

12.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
6.0ms	(-.f64 (.f64 1/2 (.f64 n K)) M)
4.0ms	(.f64 1/2 (.f64 n K))

rewrite74.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

856×	`fma-neg_binary64`
709×	`prod-diff_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`
138×	`egg-rr`

Counts

3 → 138

Calls

3 calls:

72.0ms	(-.f64 (.f64 1/2 (.f64 n K)) M)
72.0ms	(.f64 1/2 (.f64 n K))
71.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	225	29
2	2978	29
3	5343	29
0	0	0
1	0	0

simplify43.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

764×	`rules-11_binary64`
682×	`fma-def_binary64`
355×	`rules-40_binary64`
355×	`rules-41_binary64`
355×	`rules-42_binary64`

Counts

159 → 156

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	419
1	339	413
2	1461	413
3	6164	413

prune467.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	217	5	222

Error

0.8b

Counts

222 → 5

Alt Table

Status	Error	Program
▶	11.4b	(.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) 2)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	46.0b	(.f64 (cos.f64 (-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 (.f64 K (+.f64 m n)) 2)))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	33.8b	(.f64 (cos.f64 (-.f64 (pow.f64 (sqrt.f64 (.f64 1/2 (*.f64 n K))) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	1.2b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	18.3b	(.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 7962 to 4134 computations (48.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M))) 2))
✓	0.4b	(pow.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) 2)
✓	0.4b	(cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))
	28.6b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series2.0s (18.6%)

Counts

3 → 108

Calls

3 calls:

1.1s

(pow.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) 2)

954.0ms

(cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))

13.0ms

(*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) 2))

rewrite90.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

770×	`prod-diff_binary64`
133×	`egg-rr`
130×	`add-sqr-sqrt_binary64`
125×	`log1p-expm1-u_binary64`
125×	`expm1-log1p-u_binary64`

Counts

3 → 133

Calls

3 calls:

86.0ms

(*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) 2))

86.0ms

(pow.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) 2)

86.0ms

(cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	296	41
2	3606	41
3	4902	41
0	0	0
1	0	0

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

438×	`fma-neg_binary64`
365×	`rules-20_binary64`
318×	`fma-def_binary64`
309×	`rules-7-rev_binary64`
277×	`rules-40_binary64`

Counts

241 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	181	3170
1	1287	3131
2	4905	3131

prune559.0ms (5.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	352	1	353
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	353	5	358

Error

0.8b

Counts

358 → 5

Alt Table

Status	Error	Program
	11.4b	(.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (pow.f64 (-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))))) 1) 2)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	46.0b	(.f64 (cos.f64 (-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 (.f64 K (+.f64 m n)) 2)))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	33.8b	(.f64 (cos.f64 (-.f64 (pow.f64 (sqrt.f64 (.f64 1/2 (*.f64 n K))) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	1.2b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	18.3b	(.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 19686 to 11310 computations (42.5% saved)

regimes1.0s (9.4%)

Accuracy

Total 0.2b remaining (17.1%)

Threshold costs 0.2b (17.1%)

Counts

149 → 1

Compiler

Compiled 27872 to 20274 computations (27.3% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	17	31

end120.0ms (1.1%)

Compiler: Compiled 234 to 169 computations (27.8% saved)

Details

analyze2.9s (26.3%)

sample2.3s (20.8%)

simplify96.0ms (0.9%)

prune3.0ms (0%)

localize20.0ms (0.2%)

series56.0ms (0.5%)

rewrite91.0ms (0.8%)

simplify68.0ms (0.6%)

prune241.0ms (2.2%)

localize14.0ms (0.1%)

series128.0ms (1.2%)

rewrite93.0ms (0.9%)

simplify69.0ms (0.6%)

prune327.0ms (3%)

localize19.0ms (0.2%)

series23.0ms (0.2%)

rewrite74.0ms (0.7%)

simplify43.0ms (0.4%)

prune467.0ms (4.3%)

localize23.0ms (0.2%)

series2.0s (18.6%)

rewrite90.0ms (0.8%)

simplify76.0ms (0.7%)

prune559.0ms (5.1%)

regimes1.0s (9.4%)

simplify1.0ms (0%)

end120.0ms (1.1%)

Profiling