Details

analyze1.6s (18%)

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
18.7%	81.1%	0.2%	10
21.8%	67.1%	11.1%	11
21.8%	67.1%	11.1%	12
32.7%	56.1%	11.1%	13
35.1%	53%	11.9%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample5.6s (64%)

Alt Table

Status	Error	Program
▶	15.7b	(+.f64 (.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)

Results

1.4s	2154×	body	1024	invalid
1.4s	1725×	body	1024	valid
747.0ms	4551×	body	128	valid
616.0ms	1246×	body	512	valid
501.0ms	1070×	body	512	invalid
451.0ms	2726×	body	128	invalid
203.0ms	683×	body	256	valid
161.0ms	536×	body	256	invalid
64.0ms	51×	body	2048	valid

Compiler

Compiled 97 to 72 computations (25.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	0.0b	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
✓	4.3b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series38.0ms (0.4%)

Counts

3 → 68

Calls

3 calls:

28.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
8.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite78.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite
3×	egg-rewrite

Rules

141×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`
131×	`add-log-exp_binary64`
129×	`add-cbrt-cube_binary64`

Counts

3 → 0

Calls

3 calls:

77.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
77.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
77.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	277	18
2	32	18
0	6	6
1	130	6
2	71	6
0	13	17
1	277	17
2	32	17
0	8	9
1	169	9
2	73	9
0	0	0
1	0	0

prune59.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Error

0.0b

Counts

69 → 3

Alt Table

Status	Error	Program
	0.6b	(+.f64 (.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) U)
▶	0.6b	(+.f64 (.f64 (.f64 J (+.f64 (.f64 2 l) (.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2))) U)
✓	15.7b	(+.f64 (.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 1401 to 752 computations (46.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 J (+.f64 (.f64 2 l) (.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2))) U)
✓	0.0b	(.f64 J (+.f64 (.f64 2 l) (*.f64 1/3 (pow.f64 l 3))))
✓	0.1b	(.f64 (.f64 J (+.f64 (.f64 2 l) (.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2)))
✓	0.2b	(*.f64 1/3 (pow.f64 l 3))

series136.0ms (1.5%)

Counts

4 → 108

Calls

4 calls:

67.0ms	(+.f64 (.f64 (.f64 J (+.f64 (.f64 2 l) (.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2))) U)
47.0ms	(.f64 (.f64 J (+.f64 (.f64 2 l) (.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2)))
17.0ms	(.f64 J (+.f64 (.f64 2 l) (*.f64 1/3 (pow.f64 l 3))))
4.0ms	(*.f64 1/3 (pow.f64 l 3))

rewrite81.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

327×	`log1p-udef_binary64`
186×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`
174×	`add-log-exp_binary64`

Counts

4 → 92

Calls

4 calls:

78.0ms	(+.f64 (.f64 (.f64 J (+.f64 (.f64 2 l) (.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2))) U)
78.0ms	(.f64 J (+.f64 (.f64 2 l) (*.f64 1/3 (pow.f64 l 3))))
78.0ms	(.f64 (.f64 J (+.f64 (.f64 2 l) (.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2)))
78.0ms	(*.f64 1/3 (pow.f64 l 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	66
1	379	66
2	4661	66
3	5052	66
0	0	0
1	0	0

prune188.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	200	3	203

Error

Counts

203 → 3

Alt Table

Status	Error	Program
	0.6b	(+.f64 (.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) U)
✓	15.7b	(+.f64 (.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)
▶	0.6b	(+.f64 (.f64 (fma.f64 J (.f64 l 2) (.f64 (.f64 1/3 (pow.f64 l 3)) J)) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 4907 to 3536 computations (27.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (fma.f64 J (.f64 l 2) (.f64 (.f64 1/3 (pow.f64 l 3)) J)) (cos.f64 (/.f64 K 2))) U)
✓	0.1b	(.f64 (fma.f64 J (.f64 l 2) (.f64 (.f64 1/3 (pow.f64 l 3)) J)) (cos.f64 (/.f64 K 2)))
✓	0.2b	(*.f64 1/3 (pow.f64 l 3))
✓	5.1b	(.f64 (.f64 1/3 (pow.f64 l 3)) J)

series143.0ms (1.6%)

Counts

4 → 108

Calls

4 calls:

72.0ms	(+.f64 (.f64 (fma.f64 J (.f64 l 2) (.f64 (.f64 1/3 (pow.f64 l 3)) J)) (cos.f64 (/.f64 K 2))) U)
56.0ms	(.f64 (fma.f64 J (.f64 l 2) (.f64 (.f64 1/3 (pow.f64 l 3)) J)) (cos.f64 (/.f64 K 2)))
13.0ms	(.f64 (.f64 1/3 (pow.f64 l 3)) J)
3.0ms	(*.f64 1/3 (pow.f64 l 3))

rewrite79.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

313×	`expm1-udef_binary64`
313×	`log1p-udef_binary64`
177×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`

Counts

4 → 80

Calls

4 calls:

77.0ms	(+.f64 (.f64 (fma.f64 J (.f64 l 2) (.f64 (.f64 1/3 (pow.f64 l 3)) J)) (cos.f64 (/.f64 K 2))) U)
77.0ms	(.f64 (fma.f64 J (.f64 l 2) (.f64 (.f64 1/3 (pow.f64 l 3)) J)) (cos.f64 (/.f64 K 2)))
77.0ms	(*.f64 1/3 (pow.f64 l 3))
76.0ms	(.f64 (.f64 1/3 (pow.f64 l 3)) J)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	68
1	363	66
2	4217	66
3	5004	66
0	0	0
1	0	0

prune173.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	188	3	191

Error

Counts

191 → 3

Alt Table

Status	Error	Program
▶	0.6b	(+.f64 (.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) U)
✓	15.7b	(+.f64 (.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)
✓	0.6b	(+.f64 (.f64 (fma.f64 J (.f64 l 2) (.f64 (.f64 1/3 (pow.f64 l 3)) J)) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 4656 to 3344 computations (28.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))))
✓	0.1b	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))

series57.0ms (0.6%)

Counts

3 → 52

Calls

3 calls:

25.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
23.0ms	(.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))))
8.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

rewrite58.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

561×	`log-prod_binary64`
280×	`pow2_binary64`
199×	`pow1/3_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`

Counts

3 → 57

Calls

3 calls:

56.0ms	(.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))))
56.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
56.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	222	36
2	2511	36
3	4955	36
0	0	0
1	0	0

prune89.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	109	3	112

Error

Counts

112 → 3

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) U)
✓	15.7b	(+.f64 (.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)
✓	0.6b	(+.f64 (.f64 (fma.f64 J (.f64 l 2) (.f64 (.f64 1/3 (pow.f64 l 3)) J)) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 1745 to 1205 computations (30.9% saved)

regimes290.0ms (3.3%)

Accuracy

Total 0.4b remaining (87.3%)

Threshold costs 0.4b (87.3%)

Counts

29 → 1

Compiler

Compiled 6120 to 4690 computations (23.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	23
1	21	23
2	20	23

end78.0ms (0.9%)

Compiler: Compiled 98 to 73 computations (25.5% saved)

Iter	Nodes	Cost
0	13	18
1	277	18
2	32	18
0	6	6
1	130	6
2	71	6
0	13	17
1	277	17
2	32	17
0	8	9
1	169	9
2	73	9
0	0	0
1	0	0

Iter	Nodes	Cost
0	13	18
1	277	18
2	32	18
0	6	6
1	130	6
2	71	6
0	13	17
1	277	17
2	32	17
0	8	9
1	169	9
2	73	9
0	0	0
1	0	0

Details

analyze1.6s (18%)

sample5.6s (64%)

localize10.0ms (0.1%)

series38.0ms (0.4%)

rewrite78.0ms (0.9%)

prune59.0ms (0.7%)

localize11.0ms (0.1%)

series136.0ms (1.5%)

rewrite81.0ms (0.9%)

prune188.0ms (2.1%)

localize13.0ms (0.1%)

series143.0ms (1.6%)

rewrite79.0ms (0.9%)

prune173.0ms (2%)

localize8.0ms (0.1%)

series57.0ms (0.6%)

rewrite58.0ms (0.7%)

prune89.0ms (1%)

regimes290.0ms (3.3%)

simplify2.0ms (0%)

end78.0ms (0.9%)

Profiling

Iter	Nodes	Cost
0	13	18
1	277	18
2	32	18
0	6	6
1	130	6
2	71	6
0	13	17
1	277	17
2	32	17
0	8	9
1	169	9
2	73	9
0	0	0
1	0	0