Details

analyze2.6s (21.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 28 to 23 computations (17.9% saved)

sample4.3s (35.9%)

Results

2.3s	2135×	body	1024	valid
964.0ms	4569×	body	128	valid
680.0ms	1048×	body	512	valid
229.0ms	501×	body	256	valid
6.0ms	3×	body	2048	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1043×	`associate-*l/_binary64`
692×	`associate-/l/_binary64`
651×	`associate-/r/_binary64`
474×	`associate-/l*_binary64`
398×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	37	32
2	83	32
3	208	32
4	742	32
5	2273	32
6	2474	32
7	2875	32
8	3015	32
9	3126	32
10	3234	32
11	4835	32
12	4953	32
13	4880	32

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

9.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 96 to 76 computations (20.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
✓	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	8.5b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series157.0ms (1.3%)

Counts

4 → 120

Calls

4 calls:

94.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
41.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
12.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
10.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

rewrite110.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

258×	`prod-diff_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
219×	`log-pow_binary64`
161×	`add-sqr-sqrt_binary64`

Counts

4 → 100

Calls

4 calls:

108.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
108.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
108.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
107.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	71
1	332	71
2	3564	71
3	4970	71
4	5134	71
0	0	0
1	0	0

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
616×	`fma-neg_binary64`
345×	`cancel-sign-sub-inv_binary64`
218×	`neg-mul-1_binary64`
192×	`associate-/r/_binary64`

Counts

220 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	3231
1	559	3137
2	2104	3011
3	4617	3003
4	5065	3003

prune134.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	135	7	142

Error

0.0b

Counts

142 → 7

Alt Table

Status	Error	Program
▶	10.1b	(pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)
	47.4b	(neg.f64 U)
✓	9.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	37.4b	(pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 2)
	34.9b	(.f64 (-.f64 (.f64 1/4 (.f64 (pow.f64 K 2) J)) (.f64 2 J)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	47.7b	U
	42.9b	(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 4696 to 3527 computations (24.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	0.5b	(cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))))))
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)
✓	8.5b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))

series2.1s (17.6%)

Counts

3 → 108

Calls

3 calls:

1.2s

(pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)

854.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))))))

98.0ms

(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))

rewrite78.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

275×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`

Counts

3 → 87

Calls

3 calls:

76.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))))))

76.0ms

(pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)

76.0ms

(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	98
1	338	98
2	3911	98
3	4899	98
0	0	0
1	0	0

simplify127.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

437×	`fma-def_binary64`
387×	`times-frac_binary64`
331×	`associate-/l*_binary64`
295×	`associate-/r*_binary64`
250×	`*-commutative_binary64`

Counts

195 → 215

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	614	9058
1	1848	8304
2	4960	8304

prune401.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	271	7	278

Error

0.0b

Counts

278 → 7

Alt Table

Status	Error	Program
✓	10.1b	(pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)
	47.4b	(neg.f64 U)
✓	9.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	37.4b	(pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 2)
▶	34.9b	(.f64 (-.f64 (.f64 1/4 (.f64 (pow.f64 K 2) J)) (.f64 2 J)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	47.7b	U
	42.9b	(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 13424 to 10789 computations (19.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	5.4b	(.f64 (-.f64 (.f64 1/4 (.f64 (pow.f64 K 2) J)) (.f64 2 J)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
✓	7.7b	(*.f64 (pow.f64 K 2) J)

series103.0ms (0.9%)

Counts

2 → 36

Calls

2 calls:

95.0ms	(.f64 (-.f64 (.f64 1/4 (.f64 (pow.f64 K 2) J)) (.f64 2 J)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
7.0ms	(*.f64 (pow.f64 K 2) J)

rewrite72.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

335×	`log1p-udef_binary64`
189×	`add-sqr-sqrt_binary64`
182×	`log1p-expm1-u_binary64`
182×	`expm1-log1p-u_binary64`
179×	`add-log-exp_binary64`

Counts

2 → 38

Calls

2 calls:

71.0ms	(.f64 (-.f64 (.f64 1/4 (.f64 (pow.f64 K 2) J)) (.f64 2 J)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
71.0ms	(*.f64 (pow.f64 K 2) J)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	43
1	394	40
2	4869	40
3	5302	40
0	0	0
1	0	0

simplify98.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

470×	`fma-neg_binary64`
436×	`cancel-sign-sub-inv_binary64`
280×	`sub-neg_binary64`
213×	`unswap-sqr_binary64`
210×	`fma-def_binary64`

Counts

74 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	3459
1	731	3361
2	3005	2970
3	4768	2959
4	4968	2959

prune159.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	150	7	157

Error

0.0b

Counts

157 → 7

Alt Table

Status	Error	Program
✓	10.1b	(pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 3)
	47.4b	(neg.f64 U)
✓	9.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
▶	37.4b	(pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 2)
✓	34.9b	(.f64 (-.f64 (.f64 1/4 (.f64 (pow.f64 K 2) J)) (.f64 2 J)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	47.7b	U
	42.9b	(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 6457 to 4686 computations (27.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 U (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))
	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	0.2b	(pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 2)
	8.5b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))

series223.0ms (1.8%)

Counts

2 → 56

Calls

2 calls:

180.0ms	(pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 2)
42.0ms	(/.f64 U (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))

rewrite126.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

260×	`expm1-udef_binary64`
260×	`log1p-udef_binary64`
216×	`fma-neg_binary64`
153×	`prod-diff_binary64`
147×	`add-sqr-sqrt_binary64`

Counts

2 → 85

Calls

2 calls:

124.0ms	(/.f64 U (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))
124.0ms	(pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	47
1	315	47
2	3687	47
3	4911	47
4	4990	47
5	5015	47
0	0	0
1	0	0

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

930×	`associate-/l*_binary64`
866×	`fma-def_binary64`
220×	`cancel-sign-sub-inv_binary64`
214×	`associate-/r/_binary64`
151×	`fma-neg_binary64`

Counts

141 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2333
1	564	2074
2	2137	1971
3	5933	1971

prune249.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	0	3	3
Picked	0	1	1
Done	1	2	3
Total	231	7	238

Error

0.0b

Counts

238 → 7

Alt Table

Status	Error	Program
	47.4b	(neg.f64 U)
✓	9.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	37.4b	(pow.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))) 2)
✓	34.9b	(.f64 (-.f64 (.f64 1/4 (.f64 (pow.f64 K 2) J)) (.f64 2 J)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	47.7b	U
	42.9b	(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	37.6b	(.f64 (.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))))))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))))))))

Compiler

Compiled 8764 to 6679 computations (23.8% saved)

regimes453.0ms (3.8%)

Accuracy

Total 9.3b remaining (99.5%)

Threshold costs 0b (0%)

Counts

55 → 2

Compiler

Compiled 7124 to 5730 computations (19.6% saved)

bsearch46.0ms (0.4%)

Steps

Iters	Range		Point
5	1.8496974450358866e+172	7.358482293982686e+172	7.165885222303086e+172

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	41
1	31	41
2	33	41
3	34	41
4	33	41

end141.0ms (1.2%)

Compiler: Compiled 248 to 196 computations (21% saved)

Details

analyze2.6s (21.9%)

sample4.3s (35.9%)

simplify79.0ms (0.7%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series157.0ms (1.3%)

rewrite110.0ms (0.9%)

simplify96.0ms (0.8%)

prune134.0ms (1.1%)

localize12.0ms (0.1%)

series2.1s (17.6%)

rewrite78.0ms (0.6%)

simplify127.0ms (1.1%)

prune401.0ms (3.3%)

localize15.0ms (0.1%)

series103.0ms (0.9%)

rewrite72.0ms (0.6%)

simplify98.0ms (0.8%)

prune159.0ms (1.3%)

localize11.0ms (0.1%)

series223.0ms (1.8%)

rewrite126.0ms (1%)

simplify63.0ms (0.5%)

prune249.0ms (2.1%)

regimes453.0ms (3.8%)

bsearch46.0ms (0.4%)

simplify3.0ms (0%)

end141.0ms (1.2%)

Profiling