Details

analyze2.6s (23.2%)

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 (38.1%)

Results

2.2s	1996×	body	1024	valid
1.1s	4731×	body	128	valid
684.0ms	985×	body	512	valid
266.0ms	541×	body	256	valid
5.0ms	3×	body	2048	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify42.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l/_binary64`
443×	`associate-/l*_binary64`
398×	`times-frac_binary64`
330×	`unswap-sqr_binary64`
265×	`associate-*l/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	37	32
2	89	32
3	253	32
4	968	32
5	3686	32
6	3897	32
7	4521	32
8	4720	32
9	4865	32

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

10.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.1b	(.f64 -2 (.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (*.f64 J (cos.f64 (/.f64 K 2)))))

Compiler

Compiled 96 to 76 computations (20.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 J (cos.f64 (/.f64 K 2)))
✓	0.1b	(/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))
✓	9.4b	(.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (.f64 J (cos.f64 (/.f64 K 2))))

series129.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

81.0ms	(.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (.f64 J (cos.f64 (/.f64 K 2))))
40.0ms	(/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))
8.0ms	(*.f64 J (cos.f64 (/.f64 K 2)))

rewrite59.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

237×	`expm1-udef_binary64`
237×	`log1p-udef_binary64`
210×	`log-pow_binary64`
137×	`prod-diff_binary64`
134×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	53
1	271	53
2	3455	53

Stop Event

1×	node limit

Counts

3 → 73

Calls

3 calls:

58.0ms	(*.f64 J (cos.f64 (/.f64 K 2)))
58.0ms	(/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))
57.0ms	(.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (.f64 J (cos.f64 (/.f64 K 2))))

simplify54.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

767×	`associate-/l*_binary64`
677×	`fma-def_binary64`
293×	`cancel-sign-sub-inv_binary64`
164×	`associate-/r/_binary64`
140×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2762
1	542	2621
2	1956	2561

Stop Event

1×	node limit

Counts

169 → 127

prune135.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	145	6	151

Error

0.0b

Counts

151 → 6

Alt Table

Status	Error	Program
✓	10.1b	(.f64 -2 (.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (*.f64 J (cos.f64 (/.f64 K 2)))))
	46.1b	(.f64 -2 (-.f64 (.f64 U -1/2) (.f64 (/.f64 J (/.f64 U J)) (pow.f64 (cos.f64 (.f64 1/2 K)) 2))))
	46.0b	(.f64 -2 (.f64 1/2 U))
	44.4b	(.f64 -2 (cbrt.f64 (pow.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))))) 3)))
	35.2b	(.f64 -2 (pow.f64 (sqrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J))))))) 2))
▶	11.2b	(.f64 -2 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J))))))) 3))

Compiler

Compiled 4857 to 3652 computations (24.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))
✓	0.6b	(cbrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))))))
✓	0.8b	(pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J))))))) 3)
✓	9.4b	(.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))))

series980.0ms (8.7%)

Counts

4 → 112

Calls

4 calls:

482.0ms	(pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J))))))) 3)
379.0ms	(cbrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))))))
77.0ms	(.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))))
41.0ms	(/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))

rewrite74.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

291×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
158×	`log1p-expm1-u_binary64`
158×	`expm1-log1p-u_binary64`
158×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	96
1	365	96
2	4254	96

Stop Event

1×	node limit

Counts

4 → 126

Calls

4 calls:

71.0ms	(/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))
71.0ms	(cbrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))))))
71.0ms	(pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J))))))) 3)
71.0ms	(.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (.f64 2 J)))))

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

316×	`fma-neg_binary64`
313×	`associate-r_binary64`
309×	`fma-def_binary64`
247×	`associate-l_binary64`
228×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	5434
1	1164	4893
2	4545	4873

Stop Event

1×	node limit

Counts

238 → 219

prune225.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	216	3	219
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	217	8	225

Error

0.0b

Counts

225 → 8

Alt Table

Status	Error	Program
✓	10.1b	(.f64 -2 (.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (*.f64 J (cos.f64 (/.f64 K 2)))))
	21.9b	(.f64 -2 (.f64 (sqrt.f64 (cos.f64 (.f64 K 1/2))) (.f64 (sqrt.f64 (cos.f64 (.f64 K 1/2))) (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (.f64 K 1/2))))))))
	46.1b	(.f64 -2 (-.f64 (.f64 U -1/2) (.f64 (/.f64 J (/.f64 U J)) (pow.f64 (cos.f64 (.f64 1/2 K)) 2))))
	46.0b	(.f64 -2 (.f64 1/2 U))
	44.4b	(.f64 -2 (cbrt.f64 (pow.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))))) 3)))
✓	11.2b	(.f64 -2 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J))))))) 3))
	11.3b	(.f64 -2 (pow.f64 (.f64 (cbrt.f64 (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (.f64 K 1/2)))))) (cbrt.f64 (cos.f64 (.f64 K 1/2)))) 3))
▶	10.3b	(.f64 -2 (.f64 (.f64 (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (.f64 K 1/2))))) (cbrt.f64 (pow.f64 (cos.f64 (.f64 K 1/2)) 2))) (cbrt.f64 (cos.f64 (.f64 K 1/2)))))

Compiler

Compiled 9703 to 7476 computations (23% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (cos.f64 (*.f64 K 1/2)) 2)
✓	0.3b	(cbrt.f64 (cos.f64 (*.f64 K 1/2)))
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 (*.f64 K 1/2)) 2))
✓	9.4b	(.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (*.f64 K 1/2)))))

series156.0ms (1.4%)

Counts

4 → 72

Calls

4 calls:

65.0ms	(.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (*.f64 K 1/2)))))
52.0ms	(cbrt.f64 (pow.f64 (cos.f64 (*.f64 K 1/2)) 2))
35.0ms	(cbrt.f64 (cos.f64 (*.f64 K 1/2)))
3.0ms	(pow.f64 (cos.f64 (*.f64 K 1/2)) 2)

rewrite63.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

285×	`log1p-udef_binary64`
176×	`prod-diff_binary64`
164×	`add-sqr-sqrt_binary64`
154×	`add-cbrt-cube_binary64`
154×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	345	49
2	4282	49

Stop Event

1×	node limit

Counts

4 → 86

Calls

4 calls:

62.0ms	(pow.f64 (cos.f64 (*.f64 K 1/2)) 2)
62.0ms	(cbrt.f64 (cos.f64 (*.f64 K 1/2)))
62.0ms	(cbrt.f64 (pow.f64 (cos.f64 (*.f64 K 1/2)) 2))
62.0ms	(.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (*.f64 K 1/2)))))

simplify47.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

723×	`associate-/l*_binary64`
541×	`associate-/r*_binary64`
493×	`fma-def_binary64`
275×	`cancel-sign-sub-inv_binary64`
141×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2060
1	495	1962
2	1742	1891

Stop Event

1×	node limit

Counts

158 → 144

prune190.0ms (1.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	144	8	152

Error

Counts

152 → 8

Alt Table

Status	Error	Program
✓	10.1b	(.f64 -2 (.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (*.f64 J (cos.f64 (/.f64 K 2)))))
	21.9b	(.f64 -2 (.f64 (sqrt.f64 (cos.f64 (.f64 K 1/2))) (.f64 (sqrt.f64 (cos.f64 (.f64 K 1/2))) (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (.f64 K 1/2))))))))
	46.1b	(.f64 -2 (-.f64 (.f64 U -1/2) (.f64 (/.f64 J (/.f64 U J)) (pow.f64 (cos.f64 (.f64 1/2 K)) 2))))
▶	10.6b	(.f64 -2 (.f64 (.f64 (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (.f64 K 1/2))))) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 K 1/2))) 2))) 1)) (cbrt.f64 (cos.f64 (.f64 K 1/2)))))
	46.0b	(.f64 -2 (.f64 1/2 U))
	44.4b	(.f64 -2 (cbrt.f64 (pow.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))))) 3)))
✓	11.2b	(.f64 -2 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J))))))) 3))
✓	10.3b	(.f64 -2 (.f64 (.f64 (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (.f64 K 1/2))))) (cbrt.f64 (pow.f64 (cos.f64 (.f64 K 1/2)) 2))) (cbrt.f64 (cos.f64 (.f64 K 1/2)))))

Compiler

Compiled 6021 to 4786 computations (20.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (cbrt.f64 (cos.f64 (*.f64 K 1/2))) 2)
	0.3b	(cbrt.f64 (cos.f64 (*.f64 K 1/2)))
✓	0.3b	(-.f64 (exp.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cos.f64 (*.f64 K 1/2))) 2))) 1)
	9.4b	(.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (*.f64 K 1/2)))))

series324.0ms (2.9%)

Counts

2 → 24

Calls

2 calls:

284.0ms	(-.f64 (exp.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cos.f64 (*.f64 K 1/2))) 2))) 1)
40.0ms	(pow.f64 (cbrt.f64 (cos.f64 (*.f64 K 1/2))) 2)

rewrite59.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

851×	`expm1-log1p-u_binary64`
850×	`log1p-expm1-u_binary64`
284×	`prod-diff_binary64`
101×	`add-sqr-sqrt_binary64`
96×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	226	22
2	2433	22

Stop Event

1×	node limit

Counts

2 → 74

Calls

2 calls:

57.0ms	(pow.f64 (cbrt.f64 (cos.f64 (*.f64 K 1/2))) 2)
57.0ms	(-.f64 (exp.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cos.f64 (*.f64 K 1/2))) 2))) 1)

simplify39.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

403×	`distribute-rgt-neg-in_binary64`
345×	`distribute-lft-neg-in_binary64`
272×	`*-commutative_binary64`
227×	`sub-neg_binary64`
226×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	280
1	74	280
2	165	276
3	500	272
4	2077	272
5	4495	272

Stop Event

1×	node limit

Counts

98 → 49

prune227.0ms (2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	162	8	170

Error

Counts

170 → 8

Alt Table

Status	Error	Program
✓	10.1b	(.f64 -2 (.f64 (hypot.f64 1 (/.f64 U (.f64 2 (.f64 J (cos.f64 (/.f64 K 2)))))) (*.f64 J (cos.f64 (/.f64 K 2)))))
	21.9b	(.f64 -2 (.f64 (sqrt.f64 (cos.f64 (.f64 K 1/2))) (.f64 (sqrt.f64 (cos.f64 (.f64 K 1/2))) (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (.f64 K 1/2))))))))
	46.1b	(.f64 -2 (-.f64 (.f64 U -1/2) (.f64 (/.f64 J (/.f64 U J)) (pow.f64 (cos.f64 (.f64 1/2 K)) 2))))
✓	10.6b	(.f64 -2 (.f64 (.f64 (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (.f64 K 1/2))))) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 K 1/2))) 2))) 1)) (cbrt.f64 (cos.f64 (.f64 K 1/2)))))
	46.0b	(.f64 -2 (.f64 1/2 U))
	44.4b	(.f64 -2 (cbrt.f64 (pow.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J)))))) 3)))
✓	11.2b	(.f64 -2 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 K 1/2)) (.f64 J (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (.f64 K 1/2)) (*.f64 2 J))))))) 3))
✓	10.3b	(.f64 -2 (.f64 (.f64 (.f64 J (hypot.f64 1 (/.f64 (/.f64 U (.f64 J 2)) (cos.f64 (.f64 K 1/2))))) (cbrt.f64 (pow.f64 (cos.f64 (.f64 K 1/2)) 2))) (cbrt.f64 (cos.f64 (.f64 K 1/2)))))

Compiler

Compiled 7253 to 5925 computations (18.3% saved)

regimes451.0ms (4%)

Accuracy

Total 8.6b remaining (99.7%)

Threshold costs 0b (0%)

Counts

43 → 3

Compiler

Compiled 6722 to 5430 computations (19.2% saved)

bsearch174.0ms (1.5%)

Steps

Iters	Range		Point
9	-2.039467559549915e-265	-3.126946728156957e-272	-3.434501974673543e-266
9	-4.57114241983531e-169	-1.6115822011707699e-174	-1.6294791308598196e-174

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	83
1	33	83

Stop Event

1×

saturated

end786.0ms (6.9%)

Compiler: Compiled 324 to 259 computations (20.1% saved)

Details

analyze2.6s (23.2%)

sample4.3s (38.1%)

simplify42.0ms (0.4%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series129.0ms (1.1%)

rewrite59.0ms (0.5%)

simplify54.0ms (0.5%)

prune135.0ms (1.2%)

localize17.0ms (0.1%)

series980.0ms (8.7%)

rewrite74.0ms (0.7%)

simplify94.0ms (0.8%)

prune225.0ms (2%)

localize17.0ms (0.2%)

series156.0ms (1.4%)

rewrite63.0ms (0.6%)

simplify47.0ms (0.4%)

prune190.0ms (1.7%)

localize20.0ms (0.2%)

series324.0ms (2.9%)

rewrite59.0ms (0.5%)

simplify39.0ms (0.3%)

prune227.0ms (2%)

regimes451.0ms (4%)

bsearch174.0ms (1.5%)

simplify3.0ms (0%)

end786.0ms (6.9%)

Profiling