Details

analyze2.7s (23.9%)

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)

sample115.0ms (1%)

Algorithm

1×

intervals

Results

62.0ms	70×	body	1024	valid
23.0ms	148×	body	128	valid
10.0ms	20×	body	512	valid
8.0ms	18×	body	256	valid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify93.0ms (0.8%)

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 → 1

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

8.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.4b	(.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 72 to 57 computations (20.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)))
7.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

rewrite224.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

8.3b

Rules

57×	`pow1_binary64`
36×	`add-exp-log_binary64`
35×	`pow-prod-down_binary64`
28×	`add-sqr-sqrt_binary64`
22×	`add-cbrt-cube_binary64`

Counts

4 → 154

Calls

4 calls:

18.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
17.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
17.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
14.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 3630 to 2811 computations (22.6% saved)

series206.0ms (1.8%)

Error

0.1b

Counts

4 → 43

Calls

4 calls:

113.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
36.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
20.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
17.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2502 to 1983 computations (20.7% saved)

simplify129.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-def_binary64`
439×	`unswap-sqr_binary64`
273×	`associate-l_binary64`
256×	`fma-neg_binary64`
238×	`associate-r_binary64`

Counts

197 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	3586
1	572	3185
2	2277	3145
3	4774	3141
4	5119	3141

prune113.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	111	8	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	9	120

Error

2.7b

Counts

120 → 9

Alt Table

Status	Error	Program
✓	8.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	9.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	8.8b	(.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
	43.3b	(neg.f64 U)
	44.6b	(cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 3))
	31.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 J (-.f64 (fma.f64 1/192 (pow.f64 K 4) 2) (fma.f64 1/4 (.f64 K K) (.f64 1/23040 (pow.f64 K 6))))))))
▶	8.8b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	32.9b	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) 2)) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	19.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 J (fma.f64 (*.f64 K K) -1/4 2)))))

Compiler

Compiled 2816 to 2160 computations (23.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
7.8b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

rewrite205.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

25×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`pow1_binary64`
13×	`pow1/3_binary64`

Counts

4 → 126

Calls

4 calls:

19.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
12.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
10.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
10.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3866 to 3126 computations (19.1% saved)

series177.0ms (1.6%)

Error

2.7b

Counts

4 → 29

Calls

4 calls:

115.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
13.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
13.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
13.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2208 to 1792 computations (18.8% saved)

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

535×	`unswap-sqr_binary64`
426×	`fma-def_binary64`
403×	`*-commutative_binary64`
342×	`fma-neg_binary64`
324×	`times-frac_binary64`

Counts

155 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	2408
1	347	2212
2	1207	2139
3	3557	2135
4	5451	2135

prune63.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	64	8	72

Error

2.7b

Counts

72 → 8

Alt Table

Status	Error	Program
✓	8.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	9.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
▶	8.8b	(.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
	43.3b	(neg.f64 U)
	19.1b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 1/6) (pow.f64 (cos.f64 (/.f64 K 2)) 1/6))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	31.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 J (-.f64 (fma.f64 1/192 (pow.f64 K 4) 2) (fma.f64 1/4 (.f64 K K) (.f64 1/23040 (pow.f64 K 6))))))))
	32.9b	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) 2)) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	19.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 J (fma.f64 (*.f64 K K) -1/4 2)))))

Compiler

Compiled 1882 to 1469 computations (21.9% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))))))
8.1b	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
8.1b	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))))
8.1b	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))))

rewrite201.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

24×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`pow1/3_binary64`
12×	`log1p-expm1-u_binary64`

Counts

4 → 125

Calls

4 calls:

16.0ms	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))))))
13.0ms	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))))
10.0ms	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))))
9.0ms	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))

Compiler

Compiled 5429 to 4286 computations (21.1% saved)

series482.0ms (4.3%)

Error

2.7b

Counts

4 → 43

Calls

4 calls:

138.0ms	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))))))
101.0ms	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))))
100.0ms	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))))
99.0ms	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))

Compiler

Compiled 7032 to 5694 computations (19% saved)

simplify125.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-def_binary64`
496×	`*-commutative_binary64`
261×	`unswap-sqr_binary64`
214×	`times-frac_binary64`
195×	`associate-/l*_binary64`

Counts

168 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	4478
1	434	3826
2	1378	3617
3	3695	3613
4	4999	3613

prune128.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	100	8	108

Error

2.7b

Counts

108 → 8

Alt Table

Status	Error	Program
✓	8.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
▶	9.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	8.8b	(.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
	43.3b	(neg.f64 U)
	19.1b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 1/6) (pow.f64 (cos.f64 (/.f64 K 2)) 1/6))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	31.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 J (-.f64 (fma.f64 1/192 (pow.f64 K 4) 2) (fma.f64 1/4 (.f64 K K) (.f64 1/23040 (pow.f64 K 6))))))))
	32.9b	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) 2)) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	19.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 J (fma.f64 (*.f64 K K) -1/4 2)))))

Compiler

Compiled 4811 to 3752 computations (22% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
0.6b	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
0.6b	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
7.8b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

rewrite166.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

20×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
16×	`pow1/3_binary64`
12×	`log1p-expm1-u_binary64`

Counts

4 → 128

Calls

4 calls:

17.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
14.0ms	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
12.0ms	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
11.0ms	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))

Compiler

Compiled 4866 to 3879 computations (20.3% saved)

series384.0ms (3.4%)

Error

0.1b

Counts

4 → 35

Calls

4 calls:

182.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
61.0ms	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
59.0ms	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))
55.0ms	(cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))

Compiler

Compiled 3990 to 3296 computations (17.4% saved)

simplify115.0ms (1%)

Algorithm

1×	egg-herbie

Rules

657×	`fma-def_binary64`
642×	`times-frac_binary64`
470×	`*-commutative_binary64`
308×	`associate-/l*_binary64`
293×	`fma-neg_binary64`

Counts

163 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	168	3007
1	403	2750
2	1261	2681
3	4290	2671
4	5037	2671

prune100.0ms (0.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	102	10	112

Error

2.7b

Counts

112 → 10

Alt Table

Status	Error	Program
	9.5b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	8.8b	(.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
	9.8b	(.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	43.3b	(neg.f64 U)
	19.1b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 1/6) (pow.f64 (cos.f64 (/.f64 K 2)) 1/6))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	31.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 J (-.f64 (fma.f64 1/192 (pow.f64 K 4) 2) (fma.f64 1/4 (.f64 K K) (.f64 1/23040 (pow.f64 K 6))))))))
	9.5b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 -2) (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	32.9b	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) 2)) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	8.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	19.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 J (fma.f64 (*.f64 K K) -1/4 2)))))

Compiler

Compiled 3747 to 2939 computations (21.6% saved)

regimes1.1s (9.9%)

Accuracy

Total 5.7b remaining (59.3%)

Threshold costs 0b (0%)

Compiler

Compiled 17960 to 14442 computations (19.6% saved)

bsearch213.0ms (1.9%)

Steps

Iters	Range		Point
4	1.9016068518724104e-169	3.2236528699457374e-169	1.9339533218706902e-169
7	1.3597580561152897e-289	2.2863060651985639e-287	3.0750365055579345e-288
8	-4.899227537000375e-280	-1.9470108701864399e-283	-2.4993835334593255e-282
7	-3.234575388623567e-254	-5.218217504339229e-256	-5.636250867741126e-255

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

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	30	95
1	40	95
2	42	95
3	43	95
4	42	95

end1.0ms (0%)

Compiler: Compiled 66 to 48 computations (27.3% saved)

sample4.0s (35.5%)

Algorithm

1×

intervals

Results

1.9s	2002×	body	1024	valid
655.0ms	4471×	body	128	valid
597.0ms	1042×	body	512	valid
166.0ms	480×	body	256	valid
7.0ms	5×	body	2048	valid
1.0ms	2×	body	512	invalid
0.0ms	2×	body	128	invalid

Compiler

Compiled 480 to 380 computations (20.8% saved)

Details

analyze2.7s (23.9%)

sample115.0ms (1%)

simplify93.0ms (0.8%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite224.0ms (2%)

series206.0ms (1.8%)

simplify129.0ms (1.2%)

prune113.0ms (1%)

localize17.0ms (0.2%)

rewrite205.0ms (1.8%)

series177.0ms (1.6%)

simplify101.0ms (0.9%)

prune63.0ms (0.6%)

localize27.0ms (0.2%)

rewrite201.0ms (1.8%)

series482.0ms (4.3%)

simplify125.0ms (1.1%)

prune128.0ms (1.1%)

localize17.0ms (0.2%)

rewrite166.0ms (1.5%)

series384.0ms (3.4%)

simplify115.0ms (1%)

prune100.0ms (0.9%)

regimes1.1s (9.9%)

bsearch213.0ms (1.9%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample4.0s (35.5%)

Profiling