Details

analyze2.6s (20.2%)

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)

sample105.0ms (0.8%)

Algorithm

1×

intervals

Results

51.0ms	57×	body	1024	valid
23.0ms	158×	body	128	valid
14.0ms	27×	body	512	valid
5.0ms	14×	body	256	valid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify107.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1043×	`associate-*l/_binary64`
692×	`associate-/l/_binary64`
651×	`associate-/r/_binary64`
525×	`associate-*r/_binary64`
474×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	37	37
2	81	37
3	206	37
4	726	37
5	2242	37
6	2396	37
7	2777	37
8	2829	37
9	2940	37
10	3048	37
11	4535	37
12	4712	37
13	4916	37
14	4945	37
15	4849	37

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

17.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

Compiler

Compiled 81 to 66 computations (18.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
8.0b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite151.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

17.9b

Rules

28×	`add-exp-log_binary64`
20×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
12×	`prod-exp_binary64`

Counts

4 → 86

Calls

4 calls:

13.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
6.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
5.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
4.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2850 to 2286 computations (19.8% saved)

series296.0ms (2.3%)

Error

0.0b

Counts

4 → 51

Calls

4 calls:

104.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
72.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
71.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
22.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3428 to 2780 computations (18.9% saved)

simplify136.0ms (1%)

Algorithm

1×	egg-herbie

Rules

800×	`times-frac_binary64`
277×	`associate-l_binary64`
203×	`associate-r_binary64`
146×	`distribute-rgt-in_binary64`
140×	`*-commutative_binary64`

Counts

137 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	3789
1	563	3466
2	1965	3428
3	4776	3428
4	4983	3428

prune69.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	98	7	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	8	106

Error

4.7b

Counts

106 → 8

Alt Table

Status	Error	Program
✓	17.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	46.9b	(neg.f64 U)
	28.2b	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	52.7b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (/.f64 U (.f64 (cos.f64 (.f64 1/2 K)) J)) -1/2))
	30.0b	(.f64 (.f64 (cos.f64 (*.f64 1/2 K)) J) -2)
	27.2b	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
▶	18.7b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))))))
	47.0b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2)))) 3))

Compiler

Compiled 2229 to 1715 computations (23.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.0b	(.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))))
8.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite168.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

17×	`*-un-lft-identity_binary64`
16×	`sqrt-prod_binary64`
16×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

4 → 75

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))))
7.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
6.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
6.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 5980 to 4842 computations (19% saved)

series481.0ms (3.7%)

Error

4.7b

Counts

4 → 68

Calls

4 calls:

129.0ms	(.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))))
101.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
95.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
94.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 12237 to 9890 computations (19.2% saved)

simplify135.0ms (1%)

Algorithm

1×	egg-herbie

Rules

607×	`times-frac_binary64`
431×	`associate-/l*_binary64`
295×	`associate-/r*_binary64`
240×	`associate-*l/_binary64`
238×	`associate-*r/_binary64`

Counts

143 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	4468
1	423	4212
2	1481	4159
3	4830	4141
4	4959	4141

prune123.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	95	9	104

Error

4.7b

Counts

104 → 9

Alt Table

Status	Error	Program
	30.0b	(.f64 (.f64 (cos.f64 (*.f64 1/2 K)) J) -2)
▶	18.7b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))))
✓	17.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	46.9b	(neg.f64 U)
	28.2b	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	52.7b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (/.f64 U (.f64 (cos.f64 (.f64 1/2 K)) J)) -1/2))
	27.2b	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
✓	18.7b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))))))
	47.0b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2)))) 3))

Compiler

Compiled 5837 to 4587 computations (21.4% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
13.8b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
13.8b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite165.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

16×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`sqrt-prod_binary64`
8×	`cbrt-prod_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 60

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
6.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
6.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 6029 to 4907 computations (18.6% saved)

series578.0ms (4.4%)

Error

4.7b

Counts

4 → 54

Calls

4 calls:

139.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
131.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
90.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
87.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 14139 to 11588 computations (18% saved)

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

521×	`times-frac_binary64`
425×	`associate-/l*_binary64`
412×	`associate-r_binary64`
346×	`associate-l_binary64`
279×	`associate-/r*_binary64`

Counts

114 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	3722
1	325	3670
2	925	3628
3	5074	3628

prune183.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	88	9	97

Error

4.7b

Counts

97 → 9

Alt Table

Status	Error	Program
	30.0b	(.f64 (.f64 (cos.f64 (*.f64 1/2 K)) J) -2)
✓	18.7b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))))
✓	17.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	46.9b	(neg.f64 U)
	28.2b	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	52.7b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (/.f64 U (.f64 (cos.f64 (.f64 1/2 K)) J)) -1/2))
▶	27.2b	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
✓	18.7b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))))))
	47.0b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2)))) 3))

Compiler

Compiled 8396 to 6663 computations (20.6% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))
6.1b	(sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
14.2b	(-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
21.0b	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))

rewrite269.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
16×	`sqrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

4 → 82

Calls

4 calls:

26.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
14.0ms	(sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
10.0ms	(-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
6.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))

Compiler

Compiled 8371 to 6730 computations (19.6% saved)

series978.0ms (7.5%)

Error

4.7b

Counts

4 → 58

Calls

4 calls:

567.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
125.0ms	(sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
115.0ms	(-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
113.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))

Compiler

Compiled 9101 to 7485 computations (17.8% saved)

simplify262.0ms (2%)

Algorithm

1×	egg-herbie

Rules

251×	`associate-r_binary64`
242×	`associate-l_binary64`
236×	`cancel-sign-sub-inv_binary64`
195×	`associate-/l*_binary64`
190×	`times-frac_binary64`

Counts

140 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	332	8471
1	833	7437
2	3242	7355
3	4641	7355
4	5000	7355
5	4931	7355

prune164.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	5	5
Picked	0	1	1
Done	1	2	3
Total	117	9	126

Error

4.7b

Counts

126 → 9

Alt Table

Status	Error	Program
	28.2b	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	27.3b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 -2 J)))))
	17.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	46.9b	(neg.f64 U)
	52.7b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (/.f64 U (.f64 (cos.f64 (.f64 1/2 K)) J)) -1/2))
	30.0b	(.f64 (.f64 (cos.f64 (*.f64 1/2 K)) J) -2)
	27.2b	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
	18.7b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))))))
	47.0b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2)))) 3))

Compiler

Compiled 5850 to 4608 computations (21.2% saved)

regimes2.2s (16.5%)

Accuracy

Total 5.7b remaining (59.5%)

Threshold costs 0b (0%)

Compiler

Compiled 37065 to 29998 computations (19.1% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 27 to 22 computations (18.5% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	146
1	51	146
2	55	146
3	57	146
4	58	146
5	57	146

end2.0ms (0%)

Compiler: Compiled 98 to 77 computations (21.4% saved)

sample3.7s (28.2%)

Algorithm

1×

intervals

Results

1.7s	1912×	body	1024	valid
663.0ms	4546×	body	128	valid
545.0ms	1022×	body	512	valid
182.0ms	517×	body	256	valid
5.0ms	3×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid
0.0ms	3×	body	128	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 469 to 379 computations (19.2% saved)

Details

analyze2.6s (20.2%)

sample105.0ms (0.8%)

simplify107.0ms (0.8%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite151.0ms (1.2%)

series296.0ms (2.3%)

simplify136.0ms (1%)

prune69.0ms (0.5%)

localize24.0ms (0.2%)

rewrite168.0ms (1.3%)

series481.0ms (3.7%)

simplify135.0ms (1%)

prune123.0ms (0.9%)

localize34.0ms (0.3%)

rewrite165.0ms (1.3%)

series578.0ms (4.4%)

simplify93.0ms (0.7%)

prune183.0ms (1.4%)

localize27.0ms (0.2%)

rewrite269.0ms (2.1%)

series978.0ms (7.5%)

simplify262.0ms (2%)

prune164.0ms (1.3%)

regimes2.2s (16.5%)

bsearch8.0ms (0.1%)

simplify6.0ms (0%)

end2.0ms (0%)

sample3.7s (28.2%)

Profiling