Details

analyze2.0s (18.9%)

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)

sample84.0ms (0.8%)

Algorithm

1×

intervals

Results

38.0ms	61×	body	1024	valid
16.0ms	144×	body	128	valid
14.0ms	35×	body	512	valid
4.0ms	16×	body	256	valid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify124.0ms (1.2%)

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

prune4.0ms (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

19.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	19.2b	(.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)

localize15.0ms (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)
7.6b	(.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))))
10.3b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite254.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

19.1b

Rules

28×	`add-exp-log_binary64`
20×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64` `prod-exp_binary64`

Counts

4 → 86

Calls

4 calls:

15.0ms	(.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))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2850 to 2286 computations (19.8% saved)

series390.0ms (3.7%)

Error

0.1b

Counts

4 → 54

Calls

4 calls:

154.0ms	(.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))))
100.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
67.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
31.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3516 to 2836 computations (19.3% saved)

simplify143.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

702×	`times-frac_binary64`
274×	`associate-l_binary64`
204×	`associate-r_binary64`
150×	`distribute-rgt-in_binary64`
141×	`cancel-sign-sub-inv_binary64` `*-commutative_binary64`

Counts

140 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	3878
1	573	3550
2	1982	3503
3	4745	3503
4	4951	3503

prune112.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	8	109

Error

0.0b

Counts

109 → 8

Alt Table

Status	Error	Program
	19.5b	(.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)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	19.3b	(.f64 (.f64 (fabs.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)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	20.0b	(.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))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
▶	19.3b	(.f64 (.f64 (sqrt.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)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	49.0b	(.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) 3)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓	19.2b	(.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))))
	49.9b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	45.9b	(neg.f64 U)

Compiler

Compiled 2245 to 1744 computations (22.3% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.6b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.6b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.3b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.3b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite211.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

32×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64`

Counts

4 → 76

Calls

4 calls:

9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 3667 to 2999 computations (18.2% saved)

series593.0ms (5.6%)

Error

0.0b

Counts

4 → 64

Calls

4 calls:

144.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
141.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
119.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
119.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 7563 to 6200 computations (18% saved)

simplify146.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

514×	`unswap-sqr_binary64`
466×	`times-frac_binary64`
320×	`associate-/l*_binary64`
235×	`associate-/r*_binary64`
221×	`associate-l_binary64` `associate-r_binary64`

Counts

140 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	4114
1	294	4002
2	806	3972
3	3668	3858
4	5403	3858

prune137.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	84	8	92

Error

0.0b

Counts

92 → 8

Alt Table

Status	Error	Program
	19.5b	(.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)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
▶	19.3b	(.f64 (.f64 (fabs.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)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	20.0b	(.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))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓	19.3b	(.f64 (.f64 (sqrt.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)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	49.0b	(.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) 3)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓	19.2b	(.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))))
	49.9b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	45.9b	(neg.f64 U)

Compiler

Compiled 3279 to 2572 computations (21.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.5b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
1.6b	(.f64 (fabs.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))))
16.6b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
16.6b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite231.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`*-un-lft-identity_binary64`
18×	`cbrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`pow1_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`

Counts

4 → 81

Calls

4 calls:

17.0ms	(.f64 (fabs.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))))
9.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 4380 to 3578 computations (18.3% saved)

series610.0ms (5.8%)

Error

0.0b

Counts

4 → 52

Calls

4 calls:

148.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
144.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
140.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
114.0ms	(.f64 (fabs.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))))

Compiler

Compiled 6962 to 5827 computations (16.3% saved)

simplify165.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

605×	`*-commutative_binary64`
433×	`unswap-sqr_binary64`
407×	`times-frac_binary64`
289×	`associate-/l*_binary64`
250×	`associate-/r*_binary64`

Counts

133 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	5104
1	483	4642
2	1491	4556
3	3721	4425
4	5277	4425

prune143.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	94	8	102

Error

0.0b

Counts

102 → 8

Alt Table

Status	Error	Program
▶	19.5b	(.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)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓	19.3b	(.f64 (.f64 (fabs.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)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	20.0b	(.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))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓	19.3b	(.f64 (.f64 (sqrt.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)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	49.0b	(.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) 3)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓	19.2b	(.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))))
	49.9b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	45.9b	(neg.f64 U)

Compiler

Compiled 3560 to 2805 computations (21.2% saved)

localize21.0ms (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)))
7.6b	(.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)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.3b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite200.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`pow1_binary64`
29×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
19×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
13×	`*-un-lft-identity_binary64`

Counts

4 → 74

Calls

4 calls:

29.0ms	(.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)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3481 to 2847 computations (18.2% saved)

series361.0ms (3.4%)

Error

0.0b

Counts

4 → 47

Calls

4 calls:

156.0ms	(.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)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
112.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
24.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
22.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3877 to 3152 computations (18.7% saved)

simplify141.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

572×	`times-frac_binary64`
372×	`associate-/l*_binary64`
365×	`associate-l_binary64`
293×	`associate-/r*_binary64`
260×	`associate-r_binary64`

Counts

121 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	3557
1	520	3183
2	1978	3145
3	4931	3145
4	4952	3145

prune91.0ms (0.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	83	8	91

Error

0.0b

Counts

91 → 8

Alt Table

Status	Error	Program
	19.5b	(.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)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	19.3b	(.f64 (.f64 (fabs.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)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	20.0b	(.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))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	19.3b	(.f64 (.f64 (sqrt.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)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	49.0b	(.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) 3)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	19.2b	(.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))))
	49.9b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	45.9b	(neg.f64 U)

Compiler

Compiled 2014 to 1568 computations (22.1% saved)

regimes1.4s (13.4%)

Accuracy

Total 9.8b remaining (99.3%)

Threshold costs 0b (0%)

Compiler

Compiled 19729 to 16072 computations (18.5% saved)

bsearch8.0ms (0.1%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`if-if-or-not_binary64` `1-exp_binary64` `neg-sub0_binary64` `sub-neg_binary64` `mul-1-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	126
1	40	126
2	41	126
3	42	126
4	43	126
5	42	126

end3.0ms (0%)

Compiler: Compiled 84 to 68 computations (19% saved)

sample2.9s (27.5%)

Algorithm

1×

intervals

Results

1.1s	1981×	body	1024	valid
529.0ms	4520×	body	128	valid
415.0ms	1004×	body	512	valid
135.0ms	493×	body	256	valid
2.0ms	2×	body	2048	valid
0.0ms	1×	body	256	invalid
0.0ms	2×	body	128	invalid

Compiler

Compiled 374 to 305 computations (18.4% saved)

Details

analyze2.0s (18.9%)

sample84.0ms (0.8%)

simplify124.0ms (1.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite254.0ms (2.4%)

series390.0ms (3.7%)

simplify143.0ms (1.4%)

prune112.0ms (1.1%)

localize23.0ms (0.2%)

rewrite211.0ms (2%)

series593.0ms (5.6%)

simplify146.0ms (1.4%)

prune137.0ms (1.3%)

localize21.0ms (0.2%)

rewrite231.0ms (2.2%)

series610.0ms (5.8%)

simplify165.0ms (1.6%)

prune143.0ms (1.4%)

localize21.0ms (0.2%)

rewrite200.0ms (1.9%)

series361.0ms (3.4%)

simplify141.0ms (1.3%)

prune91.0ms (0.9%)

regimes1.4s (13.4%)

bsearch8.0ms (0.1%)

simplify7.0ms (0.1%)

end3.0ms (0%)

sample2.9s (27.5%)

Profiling