Details

analyze4.9s (24.3%)

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)

sample239.0ms (1.2%)

Algorithm

1×

intervals

Results

136.0ms	74×	body	1024	valid
36.0ms	131×	body	128	valid
35.0ms	35×	body	512	valid
10.0ms	16×	body	256	valid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify96.0ms (0.5%)

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

prune8.0ms (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

7.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.4b	(.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 96 to 76 computations (20.8% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	0.1b	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
✓	6.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series422.0ms (2.1%)

Counts

4 → 120

Calls

4 calls:

274.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
100.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
24.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
24.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

rewrite52.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
23×	`pow1_binary64`
15×	`cbrt-unprod_binary64`
15×	`prod-exp_binary64`

Counts

4 → 88

Calls

4 calls:

11.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
11.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
8.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
8.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

simplify320.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-def_binary64`
375×	`associate-l_binary64`
303×	`fma-neg_binary64`
300×	`associate-r_binary64`
204×	`*-commutative_binary64`

Counts

208 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	323	5501
1	854	4903
2	3368	4868
3	4900	4868
4	4981	4868
5	4956	4868

prune397.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	183	7	190
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	183	8	191

Error

0.0b

Counts

191 → 8

Alt Table

Status	Error	Program
✓	7.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	46.9b	U
▶	8.0b	(.f64 (.f64 (.f64 (.f64 -2 J) (.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)))))
	46.2b	(neg.f64 U)
	23.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	37.0b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 -2 J)) (.f64 -2 J)) (.f64 (.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	38.7b	(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))

Compiler

Compiled 6716 to 5038 computations (25% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.4b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	6.9b	(.f64 (.f64 (.f64 (.f64 -2 J) (.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)))))

series1.0s (5.1%)

Counts

4 → 84

Calls

4 calls:

420.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
314.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
265.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.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)))))
25.0ms	(.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))

rewrite96.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`pow1_binary64`
49×	`add-exp-log_binary64`
34×	`pow-prod-down_binary64`
33×	`cbrt-unprod_binary64`
33×	`prod-exp_binary64`

Counts

4 → 119

Calls

4 calls:

34.0ms	(.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
23.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.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)))))
8.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify296.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

852×	`fma-def_binary64`
491×	`associate-l_binary64`
370×	`associate-r_binary64`
270×	`fma-neg_binary64`
205×	`*-commutative_binary64`

Counts

203 → 214

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	5881
1	836	5091
2	3332	4908
3	4961	4908
4	4995	4908

prune680.0ms (3.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	260	10	270

Error

0.0b

Counts

270 → 10

Alt Table

Status	Error	Program
✓	7.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	46.9b	U
	37.0b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 -2 J)) (.f64 -2 J)) (.f64 (.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	8.0b	(.f64 (.f64 (.f64 (.f64 -2 J) (expm1.f64 (log1p.f64 (.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)))))
	38.7b	(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))
	8.1b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (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)))))
	46.2b	(neg.f64 U)
	23.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	8.0b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (log.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
▶	7.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 11494 to 9067 computations (21.1% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2))
	0.4b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	6.9b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series741.0ms (3.7%)

Counts

3 → 52

Calls

3 calls:

464.0ms

(cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2))

270.0ms

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

7.0ms

(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
18×	`pow1_binary64`
12×	`add-cbrt-cube_binary64`
10×	`cbrt-unprod_binary64`
10×	`prod-exp_binary64`

Counts

3 → 64

Calls

3 calls:

23.0ms

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

3.0ms

(cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2))

3.0ms

(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)

simplify188.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-def_binary64`
355×	`associate-l_binary64`
298×	`cancel-sign-sub-inv_binary64`
281×	`associate-r_binary64`
259×	`unswap-sqr_binary64`

Counts

116 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	4424
1	756	3837
2	3007	3799
3	4986	3799

prune484.0ms (2.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	155	11	166

Error

Counts

166 → 11

Alt Table

Status	Error	Program
✓	7.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	46.9b	U
▶	7.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (expm1.f64 (log1p.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	37.0b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 -2 J)) (.f64 -2 J)) (.f64 (.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	38.7b	(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))
	8.1b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (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)))))
	46.2b	(neg.f64 U)
	23.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
✓	7.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	7.9b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 7099 to 5586 computations (21.3% saved)

localize51.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2))
	0.4b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	0.5b	(log1p.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	6.9b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (expm1.f64 (log1p.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series1.1s (5.4%)

Counts

2 → 48

Calls

2 calls:

826.0ms

(log1p.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))

259.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2))) (expm1.f64 (log1p.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
16×	`pow1_binary64`
14×	`add-cbrt-cube_binary64`
10×	`cbrt-unprod_binary64`
10×	`prod-exp_binary64`

Counts

2 → 37

Calls

2 calls:

19.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2))) (expm1.f64 (log1p.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

1.0ms

(log1p.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))

simplify308.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-def_binary64`
359×	`associate-l_binary64`
316×	`fma-neg_binary64`
260×	`associate-r_binary64`
253×	`cancel-sign-sub-inv_binary64`

Counts

85 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	266	4004
1	693	3443
2	2750	3335
3	4665	3315
4	4990	3315
5	4998	3315
6	4956	3315

prune461.0ms (2.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	146	11	157

Error

Counts

157 → 11

Alt Table

Status	Error	Program
✓	7.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	46.9b	U
	38.7b	(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))
	8.1b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (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)))))
	38.7b	(cbrt.f64 (.f64 (pow.f64 (.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 2 J)))) (.f64 J -2)) 3) (.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) (cos.f64 (/.f64 K 2)))))
	46.2b	(neg.f64 U)
	23.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
✓	7.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (expm1.f64 (log1p.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	7.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	7.9b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 6589 to 5235 computations (20.5% saved)

regimes1.1s (5.7%)

Accuracy

Total 8.7b remaining (99.6%)

Threshold costs 0b (0%)

Counts

57 → 3

Compiler

Compiled 11792 to 9498 computations (19.5% saved)

bsearch205.0ms (1%)

Steps

Iters	Range		Point
7	1.978178407934875e-255	5.27342107335168e-254	2.176564396023258e-255
6	-5.734658275592066e-208	-8.525691636359108e-209	-2.8689791562071003e-208

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	68
1	43	68
2	42	68

end2.0ms (0%)

Compiler: Compiled 48 to 36 computations (25% saved)

sample6.6s (33.2%)

Algorithm

1×

intervals

Results

3.4s	1961×	body	1024	valid
1.2s	4544×	body	128	valid
976.0ms	1014×	body	512	valid
293.0ms	479×	body	256	valid
4.0ms	2×	body	2048	valid
1.0ms	1×	body	256	invalid

Compiler

Compiled 456 to 370 computations (18.9% saved)

Details

analyze4.9s (24.3%)

sample239.0ms (1.2%)

simplify96.0ms (0.5%)

prune8.0ms (0%)

localize27.0ms (0.1%)

series422.0ms (2.1%)

rewrite52.0ms (0.3%)

simplify320.0ms (1.6%)

prune397.0ms (2%)

localize37.0ms (0.2%)

series1.0s (5.1%)

rewrite96.0ms (0.5%)

simplify296.0ms (1.5%)

prune680.0ms (3.4%)

localize41.0ms (0.2%)

series741.0ms (3.7%)

rewrite38.0ms (0.2%)

simplify188.0ms (0.9%)

prune484.0ms (2.4%)

localize51.0ms (0.3%)

series1.1s (5.4%)

rewrite28.0ms (0.1%)

simplify308.0ms (1.5%)

prune461.0ms (2.3%)

regimes1.1s (5.7%)

bsearch205.0ms (1%)

simplify6.0ms (0%)

end2.0ms (0%)

sample6.6s (33.2%)

Profiling