Details

analyze2.9s (15.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample115.0ms (0.6%)

Algorithm

1×

intervals

Symmetry

(sort m n)

Results

41.0ms	253×	body	128	valid
2.0ms	3×	body	1024	invalid
2.0ms	3×	body	1024	valid
2.0ms	12×	body	128	invalid
1.0ms	2×	body	512	invalid
1.0ms	2×	body	256	invalid

Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify55.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

691×	`exp-prod_binary64`
507×	`exp-sum_binary64`
446×	`fma-neg_binary64`
375×	`associate-l_binary64`
251×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	58	45
2	129	43
3	384	43
4	1266	43
5	4023	43
6	4945	43
7	5019	43

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

16.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.2b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 128 to 80 computations (37.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	35.5b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series410.0ms (2.3%)

Counts

4 → 180

Calls

4 calls:

359.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
28.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
6.0ms	(*.f64 K (+.f64 m n))

rewrite79.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`*-un-lft-identity_binary64`
63×	`add-sqr-sqrt_binary64`
57×	`prod-diff_binary64`
48×	`associate-r_binary64`
42×	`add-cube-cbrt_binary64`

Counts

4 → 145

Calls

4 calls:

33.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
9.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
5.0ms	(*.f64 K (+.f64 m n))

simplify322.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

921×	`fma-def_binary64`
462×	`*-commutative_binary64`
308×	`associate-r_binary64`
167×	`+-commutative_binary64`
153×	`cancel-sign-sub-inv_binary64`

Counts

325 → 314

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	990	19178
1	2633	17041
2	4857	17041
3	4990	17041

prune554.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	308	6	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	309	6	315

Error

0.8b

Counts

315 → 6

Alt Table

Status	Error	Program
	51.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (sqrt.f64 K) (sqrt.f64 (+.f64 m n))) (.f64 (sqrt.f64 K) (sqrt.f64 (+.f64 m n)))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	16.2b	(expm1.f64 (log1p.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))))
	16.2b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 n m)) 2) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	16.1b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.2b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	16.2b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 25817 to 12772 computations (50.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
✓	0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series289.0ms (1.6%)

Counts

3 → 144

Calls

3 calls:

195.0ms

(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

50.0ms

(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))

44.0ms

(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

rewrite89.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64`
85×	`add-sqr-sqrt_binary64`
72×	`prod-diff_binary64`
46×	`fabs-mul_binary64`
45×	`add-cube-cbrt_binary64`

Counts

3 → 160

Calls

3 calls:

30.0ms

(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

22.0ms

(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))

11.0ms

(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

simplify243.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

730×	`associate-r_binary64`
541×	`associate-l_binary64`
512×	`fma-def_binary64`
187×	`*-commutative_binary64`
163×	`cancel-sign-sub-inv_binary64`

Counts

304 → 306

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	509	15260
1	1487	12752
2	4928	12752
3	4992	12752

prune576.0ms (3.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	369	5	374

Error

0.8b

Counts

374 → 5

Alt Table

Status	Error	Program
	16.2b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 n m)) 2) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	16.1b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.2b	(expm1.f64 (log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))))
	51.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (sqrt.f64 K) (sqrt.f64 (+.f64 m n))) (.f64 (sqrt.f64 K) (sqrt.f64 (+.f64 m n)))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	16.2b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 19228 to 9582 computations (50.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.0b	(expm1.f64 (log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))))
✓	0.0b	(log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series8.0s (44%)

Counts

2 → 96

Calls

2 calls:

7.8s

(log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))

189.0ms

(expm1.f64 (log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms

(log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))

0.0ms

(expm1.f64 (log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))))

simplify298.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

742×	`fma-def_binary64`
463×	`times-frac_binary64`
360×	`*-commutative_binary64`
226×	`associate-r_binary64`
189×	`+-commutative_binary64`

Counts

118 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	770	19789
1	2483	18208
2	4967	18204
3	4988	18204

prune741.0ms (4.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	294	5	299

Error

0.8b

Counts

299 → 5

Alt Table

Status	Error	Program
	16.2b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 n m)) 2) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	16.1b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.2b	(expm1.f64 (log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))))
	51.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (sqrt.f64 K) (sqrt.f64 (+.f64 m n))) (.f64 (sqrt.f64 K) (sqrt.f64 (+.f64 m n)))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	16.2b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 34519 to 17184 computations (50.2% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
✓	1.0b	(cbrt.f64 2)
✓	35.1b	(sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))
✓	35.4b	(cos.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))

series142.0ms (0.8%)

Counts

4 → 108

Calls

4 calls:

58.0ms	(/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
43.0ms	(sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))
41.0ms	(cos.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))
0.0ms	(cbrt.f64 2)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`

Counts

4 → 56

Calls

4 calls:

4.0ms	(/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
2.0ms	(cos.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))
1.0ms	(sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))
1.0ms	(cbrt.f64 2)

simplify100.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

903×	`cancel-sign-sub-inv_binary64`
397×	`associate-r_binary64`
306×	`associate-l_binary64`
268×	`fma-neg_binary64`
222×	`fma-def_binary64`

Counts

164 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	284	4635
1	780	4364
2	2848	4360
3	5266	4360

prune613.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	258	5	263

Error

0.8b

Counts

263 → 5

Alt Table

Status	Error	Program
	16.2b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 n m)) 2) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.2b	(expm1.f64 (log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))))
	16.1b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (log.f64 (exp.f64 (cos.f64 (fma.f64 (/.f64 K (pow.f64 (cbrt.f64 2) 2)) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	51.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (sqrt.f64 K) (sqrt.f64 (+.f64 m n))) (.f64 (sqrt.f64 K) (sqrt.f64 (+.f64 m n)))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	16.2b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 18873 to 11901 computations (36.9% saved)

regimes645.0ms (3.5%)

Accuracy

Total 0.2b remaining (13.4%)

Threshold costs 0.2b (13.4%)

Counts

87 → 1

Compiler

Compiled 15956 to 11274 computations (29.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	35
1	30	35
2	47	35
3	62	35
4	71	35
5	74	35
6	74	35

end10.0ms (0.1%)

Remove: (sort m n)
Compiler: Compiled 81 to 60 computations (25.9% saved)

sample1.9s (10.6%)

Algorithm

1×

intervals

Results

1.1s	7832×	body	128	valid
54.0ms	84×	body	1024	invalid
43.0ms	301×	body	128	invalid
43.0ms	96×	body	512	invalid
41.0ms	66×	body	1024	valid
29.0ms	69×	body	512	valid
27.0ms	30×	body	2048	invalid
20.0ms	67×	body	256	invalid
9.0ms	32×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 300 to 206 computations (31.3% saved)

Details

analyze2.9s (15.8%)

sample115.0ms (0.6%)

simplify55.0ms (0.3%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series410.0ms (2.3%)

rewrite79.0ms (0.4%)

simplify322.0ms (1.8%)

prune554.0ms (3%)

localize15.0ms (0.1%)

series289.0ms (1.6%)

rewrite89.0ms (0.5%)

simplify243.0ms (1.3%)

prune576.0ms (3.2%)

localize15.0ms (0.1%)

series8.0s (44%)

rewrite2.0ms (0%)

simplify298.0ms (1.6%)

prune741.0ms (4.1%)

localize32.0ms (0.2%)

series142.0ms (0.8%)

rewrite10.0ms (0.1%)

simplify100.0ms (0.6%)

prune613.0ms (3.4%)

regimes645.0ms (3.5%)

simplify3.0ms (0%)

end10.0ms (0.1%)

sample1.9s (10.6%)

Profiling