Details

analyze2.2s (2%)

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 30 to 24 computations (20% saved)

sample43.0ms (0%)

Algorithm

1×

intervals

Results

25.0ms	254×	body	128	valid
1.0ms	2×	body	1024	invalid
1.0ms	2×	body	512	invalid
1.0ms	1×	body	2048	invalid
1.0ms	5×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	2×	body	256	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify150.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5097	43

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

17.3b

Counts

2 → 2

Compiler

Compiled 28 to 22 computations (21.4% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite53.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_1464`
14×	`*-un-lft-identity_binary64_1442`
8×	`add-log-exp_binary64_1481` `add-cube-cbrt_binary64_1477`
6×	`cancel-sign-sub-inv_binary64_1408` `unpow-prod-down_binary64_1521`
5×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
4×	`add-cbrt-cube_binary64_1478` `cos-sum_binary64_1576`
3×	`pow-unpow_binary64_1519` `difference-of-squares_binary64_1411`
2×	`sub-neg_binary64_1435` `distribute-lft-out--_binary64_1394`
1×	`sum-log_binary64_1533` `pow-exp_binary64_1510` `unpow2_binary64_1507` `times-frac_binary64_1448` `flip3--_binary64_1446` `+-commutative_binary64_1372` `cos-diff_binary64_1579` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `diff-log_binary64_1534` `sqr-pow_binary64_1414` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

4 → 61

Calls

8 calls:

14.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series1.3s (1.2%)

Counts

4 → 92

Calls

4 calls:

663.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
301.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
194.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
144.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 4984 to 3966 computations (20.4% saved)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5015	2914

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite67.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_1442`
21×	`add-sqr-sqrt_binary64_1464`
16×	`add-log-exp_binary64_1481`
14×	`cancel-sign-sub-inv_binary64_1408`
10×	`add-cube-cbrt_binary64_1477`
9×	`distribute-lft-out--_binary64_1394`
7×	`diff-log_binary64_1534`
6×	`unpow-prod-down_binary64_1521`
5×	`add-exp-log_binary64_1480` `pow1_binary64_1503` `difference-of-squares_binary64_1411`
4×	`add-cbrt-cube_binary64_1478` `sub-neg_binary64_1435` `associate--r+_binary64_1378` `cos-sum_binary64_1576`
3×	`pow-unpow_binary64_1519`
2×	`distribute-rgt-neg-in_binary64_1400` `flip3--_binary64_1446` `neg-log_binary64_1535` `flip--_binary64_1417`
1×	`associate--l-_binary64_1380` `pow-exp_binary64_1510` `unpow2_binary64_1507` `times-frac_binary64_1448` `cos-diff_binary64_1579` `sqr-pow_binary64_1414` `neg-sub0_binary64_1437` `associate--r-_binary64_1381` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

4 → 79

Calls

8 calls:

25.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

series1.4s (1.3%)

Counts

4 → 92

Calls

4 calls:

708.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
311.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
198.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
169.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 5014 to 4024 computations (19.7% saved)

simplify105.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4991	3625
1	4991	3625

prune2.5s (2.2%)

Pruning

109 alts after pruning (107 fresh and 2 done)

	Pruned	Kept	Total
New	217	107	324
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	217	109	326

Error

0.4b

Counts

326 → 109

Compiler

Compiled 9566 to 5531 computations (42.2% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(+.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	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_1464`
8×	`*-un-lft-identity_binary64_1442`
6×	`unpow-prod-down_binary64_1521`
4×	`add-log-exp_binary64_1481` `add-cube-cbrt_binary64_1477`
3×	`pow-unpow_binary64_1519` `add-exp-log_binary64_1480` `pow1_binary64_1503`
2×	`add-cbrt-cube_binary64_1478` `difference-of-squares_binary64_1411`
1×	`sum-log_binary64_1533` `pow-exp_binary64_1510` `unpow2_binary64_1507` `times-frac_binary64_1448` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `sqr-pow_binary64_1414` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out--_binary64_1394` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

2 → 33

Calls

4 calls:

15.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series941.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

642.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
298.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 2534 to 2103 computations (17% saved)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5112	1931

localize16.0ms (0%)

Local error

Found 6 expressions with local error:

37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
0.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite35.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1464`
9×	`*-un-lft-identity_binary64_1442`
7×	`add-cube-cbrt_binary64_1477`
6×	`cancel-sign-sub-inv_binary64_1408`
5×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `pow1_binary64_1503`
4×	`add-exp-log_binary64_1480` `cos-sum_binary64_1576`
3×	`associate-r_binary64_1382` `associate-l_binary64_1383`
2×	`associate-*r/_binary64_1384` `sub-neg_binary64_1435` `exp-neg_binary64_1489`
1×	`cbrt-unprod_binary64_1475` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `cos-diff_binary64_1579` `flip--_binary64_1417` `diff-log_binary64_1534` `exp-diff_binary64_1490` `un-div-inv_binary64_1440` `prod-exp_binary64_1491` `neg-sub0_binary64_1437` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`

Counts

3 → 49

Calls

6 calls:

12.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))

series662.0ms (0.6%)

Counts

3 → 49

Calls

3 calls:

356.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
169.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
136.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 1747 to 1568 computations (10.2% saved)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5116	1785

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 m (-.f64 (.f64 n 1/2) M))
0.0b	(.f64 1/4 (.f64 m m))
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (neg.f64 (+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
0.0b	(.f64 1/4 (.f64 m m))
0.0b	(.f64 m (-.f64 (.f64 n 1/2) M))
4.9b	(+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))
37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cancel-sign-sub-inv_binary64_1408` `add-sqr-sqrt_binary64_1464`
12×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
8×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `associate-+r+_binary64_1374`
6×	`associate-l_binary64_1383` `add-log-exp_binary64_1481`
5×	`sub-neg_binary64_1435`
4×	`associate-r_binary64_1382` `cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cos-sum_binary64_1576`
2×	`associate-r/_binary64_1384` `-commutative_binary64_1373` `unswap-sqr_binary64_1410`
1×	`sum-log_binary64_1533` `flip3--_binary64_1446` `+-commutative_binary64_1372` `cos-diff_binary64_1579` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416`

Counts

4 → 78

Calls

8 calls:

9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))
7.0ms	(.f64 m (-.f64 (.f64 n 1/2) M))
6.0ms	(.f64 1/4 (.f64 m m))
0.0ms	(-.f64 (neg.f64 (+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))

series577.0ms (0.5%)

Counts

4 → 50

Calls

4 calls:

240.0ms	(+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))
155.0ms	(.f64 m (-.f64 (.f64 n 1/2) M))
151.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
31.0ms	(.f64 1/4 (.f64 m m))

Compiler

Compiled 2925 to 2303 computations (21.3% saved)

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4991	1794
1	4991	1794

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite57.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1464`
17×	`*-un-lft-identity_binary64_1442`
10×	`add-log-exp_binary64_1481`
9×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
6×	`unpow-prod-down_binary64_1521`
5×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
4×	`add-cbrt-cube_binary64_1478` `cos-sum_binary64_1576` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
3×	`sub-neg_binary64_1435` `pow-unpow_binary64_1519` `diff-log_binary64_1534`
2×	`flip3--_binary64_1446` `flip--_binary64_1417`
1×	`associate--l-_binary64_1380` `pow-exp_binary64_1510` `unpow2_binary64_1507` `times-frac_binary64_1448` `distribute-rgt-neg-in_binary64_1400` `cos-diff_binary64_1579` `neg-log_binary64_1535` `sqr-pow_binary64_1414` `neg-sub0_binary64_1437` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

4 → 68

Calls

8 calls:

20.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)

series1.3s (1.2%)

Counts

4 → 92

Calls

4 calls:

656.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
293.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
198.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
151.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 5497 to 4479 computations (18.5% saved)

simplify61.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5185	3063

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
0.0b	(sqrt.f64 (fabs.f64 (-.f64 m n)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 m n)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 m n)))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.5b	(*.f64 (neg.f64 (sqrt.f64 (fabs.f64 (-.f64 m n)))) (sqrt.f64 (fabs.f64 (-.f64 m n))))
37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1464`
17×	`*-un-lft-identity_binary64_1442`
16×	`associate-l_binary64_1383`
15×	`add-cube-cbrt_binary64_1477`
13×	`sqrt-prod_binary64_1458`
8×	`pow1_binary64_1503`
7×	`add-exp-log_binary64_1480`
6×	`associate-r_binary64_1382` `distribute-lft-neg-in_binary64_1399` `add-cbrt-cube_binary64_1478` `distribute-rgt-neg-in_binary64_1400` `unpow-prod-down_binary64_1521`
4×	`add-log-exp_binary64_1481` `cos-sum_binary64_1576`
3×	`cancel-sign-sub-inv_binary64_1408` `pow-unpow_binary64_1519`
2×	`difference-of-squares_binary64_1411` `unswap-sqr_binary64_1410`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `unpow2_binary64_1507` `times-frac_binary64_1448` `sub-neg_binary64_1435` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `cos-diff_binary64_1579` `neg-mul-1_binary64_1438` `sqr-pow_binary64_1414` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `distribute-lft-neg-out_binary64_1401` `distribute-lft-out--_binary64_1394` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

4 → 82

Calls

8 calls:

11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(*.f64 (neg.f64 (sqrt.f64 (fabs.f64 (-.f64 m n)))) (sqrt.f64 (fabs.f64 (-.f64 m n))))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 m n)))
0.0ms	(sqrt.f64 (fabs.f64 (-.f64 m n)))

series580.0ms (0.5%)

Counts

4 → 53

Calls

4 calls:

314.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
155.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
56.0ms	(sqrt.f64 (fabs.f64 (-.f64 m n)))
55.0ms	(*.f64 (neg.f64 (sqrt.f64 (fabs.f64 (-.f64 m n)))) (sqrt.f64 (fabs.f64 (-.f64 m n))))

Compiler

Compiled 3708 to 2697 computations (27.3% saved)

simplify89.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4917	2253
1	4917	2253

prune14.0s (12.7%)

Pruning

290 alts after pruning (285 fresh and 5 done)

	Pruned	Kept	Total
New	412	202	614
Fresh	19	83	102
Picked	0	0	0
Done	2	5	7
Total	433	290	723

Error

0.4b

Counts

723 → 290

Compiler

Compiled 21190 to 12735 computations (39.9% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(+.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	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_1464`
8×	`*-un-lft-identity_binary64_1442`
6×	`unpow-prod-down_binary64_1521`
4×	`add-log-exp_binary64_1481` `add-cube-cbrt_binary64_1477`
3×	`pow-unpow_binary64_1519` `add-exp-log_binary64_1480` `pow1_binary64_1503`
2×	`add-cbrt-cube_binary64_1478` `difference-of-squares_binary64_1411`
1×	`sum-log_binary64_1533` `pow-exp_binary64_1510` `unpow2_binary64_1507` `times-frac_binary64_1448` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `sqr-pow_binary64_1414` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out--_binary64_1394` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

2 → 33

Calls

4 calls:

15.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series943.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

644.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
299.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 2696 to 2265 computations (16% saved)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5112	1931

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

37.6b	(cos.f64 (-.f64 (.f64 (.f64 K (+.f64 m n)) 1/2) M))
0.0b	(-.f64 (.f64 (.f64 K (+.f64 m n)) 1/2) M)
0.0b	(-.f64 (.f64 (.f64 K (+.f64 m n)) 1/2) M)
37.6b	(cos.f64 (-.f64 (.f64 (.f64 K (+.f64 m n)) 1/2) M))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cancel-sign-sub-inv_binary64_1408`
4×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464` `cos-sum_binary64_1576` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
2×	`add-cbrt-cube_binary64_1478` `sub-neg_binary64_1435` `add-exp-log_binary64_1480` `pow1_binary64_1503`
1×	`flip3--_binary64_1446` `cos-diff_binary64_1579` `flip--_binary64_1417` `diff-log_binary64_1534`

Counts

2 → 26

Calls

4 calls:

10.0ms	(cos.f64 (-.f64 (.f64 (.f64 K (+.f64 m n)) 1/2) M))
8.0ms	(-.f64 (.f64 (.f64 K (+.f64 m n)) 1/2) M)
0.0ms	(-.f64 (.f64 (.f64 K (+.f64 m n)) 1/2) M)
0.0ms	(cos.f64 (-.f64 (.f64 (.f64 K (+.f64 m n)) 1/2) M))

series312.0ms (0.3%)

Counts

2 → 32

Calls

2 calls:

179.0ms	(-.f64 (.f64 (.f64 K (+.f64 m n)) 1/2) M)
132.0ms	(cos.f64 (-.f64 (.f64 (.f64 K (+.f64 m n)) 1/2) M))

Compiler

Compiled 794 to 786 computations (1% saved)

simplify48.0ms (0%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5227	934

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 m (-.f64 (.f64 n 1/2) M))
0.0b	(.f64 1/4 (.f64 m m))
0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M))) l))
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(.f64 1/4 (.f64 m m))
0.0b	(.f64 m (-.f64 (.f64 n 1/2) M))
4.9b	(+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))
37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cancel-sign-sub-inv_binary64_1408` `add-sqr-sqrt_binary64_1464`
12×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
8×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `associate-+r+_binary64_1374`
6×	`associate-l_binary64_1383` `add-log-exp_binary64_1481`
5×	`sub-neg_binary64_1435`
4×	`associate-r_binary64_1382` `cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cos-sum_binary64_1576`
2×	`associate-r/_binary64_1384` `-commutative_binary64_1373` `unswap-sqr_binary64_1410`
1×	`sum-log_binary64_1533` `flip3--_binary64_1446` `+-commutative_binary64_1372` `cos-diff_binary64_1579` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416`

Counts

4 → 78

Calls

8 calls:

9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(.f64 m (-.f64 (.f64 n 1/2) M))
7.0ms	(+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))
6.0ms	(.f64 1/4 (.f64 m m))
0.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

series833.0ms (0.8%)

Counts

4 → 50

Calls

4 calls:

415.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
250.0ms	(+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))
139.0ms	(.f64 m (-.f64 (.f64 n 1/2) M))
29.0ms	(.f64 1/4 (.f64 m m))

Compiler

Compiled 2842 to 2220 computations (21.9% saved)

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4991	1794
1	4991	1794

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

12.8b	(.f64 (-.f64 (cos.f64 M) (.f64 (neg.f64 (sin.f64 M)) (.f64 (.f64 K (+.f64 m n)) 1/2))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
3.7b	(.f64 (neg.f64 (sin.f64 M)) (.f64 (*.f64 K (+.f64 m n)) 1/2))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
3.7b	(.f64 (neg.f64 (sin.f64 M)) (.f64 (*.f64 K (+.f64 m n)) 1/2))
12.8b	(.f64 (-.f64 (cos.f64 M) (.f64 (neg.f64 (sin.f64 M)) (.f64 (.f64 K (+.f64 m n)) 1/2))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

rewrite96.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64_1442`
27×	`add-sqr-sqrt_binary64_1464`
16×	`pow1_binary64_1503`
15×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
14×	`add-log-exp_binary64_1481` `add-cube-cbrt_binary64_1477`
13×	`cancel-sign-sub-inv_binary64_1408` `associate-l_binary64_1383`
11×	`associate-r_binary64_1382`
9×	`distribute-lft-out--_binary64_1394`
7×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `exp-sum_binary64_1488`
6×	`diff-log_binary64_1534` `unpow-prod-down_binary64_1521`
5×	`associate-*r/_binary64_1384` `distribute-rgt-neg-in_binary64_1400` `difference-of-squares_binary64_1411`
4×	`associate--r+_binary64_1378` `associate-*l/_binary64_1385`
3×	`distribute-lft-neg-in_binary64_1399` `sub-neg_binary64_1435` `flip3--_binary64_1446` `pow-unpow_binary64_1519` `flip--_binary64_1417` `exp-diff_binary64_1490`
2×	`*-commutative_binary64_1373` `neg-log_binary64_1535` `frac-times_binary64_1452` `associate--r-_binary64_1381`
1×	`associate--l-_binary64_1380` `pow-exp_binary64_1510` `unpow2_binary64_1507` `times-frac_binary64_1448` `neg-mul-1_binary64_1438` `sqr-pow_binary64_1414` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-neg-out_binary64_1401` `neg-sub0_binary64_1437` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410` `pow-pow_binary64_1514`

Counts

4 → 112

Calls

8 calls:

35.0ms	(.f64 (-.f64 (cos.f64 M) (.f64 (neg.f64 (sin.f64 M)) (.f64 (.f64 K (+.f64 m n)) 1/2))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
24.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
11.0ms	(.f64 (neg.f64 (sin.f64 M)) (.f64 (*.f64 K (+.f64 m n)) 1/2))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))

series3.1s (2.8%)

Counts

4 → 102

Calls

4 calls:

1.8s	(.f64 (-.f64 (cos.f64 M) (.f64 (neg.f64 (sin.f64 M)) (.f64 (.f64 K (+.f64 m n)) 1/2))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
674.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
307.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
284.0ms	(.f64 (neg.f64 (sin.f64 M)) (.f64 (*.f64 K (+.f64 m n)) 1/2))

Compiler

Compiled 10108 to 7014 computations (30.6% saved)

simplify116.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5082	8272

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
0.0b	(sqrt.f64 (fabs.f64 (-.f64 m n)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 m n)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 m n)))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.5b	(.f64 (neg.f64 (sqrt.f64 (fabs.f64 (-.f64 m n)))) (.f64 1 (sqrt.f64 (fabs.f64 (-.f64 m n)))))
37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1464`
16×	`associate-l_binary64_1383`
15×	`*-un-lft-identity_binary64_1442`
13×	`add-cube-cbrt_binary64_1477`
12×	`add-exp-log_binary64_1480`
11×	`pow1_binary64_1503`
9×	`add-cbrt-cube_binary64_1478` `sqrt-prod_binary64_1458`
6×	`distribute-lft-neg-in_binary64_1399` `distribute-rgt-neg-in_binary64_1400` `unpow-prod-down_binary64_1521`
5×	`prod-exp_binary64_1491`
4×	`add-log-exp_binary64_1481` `cos-sum_binary64_1576`
3×	`cancel-sign-sub-inv_binary64_1408` `cbrt-unprod_binary64_1475` `pow-unpow_binary64_1519` `pow-prod-down_binary64_1513`
2×	`difference-of-squares_binary64_1411`
1×	`sqrt-pow1_binary64_1460` `associate-r_binary64_1382` `rem-sqrt-square_binary64_1455` `pow-exp_binary64_1510` `unpow2_binary64_1507` `times-frac_binary64_1448` `sub-neg_binary64_1435` `1-exp_binary64_1486` `*-commutative_binary64_1373` `cos-diff_binary64_1579` `neg-mul-1_binary64_1438` `sqr-pow_binary64_1414` `pow1/2_binary64_1522` `distribute-lft-neg-out_binary64_1401` `distribute-lft-out--_binary64_1394` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

4 → 79

Calls

8 calls:

11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(.f64 (neg.f64 (sqrt.f64 (fabs.f64 (-.f64 m n)))) (.f64 1 (sqrt.f64 (fabs.f64 (-.f64 m n)))))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 m n)))
0.0ms	(sqrt.f64 (fabs.f64 (-.f64 m n)))

series568.0ms (0.5%)

Counts

4 → 53

Calls

4 calls:

307.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
152.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
55.0ms	(.f64 (neg.f64 (sqrt.f64 (fabs.f64 (-.f64 m n)))) (.f64 1 (sqrt.f64 (fabs.f64 (-.f64 m n)))))
53.0ms	(sqrt.f64 (fabs.f64 (-.f64 m n)))

Compiler

Compiled 3856 to 2845 computations (26.2% saved)

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4905	2075
1	4905	2075

prune24.6s (22.3%)

Pruning

438 alts after pruning (429 fresh and 9 done)

	Pruned	Kept	Total
New	440	185	625
Fresh	36	244	280
Picked	0	0	0
Done	1	9	10
Total	477	438	915

Error

0.4b

Counts

915 → 438

Compiler

Compiled 29778 to 17668 computations (40.7% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite35.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1464`
11×	`*-un-lft-identity_binary64_1442`
6×	`add-log-exp_binary64_1481` `unpow-prod-down_binary64_1521`
5×	`add-cube-cbrt_binary64_1477`
3×	`cancel-sign-sub-inv_binary64_1408` `pow-unpow_binary64_1519` `add-exp-log_binary64_1480` `pow1_binary64_1503` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
2×	`add-cbrt-cube_binary64_1478` `diff-log_binary64_1534`
1×	`associate--l-_binary64_1380` `pow-exp_binary64_1510` `unpow2_binary64_1507` `times-frac_binary64_1448` `sub-neg_binary64_1435` `distribute-rgt-neg-in_binary64_1400` `flip3--_binary64_1446` `neg-log_binary64_1535` `flip--_binary64_1417` `sqr-pow_binary64_1414` `neg-sub0_binary64_1437` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

2 → 40

Calls

4 calls:

20.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
0.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series925.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

636.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l)
288.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 2823 to 2392 computations (15.3% saved)

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5007	2077

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 m (+.f64 (.f64 n 1/2) (.f64 1/4 m))) (.f64 M (-.f64 M (+.f64 m n)))) l)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 M (+.f64 m n))
0.0b	(*.f64 M (-.f64 M (+.f64 m n)))
0.0b	(+.f64 (+.f64 (.f64 m (+.f64 (.f64 n 1/2) (.f64 1/4 m))) (.f64 M (-.f64 M (+.f64 m n)))) l)
0.0b	(.f64 m (+.f64 (.f64 n 1/2) (*.f64 1/4 m)))
2.5b	(+.f64 (.f64 m (+.f64 (.f64 n 1/2) (.f64 1/4 m))) (.f64 M (-.f64 M (+.f64 m n))))
37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite51.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1442`
11×	`cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464`
10×	`associate-*r/_binary64_1384` `associate-+r+_binary64_1374`
9×	`add-cube-cbrt_binary64_1477`
7×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
6×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
5×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
4×	`sum-log_binary64_1533` `cos-sum_binary64_1576` `frac-add_binary64_1450`
3×	`associate-r_binary64_1382` `associate-+l+_binary64_1375` `sub-neg_binary64_1435` `associate-l_binary64_1383` `distribute-lft-out_binary64_1393`
2×	`flip3--_binary64_1446` `+-commutative_binary64_1372` `flip--_binary64_1417`
1×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `cos-diff_binary64_1579` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`

Counts

4 → 75

Calls

8 calls:

12.0ms	(+.f64 (.f64 m (+.f64 (.f64 n 1/2) (.f64 1/4 m))) (.f64 M (-.f64 M (+.f64 m n))))
12.0ms	(+.f64 (+.f64 (.f64 m (+.f64 (.f64 n 1/2) (.f64 1/4 m))) (.f64 M (-.f64 M (+.f64 m n)))) l)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(.f64 m (+.f64 (.f64 n 1/2) (*.f64 1/4 m)))
0.0ms	(*.f64 M (-.f64 M (+.f64 m n)))

series1.2s (1.1%)

Counts

4 → 80

Calls

4 calls:

502.0ms	(+.f64 (+.f64 (.f64 m (+.f64 (.f64 n 1/2) (.f64 1/4 m))) (.f64 M (-.f64 M (+.f64 m n)))) l)
388.0ms	(+.f64 (.f64 m (+.f64 (.f64 n 1/2) (.f64 1/4 m))) (.f64 M (-.f64 M (+.f64 m n))))
151.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
127.0ms	(.f64 m (+.f64 (.f64 n 1/2) (*.f64 1/4 m)))

Compiler

Compiled 4474 to 3411 computations (23.8% saved)

simplify70.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5413	3534

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 m (-.f64 (.f64 n 1/2) M))
0.0b	(.f64 1/4 (.f64 m m))
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.f64 (neg.f64 (+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
0.1b	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
0.6b	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
4.9b	(+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))
37.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite47.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cancel-sign-sub-inv_binary64_1408`
12×	`add-sqr-sqrt_binary64_1464` `cos-sum_binary64_1576` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`exp-diff_binary64_1490` `associate-+r+_binary64_1374`
7×	`add-log-exp_binary64_1481`
6×	`exp-prod_binary64_1494`
5×	`sub-neg_binary64_1435` `pow1_binary64_1503`
4×	`add-cbrt-cube_binary64_1478` `log-prod_binary64_1528` `log-pow_binary64_1531` `add-exp-log_binary64_1480` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `log-div_binary64_1529`
3×	`cos-diff_binary64_1579`
2×	`exp-sum_binary64_1488`
1×	`sum-log_binary64_1533` `rem-exp-log_binary64_1482` `rem-log-exp_binary64_1483` `+-commutative_binary64_1372` `flip3-+_binary64_1445` `flip-+_binary64_1416`

Counts

4 → 67

Calls

8 calls:

10.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
10.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))
0.0ms	(-.f64 (neg.f64 (+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))

series1.1s (1%)

Counts

4 → 56

Calls

4 calls:

536.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
247.0ms	(+.f64 (.f64 1/4 (.f64 m m)) (.f64 m (-.f64 (.f64 n 1/2) M)))
181.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
124.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 3975 to 3137 computations (21.1% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5243	2364

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
0.9b	(pow.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2))
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
1.5b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1464`
10×	`*-un-lft-identity_binary64_1442`
9×	`cbrt-prod_binary64_1473`
8×	`add-cube-cbrt_binary64_1477`
6×	`unpow-prod-down_binary64_1521`
5×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481`
3×	`pow1/3_binary64_1524`
2×	`difference-of-squares_binary64_1411`
1×	`pow-exp_binary64_1510` `times-frac_binary64_1448` `pow-unpow_binary64_1519` `sqr-pow_binary64_1414` `distribute-lft-out--_binary64_1394` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

4 → 51

Calls

8 calls:

11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)
0.0ms	(pow.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2))

series1.2s (1.1%)

Counts

4 → 23

Calls

4 calls:

1.2s	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)

Compiler

Compiled 4434 to 3954 computations (10.8% saved)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4972	3872
1	4972	3872

prune26.2s (23.7%)

Pruning

554 alts after pruning (540 fresh and 14 done)

	Pruned	Kept	Total
New	315	137	452
Fresh	21	403	424
Picked	0	0	0
Done	0	14	14
Total	336	554	890

Error

0.4b

Counts

890 → 554

Compiler

Compiled 12347 to 6759 computations (45.3% saved)

simplify948.0ms (0.9%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5267	64108

regimes18.2s (16.5%)

Compiler: Compiled 221528 to 167007 computations (24.6% saved)

bsearch41.0ms (0%)

Steps

Iters	Range		Point
15	1.0	#hash((type . real) (value . NaN))	#hash((type . real) (value . NaN))

Compiler

Compiled 29 to 23 computations (20.7% saved)

regimes45.0ms (0%)

Compiler: Compiled 25 to 140 computations (-460% saved)

bsearch4.0ms (0%)

Compiler: Compiled 64 to 52 computations (18.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	100	94
1	100	94

end0.0ms (0%)

sample2.2s (2%)

Algorithm

1×

intervals

Results

805.0ms	7854×	body	128	valid
41.0ms	88×	body	1024	invalid
38.0ms	331×	body	128	invalid
28.0ms	62×	body	1024	valid
27.0ms	75×	body	512	invalid
18.0ms	56×	body	512	valid
12.0ms	21×	body	2048	invalid
11.0ms	56×	body	256	invalid
6.0ms	28×	body	256	valid

Compiler

Compiled 37049 to 27933 computations (24.6% saved)