Details

analyze2.4s (26.2%)

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)

sample47.0ms (0.5%)

Algorithm

1×

intervals

Results

27.0ms	249×	body	128	valid
2.0ms	3×	body	1024	valid
1.0ms	3×	body	512	valid
1.0ms	3×	body	512	invalid
1.0ms	8×	body	128	invalid
1.0ms	1×	body	2048	invalid
1.0ms	1×	body	1024	invalid
0.0ms	2×	body	256	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4960	43
1	4960	43

prune8.0ms (0.1%)

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

Merged error: 14.7b

Counts

2 → 2

Compiler

Compiled 142 to 112 computations (21.1% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
34.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite76.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
16×	`add-log-exp_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`add-cube-cbrt_binary64`
9×	`distribute-lft-out--_binary64`
7×	`diff-log_binary64`
6×	`unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64` `difference-of-squares_binary64`
4×	`sub-neg_binary64` `associate--r+_binary64` `add-cbrt-cube_binary64` `cos-sum_binary64`
3×	`pow-unpow_binary64`
2×	`flip3--_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `associate--l-_binary64` `neg-sub0_binary64` `unpow2_binary64` `associate--r-_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cos-diff_binary64` `times-frac_binary64` `pow-exp_binary64`

Counts

4 → 79

Calls

4 calls:

32.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
11.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

series627.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

277.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
156.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
102.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
92.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

simplify110.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4954	1904
1	4954	1904

prune258.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	7	91
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 1.6b

Counts

93 → 7

Compiler

Compiled 5563 to 3298 computations (40.7% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

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)

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`add-log-exp_binary64`
8×	`cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64`
6×	`diff-log_binary64` `add-cube-cbrt_binary64` `unpow-prod-down_binary64`
4×	`associate--r+_binary64` `difference-of-squares_binary64`
3×	`pow-unpow_binary64` `pow1_binary64` `add-exp-log_binary64`
2×	`sub-neg_binary64` `add-cbrt-cube_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `associate--l-_binary64` `neg-sub0_binary64` `unpow2_binary64` `associate--r-_binary64` `pow-pow_binary64` `sqr-pow_binary64` `times-frac_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

2 → 51

Calls

2 calls:

31.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series404.0ms (4.4%)

Counts

2 → 6

Calls

2 calls:

288.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
115.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5022	1230

prune117.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 1.6b

Counts

64 → 7

Compiler

Compiled 2400 to 1493 computations (37.8% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.1b	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
0.5b	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
34.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite58.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64` `cos-sum_binary64`
9×	`cancel-sign-sub-inv_binary64`
8×	`exp-diff_binary64`
6×	`pow1_binary64` `unpow-prod-down_binary64` `exp-prod_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64`
4×	`log-prod_binary64` `log-pow_binary64` `add-cbrt-cube_binary64` `log-div_binary64`
3×	`pow-unpow_binary64` `sub-neg_binary64` `cos-diff_binary64`
2×	`exp-sum_binary64` `difference-of-squares_binary64`
1×	`pow-to-exp_binary64` `unpow2_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `pow-exp_binary64`

Counts

4 → 69

Calls

4 calls:

13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
12.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
12.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series798.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

303.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
250.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
146.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
99.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4938	1718
1	4938	1718

prune210.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	81	7	88

Merged error: 1.6b

Counts

88 → 7

Compiler

Compiled 4614 to 2696 computations (41.6% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3))
0.5b	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)))
0.8b	(pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)
34.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite75.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
17×	`log-prod_binary64`
16×	`cos-sum_binary64`
12×	`cube-div_binary64` `cancel-sign-sub-inv_binary64` `exp-diff_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
8×	`cbrt-div_binary64`
7×	`cos-diff_binary64`
6×	`pow1_binary64` `exp-sum_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `pow-pow_binary64` `log-div_binary64`
3×	`pow-unpow_binary64` `sqr-pow_binary64` `unpow3_binary64` `exp-prod_binary64` `cube-mult_binary64`
2×	`pow1/3_binary64` `log-pow_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `rem-log-exp_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 102

Calls

4 calls:

18.0ms	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)))
15.0ms	(pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)
14.0ms	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3))
12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series1.4s (15.6%)

Counts

4 → 12

Calls

4 calls:

741.0ms	(pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)
284.0ms	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)))
259.0ms	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3))
137.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify112.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4863	3036
1	4863	3036

prune224.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	114	7	121

Merged error: 1.6b

Counts

121 → 7

Compiler

Compiled 4939 to 2635 computations (46.6% saved)

regimes120.0ms (1.3%)

Compiler: Compiled 1220 to 995 computations (18.4% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	159	26
1	159	26

end0.0ms (0%)

sample1.7s (18.3%)

Algorithm

1×

intervals

Results

885.0ms	7832×	body	128	valid
40.0ms	70×	body	1024	valid
37.0ms	78×	body	1024	invalid
28.0ms	263×	body	128	invalid
27.0ms	83×	body	512	invalid
21.0ms	62×	body	512	valid
13.0ms	59×	body	256	invalid
13.0ms	18×	body	2048	invalid
8.0ms	35×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 289 to 234 computations (19% saved)

Details

analyze2.4s (26.2%)

sample47.0ms (0.5%)

simplify73.0ms (0.8%)

prune8.0ms (0.1%)

localize23.0ms (0.3%)

rewrite76.0ms (0.8%)

series627.0ms (6.9%)

simplify110.0ms (1.2%)

prune258.0ms (2.8%)

localize16.0ms (0.2%)

rewrite50.0ms (0.6%)

series404.0ms (4.4%)

simplify77.0ms (0.8%)

prune117.0ms (1.3%)

localize27.0ms (0.3%)

rewrite58.0ms (0.6%)

series798.0ms (8.8%)

simplify80.0ms (0.9%)

prune210.0ms (2.3%)

localize29.0ms (0.3%)

rewrite75.0ms (0.8%)

series1.4s (15.6%)

simplify112.0ms (1.2%)

prune224.0ms (2.5%)

regimes120.0ms (1.3%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.7s (18.3%)

Profiling