Details

analyze1.9s (9.4%)

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%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample140.0ms (0.7%)

Algorithm

1×

intervals

Results

45.0ms	256×	body	80	valid
38.0ms	233×	body	80	nan
28.0ms	155×	body	80	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify64.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5140	41

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 27.3b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
9.9b	(sqrt.f64 (/.f64 d h))
12.8b	(sqrt.f64 (/.f64 d l))
15.4b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite48.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64`
41×	`prod-exp_binary64`
32×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
21×	`add-cbrt-cube_binary64`
16×	`associate-r_binary64` `div-exp_binary64`
14×	`sqrt-div_binary64`
13×	`pow1_binary64`
10×	`pow-exp_binary64`
9×	`cbrt-unprod_binary64` `frac-times_binary64`
6×	`associate-r/_binary64` `associate-l/_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `flip3--_binary64` `rem-sqrt-square_binary64` `insert-posit16` `flip--_binary64`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 129

Calls

4 calls:

20.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
14.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
4.0ms	(sqrt.f64 (/.f64 d h))
4.0ms	(sqrt.f64 (/.f64 d l))

series878.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

549.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
172.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
80.0ms	(sqrt.f64 (/.f64 d h))
76.0ms	(sqrt.f64 (/.f64 d l))

simplify178.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4971	3574
1	4971	3574

prune294.0ms (1.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	120	21	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	21	142

Merged error: 14.1b

Counts

142 → 21

Compiler

Compiled 5513 to 2762 computations (49.9% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.3b	(/.f64 (.f64 M D) (.f64 d 2))
6.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
9.9b	(sqrt.f64 (/.f64 d h))
15.4b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite70.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-exp-log_binary64`
48×	`prod-exp_binary64`
37×	`add-cbrt-cube_binary64` `sqrt-div_binary64`
29×	`frac-times_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64` `div-exp_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`associate-*r/_binary64`
16×	`pow1_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `associate-*l/_binary64`
13×	`sqrt-prod_binary64`
10×	`pow-exp_binary64`
8×	`flip3--_binary64` `flip--_binary64`
7×	`pow-prod-down_binary64`
6×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 140

Calls

4 calls:

36.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
14.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
8.0ms	(/.f64 (.f64 M D) (.f64 d 2))
4.0ms	(sqrt.f64 (/.f64 d h))

series1.9s (9.5%)

Counts

4 → 12

Calls

4 calls:

1.6s	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
169.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
84.0ms	(sqrt.f64 (/.f64 d h))
44.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify136.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5128	5224

prune334.0ms (1.6%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	141	11	152
Fresh	4	16	20
Picked	1	0	1
Done	0	0	0
Total	146	27	173

Merged error: 11.3b

Counts

173 → 27

Compiler

Compiled 7797 to 3898 computations (50% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.1b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
5.3b	(/.f64 (.f64 M D) (.f64 d 2))
6.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
15.4b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite80.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
37×	`sqrt-div_binary64`
30×	`associate-*r/_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
29×	`frac-times_binary64`
25×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
23×	`cbrt-unprod_binary64`
22×	`sqrt-prod_binary64`
20×	`div-exp_binary64`
16×	`associate-r_binary64` `associate-*l/_binary64`
14×	`pow-prod-down_binary64`
10×	`cbrt-prod_binary64` `pow-exp_binary64`
8×	`flip3--_binary64` `flip--_binary64`
6×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`rem-sqrt-square_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 156

Calls

4 calls:

42.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
14.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
8.0ms	(/.f64 (.f64 M D) (.f64 d 2))
5.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))

series3.0s (14.8%)

Counts

4 → 12

Calls

4 calls:

2.6s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
186.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
168.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
45.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify186.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4963	7167
1	4963	7167

prune431.0ms (2.1%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	159	9	168
Fresh	4	22	26
Picked	1	0	1
Done	0	0	0
Total	164	31	195

Merged error: 9.9b

Counts

195 → 31

Compiler

Compiled 10636 to 4594 computations (56.8% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
5.3b	(/.f64 (.f64 M D) (.f64 d 2))
6.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
11.4b	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite111.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

291×	`add-exp-log_binary64`
189×	`prod-exp_binary64`
70×	`add-cbrt-cube_binary64`
51×	`cbrt-unprod_binary64`
45×	`div-exp_binary64`
36×	`pow1_binary64` `sqrt-div_binary64`
30×	`associate-*r/_binary64` `pow-exp_binary64`
29×	`frac-times_binary64`
26×	`associate-r_binary64`
22×	`pow-prod-down_binary64`
19×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`associate-*l/_binary64`
9×	`cbrt-undiv_binary64` `cbrt-prod_binary64`
8×	`flip3--_binary64` `flip--_binary64`
6×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`associate-l_binary64` `*-commutative_binary64`
2×	`sub-neg_binary64` `div-inv_binary64`
1×	`associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 188

Calls

4 calls:

44.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
25.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
15.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
8.0ms	(/.f64 (.f64 M D) (.f64 d 2))

series3.2s (15.8%)

Counts

4 → 12

Calls

4 calls:

2.7s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
314.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
189.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
46.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify201.0ms (1%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	5005	8434

prune458.0ms (2.3%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	194	6	200
Fresh	1	29	30
Picked	1	0	1
Done	0	0	0
Total	196	35	231

Merged error: 9.7b

Counts

231 → 35

Compiler

Compiled 11279 to 4196 computations (62.8% saved)

regimes892.0ms (4.4%)

Compiler: Compiled 11197 to 7914 computations (29.3% saved)

bsearch163.0ms (0.8%)

Steps

Iters	Range		Point
7	3.7129633916499706e-28	6.142878123306293e-27	4.34839696867144e-28

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	182	160
1	182	160

end0.0ms (0%)

sample5.4s (26.8%)

Algorithm

1×

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8345×	body	80	nan
860.0ms	4783×	body	80	invalid

Compiler

Compiled 1755 to 1233 computations (29.7% saved)

Details

analyze1.9s (9.4%)

sample140.0ms (0.7%)

simplify64.0ms (0.3%)

prune6.0ms (0%)

localize22.0ms (0.1%)

rewrite48.0ms (0.2%)

series878.0ms (4.3%)

simplify178.0ms (0.9%)

prune294.0ms (1.5%)

localize27.0ms (0.1%)

rewrite70.0ms (0.3%)

series1.9s (9.5%)

simplify136.0ms (0.7%)

prune334.0ms (1.6%)

localize33.0ms (0.2%)

rewrite80.0ms (0.4%)

series3.0s (14.8%)

simplify186.0ms (0.9%)

prune431.0ms (2.1%)

localize37.0ms (0.2%)

rewrite111.0ms (0.5%)

series3.2s (15.8%)

simplify201.0ms (1%)

prune458.0ms (2.3%)

regimes892.0ms (4.4%)

bsearch163.0ms (0.8%)

simplify13.0ms (0.1%)

end0.0ms (0%)

sample5.4s (26.8%)

Profiling