Details

analyze1.9s (9.2%)

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%	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)

sample139.0ms (0.7%)

Algorithm

1×

intervals

Results

46.0ms	256×	body	128	valid
36.0ms	229×	body	128	nan
29.0ms	160×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify36.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5205	41

prune8.0ms (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: 27.7b

Counts

2 → 1

Compiler

Compiled 116 to 100 computations (13.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.2b	(.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))))
9.4b	(sqrt.f64 (/.f64 d h))
13.7b	(sqrt.f64 (/.f64 d l))
14.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite55.0ms (0.3%)

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` `flip--_binary64`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`

Counts

4 → 127

Calls

4 calls:

17.0ms	(.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))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d h))
3.0ms	(sqrt.f64 (/.f64 d l))

series873.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

562.0ms	(.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))))
167.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
74.0ms	(sqrt.f64 (/.f64 d l))
69.0ms	(sqrt.f64 (/.f64 d h))

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4956	3595
1	4956	3595

prune1.3s (6.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	121	18	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	18	140

Merged error: 15.7b

Counts

140 → 18

Compiler

Compiled 27760 to 19977 computations (28% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(/.f64 (.f64 M D) (.f64 d 2))
8.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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))))
13.7b	(sqrt.f64 (/.f64 d l))
14.5b	(.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`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64` `div-exp_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`pow1_binary64` `cbrt-unprod_binary64` `associate-r_binary64`
13×	`sqrt-prod_binary64` `sqrt-div_binary64`
12×	`associate-*r/_binary64`
10×	`pow-exp_binary64`
9×	`frac-times_binary64`
7×	`pow-prod-down_binary64`
6×	`cbrt-undiv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `cancel-sign-sub-inv_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 126

Calls

4 calls:

23.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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))))
13.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

series2.1s (10.3%)

Counts

4 → 12

Calls

4 calls:

1.8s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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))))
165.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
75.0ms	(sqrt.f64 (/.f64 d l))
45.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify97.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4959	4485
1	4959	4485

prune795.0ms (3.9%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	128	10	138
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	132	24	156

Merged error: 14.4b

Counts

156 → 24

Compiler

Compiled 18875 to 11510 computations (39% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 d)
6.1b	(/.f64 (.f64 M D) (.f64 d 2))
8.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
14.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite79.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
24×	`pow1_binary64`
23×	`cbrt-unprod_binary64`
20×	`div-exp_binary64`
18×	`associate-*r/_binary64`
16×	`associate-r_binary64`
14×	`pow-prod-down_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`times-frac_binary64` `pow-exp_binary64`
9×	`frac-times_binary64`
6×	`cbrt-undiv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`cbrt-prod_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `cancel-sign-sub-inv_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/3_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 118

Calls

4 calls:

33.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.0ms	(cbrt.f64 d)

series2.5s (12.3%)

Counts

4 → 12

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
162.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
150.0ms	(cbrt.f64 d)
43.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4994	5248
1	4994	5248

prune567.0ms (2.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	125	5	130
Fresh	2	21	23
Picked	1	0	1
Done	0	0	0
Total	128	26	154

Merged error: 10.7b

Counts

154 → 26

Compiler

Compiled 14565 to 7431 computations (49% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(/.f64 (.f64 M D) (.f64 d 2))
6.4b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
7.1b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
8.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))

rewrite90.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
48×	`add-cbrt-cube_binary64`
24×	`pow1_binary64`
23×	`cbrt-unprod_binary64`
21×	`div-exp_binary64`
17×	`associate-*r/_binary64`
15×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
14×	`pow-prod-down_binary64` `cancel-sign-sub-inv_binary64`
12×	`add-cube-cbrt_binary64` `sqrt-div_binary64`
10×	`times-frac_binary64` `pow-exp_binary64`
9×	`associate-r_binary64` `frac-times_binary64`
8×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
7×	`cbrt-undiv_binary64`
6×	`associate-*l/_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `flip3--_binary64` `div-inv_binary64` `flip--_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `-commutative_binary64`
1×	`distribute-lft-out--_binary64`

Counts

4 → 130

Calls

4 calls:

36.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
14.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
9.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))

series2.5s (12.3%)

Counts

4 → 12

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
150.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
148.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
42.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify112.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5062	6969

prune984.0ms (4.8%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	1	24	25
Picked	0	1	1
Done	0	0	0
Total	136	32	168

Merged error: 9.7b

Counts

168 → 32

Compiler

Compiled 25539 to 14177 computations (44.5% saved)

regimes596.0ms (2.9%)

Compiler: Compiled 9112 to 6098 computations (33.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	87	73
1	87	73

end0.0ms (0%)

sample5.4s (26.3%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
1.2s	8551×	body	128	nan
901.0ms	4810×	body	128	invalid

Compiler

Compiled 1597 to 1073 computations (32.8% saved)

Details

analyze1.9s (9.2%)

sample139.0ms (0.7%)

simplify36.0ms (0.2%)

prune8.0ms (0%)

localize19.0ms (0.1%)

rewrite55.0ms (0.3%)

series873.0ms (4.2%)

simplify81.0ms (0.4%)

prune1.3s (6.4%)

localize25.0ms (0.1%)

rewrite70.0ms (0.3%)

series2.1s (10.3%)

simplify97.0ms (0.5%)

prune795.0ms (3.9%)

localize30.0ms (0.1%)

rewrite79.0ms (0.4%)

series2.5s (12.3%)

simplify99.0ms (0.5%)

prune567.0ms (2.8%)

localize29.0ms (0.1%)

rewrite90.0ms (0.4%)

series2.5s (12.3%)

simplify112.0ms (0.5%)

prune984.0ms (4.8%)

regimes596.0ms (2.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.4s (26.3%)

Profiling