Details

analyze2.5s (17.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample57.0ms (0.4%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
7.0ms	95×	body	128	nan
2.0ms	34×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify42.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

893×	`div-sub_binary64`
645×	`distribute-neg-frac_binary64`
581×	`distribute-rgt-neg-in_binary64`
569×	`distribute-lft-neg-in_binary64`
418×	`associate-/l*_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	111	27
3	718	27
4	2816	27
5	4688	27
6	6103	27

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

15.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	15.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Compiler

Compiled 48 to 36 computations (25% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.3b	(/.f64 (.f64 M D) (.f64 2 d))
5.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
11.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite252.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

67×	`add-exp-log_binary64`
38×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
19×	`div-exp_binary64` `associate-r_binary64`

Counts

4 → 116

Calls

4 calls:

11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

Compiler

Compiled 3232 to 1835 computations (43.2% saved)

series542.0ms (3.7%)

Error

6.7b

Counts

4 → 81

Calls

4 calls:

215.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
136.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
124.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
31.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 5471 to 4152 computations (24.1% saved)

simplify176.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

354×	`times-frac_binary64`
309×	`associate-l_binary64`
292×	`associate-r_binary64`
270×	`associate-/l*_binary64`
220×	`cancel-sign-sub-inv_binary64`

Counts

197 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	5074
1	850	4772
2	3698	4771
3	4900	4771
4	4990	4771

prune169.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	140	13	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	13	154

Error

4.2b

Counts

154 → 13

Alt Table

Status	Error	Program
	61.8b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
	61.2b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (.f64 d d) l)) -1/4)) (*.f64 D w0))
	28.7b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 M M) (*.f64 h w0)) l))))
	17.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	60.0b	(-.f64 (.f64 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))) -1/2) (.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0)))
	62.1b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) l) -1/4)) d))
	14.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	61.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
▶	10.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	13.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) 2) (.f64 (/.f64 h l) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2))))))
	13.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l))))))

Compiler

Compiled 3313 to 1868 computations (43.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.2b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
4.3b	(/.f64 (.f64 M D) (.f64 2 d))
5.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
6.1b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

rewrite315.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

4.0b

Rules

165×	`add-exp-log_binary64`
91×	`prod-exp_binary64`
40×	`div-exp_binary64`
30×	`add-cbrt-cube_binary64`
25×	`pow-exp_binary64`

Counts

4 → 130

Calls

4 calls:

11.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))

Compiler

Compiled 3580 to 2299 computations (35.8% saved)

series407.0ms (2.7%)

Error

4.1b

Counts

4 → 63

Calls

4 calls:

140.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
125.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
84.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
36.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4057 to 3150 computations (22.4% saved)

simplify189.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

312×	`distribute-rgt-neg-in_binary64`
291×	`distribute-lft-neg-in_binary64`
275×	`associate-l_binary64`
262×	`times-frac_binary64`
229×	`associate-r_binary64`

Counts

193 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	280	4128
1	667	3940
2	2868	3934
3	4689	3934
4	4991	3934
5	4966	3934

prune144.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	143	5	148
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	149	12	161

Error

3.9b

Counts

161 → 12

Alt Table

Status	Error	Program
	61.8b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
▶	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2))) (/.f64 1 l)))))
	9.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) (/.f64 1 l)))))
	61.2b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (.f64 d d) l)) -1/4)) (*.f64 D w0))
	28.7b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 M M) (*.f64 h w0)) l))))
	17.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	60.0b	(-.f64 (.f64 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))) -1/2) (.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0)))
	61.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	60.5b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (pow.f64 (*.f64 M D) 2) (/.f64 l h)) -1/4)) d))
	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (*.f64 2 d))) 2)) (/.f64 1 l)))))
	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 (*.f64 d d) l)) -1/4)) (neg.f64 M)))

Compiler

Compiled 2313 to 1448 computations (37.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.3b	(/.f64 (.f64 M D) (.f64 2 d))
4.3b	(/.f64 (.f64 M D) (.f64 2 d))
5.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 2 2))) (/.f64 1 l))))
5.2b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite262.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

Rules

46×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`prod-exp_binary64` `cbrt-unprod_binary64`
12×	`div-exp_binary64` `cbrt-undiv_binary64`
10×	`add-sqr-sqrt_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 86

Calls

4 calls:

11.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
9.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 2 2))) (/.f64 1 l))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3407 to 2114 computations (38% saved)

series294.0ms (2%)

Error

3.9b

Counts

4 → 57

Calls

4 calls:

138.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 2 2))) (/.f64 1 l))))
61.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
37.0ms	(/.f64 (.f64 M D) (.f64 2 d))
36.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4213 to 3148 computations (25.3% saved)

simplify94.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

413×	`associate-/r/_binary64`
319×	`associate-/l/_binary64`
271×	`distribute-rgt-neg-in_binary64`
263×	`times-frac_binary64`
254×	`distribute-lft-neg-in_binary64`

Counts

143 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	3111
1	537	2473
2	2502	2458
3	5089	2458

prune154.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Error

3.5b

Counts

104 → 12

Alt Table

Status	Error	Program
	61.8b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
	9.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) (/.f64 1 l)))))
	61.2b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (.f64 d d) l)) -1/4)) (*.f64 D w0))
	28.7b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 M M) (*.f64 h w0)) l))))
	17.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	60.0b	(-.f64 (.f64 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))) -1/2) (.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0)))
	61.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	60.5b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (pow.f64 (*.f64 M D) 2) (/.f64 l h)) -1/4)) d))
▶	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (*.f64 2 d))) 2)) (/.f64 1 l)))))
	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) 3)) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2))) (/.f64 1 l)))))
	60.3b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 D (.f64 D h)) (.f64 (*.f64 d d) l)) -1/4)) (neg.f64 M)))

Compiler

Compiled 2706 to 1664 computations (38.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2)) (/.f64 1 l))))
6.9b	(.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))))
19.1b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
19.1b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

rewrite225.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

29×	`add-exp-log_binary64`
24×	`add-cbrt-cube_binary64`
15×	`prod-exp_binary64` `cbrt-unprod_binary64`
10×	`pow1_binary64` `cbrt-prod_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

4 → 72

Calls

4 calls:

12.0ms	(.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))))
6.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2)) (/.f64 1 l))))
4.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
4.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

Compiler

Compiled 3549 to 2153 computations (39.3% saved)

series694.0ms (4.7%)

Error

2.8b

Counts

4 → 58

Calls

4 calls:

223.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2)) (/.f64 1 l))))
216.0ms	(.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))))
90.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
89.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

Compiler

Compiled 6624 to 5064 computations (23.6% saved)

simplify117.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

409×	`associate-r_binary64`
363×	`associate-l_binary64`
301×	`times-frac_binary64`
272×	`*-commutative_binary64`
187×	`associate-/l*_binary64`

Counts

130 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	360	4339
1	1004	3427
2	3625	3016
3	4962	3016

prune170.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	106	13	119

Error

3.0b

Counts

119 → 13

Alt Table

Status	Error	Program
	61.8b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
	9.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) (/.f64 1 l)))))
	61.2b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (.f64 d d) l)) -1/4)) (*.f64 D w0))
	28.7b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 M M) (*.f64 h w0)) l))))
	17.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	60.0b	(-.f64 (.f64 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))) -1/2) (.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0)))
	61.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	60.5b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (pow.f64 (*.f64 M D) 2) (/.f64 l h)) -1/4)) d))
	59.7b	(.f64 w0 (neg.f64 (.f64 (.f64 (/.f64 D d) (.f64 M (sqrt.f64 1/2))) (sqrt.f64 (/.f64 (*.f64 -1/2 h) l)))))
	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (*.f64 2 d))) 2)) (/.f64 1 l)))))
	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) 3)) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2))) (/.f64 1 l)))))
	60.3b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 D (.f64 D h)) (.f64 (*.f64 d d) l)) -1/4)) (neg.f64 M)))

Compiler

Compiled 3042 to 1912 computations (37.1% saved)

regimes6.0s (40.1%)

Accuracy

Total 4.3b remaining (50.3%)

Threshold costs 0b (0%)

Compiler

Compiled 114913 to 84808 computations (26.2% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 21 to 16 computations (23.8% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

27×	`*-commutative_binary64`
18×	`sub-neg_binary64` `+-commutative_binary64`
17×	`neg-sub0_binary64`
16×	`neg-mul-1_binary64`
11×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	118
1	70	118
2	96	118
3	119	118
4	144	118
5	164	118
6	175	118
7	181	118
8	183	118
9	182	118

end11.0ms (0.1%)

Remove: (sort M D)
Compiler: Compiled 252 to 171 computations (32.1% saved)

sample1.9s (13.1%)

Algorithm

1×

intervals

Results

620.0ms	8000×	body	128	valid
229.0ms	3191×	body	128	nan
100.0ms	1292×	body	128	invalid

Compiler

Compiled 537 to 373 computations (30.5% saved)

Iter	Nodes	Cost
0	46	118
1	70	118
2	96	118
3	119	118
4	144	118
5	164	118
6	175	118
7	181	118
8	183	118
9	182	118

Iter	Nodes	Cost
0	46	118
1	70	118
2	96	118
3	119	118
4	144	118
5	164	118
6	175	118
7	181	118
8	183	118
9	182	118

Details

analyze2.5s (17.1%)

sample57.0ms (0.4%)

simplify42.0ms (0.3%)

prune3.0ms (0%)

localize18.0ms (0.1%)

rewrite252.0ms (1.7%)

series542.0ms (3.7%)

simplify176.0ms (1.2%)

prune169.0ms (1.1%)

localize14.0ms (0.1%)

rewrite315.0ms (2.1%)

series407.0ms (2.7%)

simplify189.0ms (1.3%)

prune144.0ms (1%)

localize16.0ms (0.1%)

rewrite262.0ms (1.8%)

series294.0ms (2%)

simplify94.0ms (0.6%)

prune154.0ms (1%)

localize19.0ms (0.1%)

rewrite225.0ms (1.5%)

series694.0ms (4.7%)

simplify117.0ms (0.8%)

prune170.0ms (1.1%)

regimes6.0s (40.1%)

bsearch9.0ms (0.1%)

simplify10.0ms (0.1%)

end11.0ms (0.1%)

sample1.9s (13.1%)

Profiling

Iter	Nodes	Cost
0	46	118
1	70	118
2	96	118
3	119	118
4	144	118
5	164	118
6	175	118
7	181	118
8	183	118
9	182	118