Details

analyze2.5s (14.2%)

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 (0.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
6.0ms	82×	body	128	nan
3.0ms	35×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify45.0ms (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

14.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	14.1b	(.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)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.9b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.2b	(/.f64 (.f64 M D) (.f64 2 d))
12.1b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite270.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

7.4b

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))
7.0ms	(.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)

series420.0ms (2.4%)

Error

7.2b

Counts

4 → 67

Calls

4 calls:

145.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
122.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
102.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
32.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3912 to 2984 computations (23.7% saved)

simplify149.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

286×	`associate-l_binary64`
282×	`distribute-rgt-neg-in_binary64`
271×	`times-frac_binary64`
263×	`distribute-lft-neg-in_binary64`
256×	`associate-r_binary64`

Counts

183 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	4240
1	693	3975
2	3021	3974
3	4653	3974
4	5030	3974

prune148.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	128	11	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	11	140

Error

4.9b

Counts

140 → 11

Alt Table

Status	Error	Program
	14.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	14.1b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
▶	9.3b	(.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)))))
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) l) -1/4)) d))
	13.4b	(.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))))))
	13.0b	(.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))))))
	61.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
	59.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	62.0b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
	61.5b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (.f64 d d) l)) -1/4)) (*.f64 D w0))

Compiler

Compiled 2635 to 1550 computations (41.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.9b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
4.9b	(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))))
5.2b	(/.f64 (.f64 M D) (.f64 2 d))
6.1b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite345.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

210×	`add-exp-log_binary64`
121×	`prod-exp_binary64`
43×	`div-exp_binary64`
33×	`add-cbrt-cube_binary64`
30×	`pow-exp_binary64`

Counts

4 → 145

Calls

4 calls:

16.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
8.0ms	(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))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4891 to 2231 computations (54.4% saved)

series432.0ms (2.5%)

Error

4.9b

Counts

4 → 58

Calls

4 calls:

143.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
131.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
109.0ms	(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))))
33.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3714 to 2844 computations (23.4% saved)

simplify179.0ms (1%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-l_binary64`
337×	`associate-r_binary64`
284×	`times-frac_binary64`
250×	`associate-/l*_binary64`
240×	`unswap-sqr_binary64`

Counts

203 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	5610
1	786	4529
2	3532	4427
3	4939	4427
4	5037	4427

prune176.0ms (1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	167	13	180

Error

4.7b

Counts

180 → 13

Alt Table

Status	Error	Program
	14.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	9.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	14.1b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) l) -1/4)) d))
	13.4b	(.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))))))
	13.0b	(.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))))))
	61.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
	59.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	62.0b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
	16.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))))
	61.5b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (.f64 d d) l)) -1/4)) (*.f64 D w0))
▶	8.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))

Compiler

Compiled 2958 to 1612 computations (45.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
5.2b	(/.f64 (.f64 M D) (.f64 2 d))
5.2b	(/.f64 (.f64 M D) (.f64 2 d))
6.1b	(.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite640.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

597×	`add-exp-log_binary64`
440×	`add-cbrt-cube_binary64`
370×	`prod-exp_binary64` `cbrt-unprod_binary64`
141×	`div-exp_binary64` `cbrt-undiv_binary64`
24×	`add-sqr-sqrt_binary64`

Counts

4 → 251

Calls

4 calls:

30.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
10.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 12260 to 5195 computations (57.6% saved)

series327.0ms (1.9%)

Error

4.7b

Counts

4 → 55

Calls

4 calls:

131.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
111.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
36.0ms	(/.f64 (.f64 M D) (.f64 2 d))
34.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3612 to 2582 computations (28.5% saved)

simplify281.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

557×	`*-commutative_binary64`
435×	`associate-*r/_binary64`
424×	`associate-*l/_binary64`
323×	`times-frac_binary64`
271×	`associate-/l*_binary64`

Counts

306 → 258

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	463	9901
1	1123	9238
2	4060	8225
3	3737	8225
4	4977	8225

prune188.0ms (1.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	254	4	258
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	255	16	271

Error

4.2b

Counts

271 → 16

Alt Table

Status	Error	Program
	14.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
▶	9.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	14.1b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) l) -1/4)) d))
	13.4b	(.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))))))
	13.0b	(.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))))))
	12.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 h) (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) (.f64 (.f64 M D) (cbrt.f64 h)))) (.f64 l (.f64 2 d))))))
	22.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 h) (.f64 (.f64 (.f64 M D) (cbrt.f64 h)) (.f64 (.f64 M D) (cbrt.f64 h)))) (.f64 l (.f64 (.f64 d d) 4))))))
	18.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 (cbrt.f64 h)) (cbrt.f64 h)) (.f64 (/.f64 M 4) (/.f64 (.f64 D (.f64 M D)) (*.f64 d d)))) (/.f64 (cbrt.f64 h) l))))))
	61.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
	59.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	62.0b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
	16.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))))
	61.5b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (.f64 d d) l)) -1/4)) (*.f64 D w0))
	61.6b	(.f64 w0 (neg.f64 (.f64 M (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 (.f64 D D) h) (.f64 (*.f64 d d) l)))))))

Compiler

Compiled 3317 to 1547 computations (53.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.9b	(.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
4.9b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
6.1b	(.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
7.1b	(/.f64 M (/.f64 2 (/.f64 D d)))

rewrite1.3s (7.6%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

750×	`times-frac_binary64`
366×	`add-sqr-sqrt_binary64`
354×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
174×	`add-exp-log_binary64`
143×	`associate-l_binary64`

Counts

4 → 449

Calls

4 calls:

46.0ms	(.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
41.0ms	(.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
13.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

Compiler

Compiled 17324 to 8089 computations (53.3% saved)

series443.0ms (2.5%)

Error

4.2b

Counts

4 → 58

Calls

4 calls:

144.0ms	(.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
130.0ms	(.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
112.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
35.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))

Compiler

Compiled 3714 to 2844 computations (23.4% saved)

simplify265.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

535×	`associate-/r/_binary64`
398×	`associate-/l/_binary64`
300×	`associate-/l*_binary64`
268×	`sqr-pow_binary64`
267×	`unswap-sqr_binary64`

Counts

507 → 396

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	920	13909
1	2531	12732
2	5001	12732

prune780.0ms (4.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	393	3	396
Fresh	3	12	15
Picked	0	1	1
Done	0	0	0
Total	396	16	412

Error

3.2b

Counts

412 → 16

Alt Table

Status	Error	Program
	9.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	14.1b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) l) -1/4)) d))
	13.0b	(.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))))))
	12.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 h) (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) (.f64 (.f64 M D) (cbrt.f64 h)))) (.f64 l (.f64 2 d))))))
	9.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (/.f64 M (sqrt.f64 2)) (/.f64 (sqrt.f64 2) (/.f64 D d))) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	22.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 h) (.f64 (.f64 (.f64 M D) (cbrt.f64 h)) (.f64 (.f64 M D) (cbrt.f64 h)))) (.f64 l (.f64 (.f64 d d) 4))))))
	58.7b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 -1/4 (.f64 (/.f64 h l) (pow.f64 (/.f64 M d) 2))))))
	18.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 (cbrt.f64 h)) (cbrt.f64 h)) (.f64 (/.f64 M 4) (/.f64 (.f64 D (.f64 M D)) (*.f64 d d)))) (/.f64 (cbrt.f64 h) l))))))
	61.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
	59.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	16.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))))
	61.5b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (.f64 d d) l)) -1/4)) (*.f64 D w0))
	10.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l))))
	61.6b	(.f64 w0 (neg.f64 (.f64 M (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 (.f64 D D) h) (.f64 (*.f64 d d) l)))))))

Compiler

Compiled 11428 to 5462 computations (52.2% saved)

regimes6.2s (35.5%)

Accuracy

Total 7.1b remaining (66.3%)

Threshold costs 0b (0%)

Compiler

Compiled 121131 to 83839 computations (30.8% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
5×	`sub-neg_binary64` `+-commutative_binary64`
4×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
1×	`if-if-or-not_binary64` `1-exp_binary64` `distribute-neg-frac_binary64` `distribute-lft-neg-out_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	78
1	55	78
2	64	78
3	72	78
4	78	78
5	81	78
6	82	78
7	81	78

end12.0ms (0.1%)

Compiler: Compiled 171 to 111 computations (35.1% saved)

sample2.2s (12.7%)

Algorithm

1×

intervals

Results

603.0ms	8000×	body	128	valid
231.0ms	3185×	body	128	nan
97.0ms	1334×	body	128	invalid

Compiler

Compiled 558 to 385 computations (31% saved)

Details

analyze2.5s (14.2%)

sample57.0ms (0.3%)

simplify45.0ms (0.3%)

prune3.0ms (0%)

localize21.0ms (0.1%)

rewrite270.0ms (1.5%)

series420.0ms (2.4%)

simplify149.0ms (0.9%)

prune148.0ms (0.8%)

localize19.0ms (0.1%)

rewrite345.0ms (2%)

series432.0ms (2.5%)

simplify179.0ms (1%)

prune176.0ms (1%)

localize18.0ms (0.1%)

rewrite640.0ms (3.6%)

series327.0ms (1.9%)

simplify281.0ms (1.6%)

prune188.0ms (1.1%)

localize22.0ms (0.1%)

rewrite1.3s (7.6%)

series443.0ms (2.5%)

simplify265.0ms (1.5%)

prune780.0ms (4.4%)

regimes6.2s (35.5%)

bsearch9.0ms (0.1%)

simplify7.0ms (0%)

end12.0ms (0.1%)

sample2.2s (12.7%)

Profiling