Details

analyze3.2s (20.7%)

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)

sample80.0ms (0.5%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
9.0ms	104×	body	128	nan
5.0ms	56×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify53.0ms (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

prune2.0ms (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

14.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	14.8b	(.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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.2b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.9b	(/.f64 (.f64 M D) (.f64 2 d))
11.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite173.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

8.1b

Rules

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

Counts

4 → 116

Calls

4 calls:

9.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.0ms	(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)

series334.0ms (2.1%)

Error

6.8b

Counts

4 → 57

Calls

4 calls:

137.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
97.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
61.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
25.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3462 to 2639 computations (23.8% saved)

simplify107.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

647×	`associate-/l/_binary64`
277×	`associate-l_binary64`
259×	`distribute-rgt-neg-in_binary64`
252×	`associate-r_binary64`
252×	`times-frac_binary64`

Counts

173 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	3951
1	687	3629
2	2921	3628
3	5496	3628

prune104.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	127	10	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	10	138

Error

4.9b

Counts

138 → 10

Alt Table

Status	Error	Program
	14.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	11.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) l))))
	13.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (/.f64 h l))))))
	14.8b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	15.9b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))))
	57.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 w0 (neg.f64 M)))
	62.1b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	61.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	57.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
▶	10.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))

Compiler

Compiled 2723 to 1597 computations (41.4% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
4.2b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
5.8b	(.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
5.9b	(/.f64 (.f64 D M) (.f64 2 d))

rewrite369.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

3.8b

Rules

609×	`add-exp-log_binary64`
325×	`prod-exp_binary64`
184×	`div-exp_binary64`
75×	`pow-exp_binary64`
54×	`add-cbrt-cube_binary64`

Counts

4 → 245

Calls

4 calls:

20.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
13.0ms	(.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
5.0ms	(/.f64 (.f64 D M) (.f64 2 d))

Compiler

Compiled 10075 to 3582 computations (64.4% saved)

series564.0ms (3.6%)

Error

4.9b

Counts

4 → 54

Calls

4 calls:

224.0ms	(.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
146.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
142.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
29.0ms	(/.f64 (.f64 D M) (.f64 2 d))

Compiler

Compiled 4242 to 3224 computations (24% saved)

simplify236.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-l_binary64`
467×	`times-frac_binary64`
440×	`associate-*l/_binary64`
390×	`associate-/l*_binary64`
350×	`associate-*r/_binary64`

Counts

299 → 270

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	494	11684
1	1128	8019
2	4786	8011
3	5076	8011

prune155.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	264	6	270
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	268	12	280

Error

3.0b

Counts

280 → 12

Alt Table

Status	Error	Program
	22.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (/.f64 (.f64 (*.f64 D D) h) l) (pow.f64 (/.f64 M d) 2))))))
	62.1b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	11.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) h) l))))
	14.8b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	15.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2)) (/.f64 h l))))))
▶	8.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (*.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	15.9b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))))
	57.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 w0 (neg.f64 M)))
	14.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 -1/4 (/.f64 D (/.f64 (/.f64 (/.f64 (/.f64 l (pow.f64 (/.f64 M d) 2)) h) -1) D))))))
	61.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	57.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	59.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (pow.f64 (/.f64 M d) 2) (/.f64 h l)) -1/4))))

Compiler

Compiled 4264 to 1959 computations (54.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b	(.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
4.2b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
5.9b	(/.f64 (.f64 D M) (.f64 d 2))
5.9b	(/.f64 (.f64 D M) (.f64 d 2))

rewrite1.3s (8%)

Algorithm

1×	rewrite-expression-head

Error

3.0b

Rules

2244×	`add-exp-log_binary64`
1560×	`add-cbrt-cube_binary64`
1286×	`cbrt-unprod_binary64`
1286×	`prod-exp_binary64`
702×	`cbrt-undiv_binary64`

Counts

4 → 635

Calls

4 calls:

48.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
10.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
5.0ms	(/.f64 (.f64 D M) (.f64 d 2))
5.0ms	(/.f64 (.f64 D M) (.f64 d 2))

Compiler

Compiled 39816 to 13320 computations (66.5% saved)

series337.0ms (2.1%)

Error

3.0b

Counts

4 → 48

Calls

4 calls:

187.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
80.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
29.0ms	(/.f64 (.f64 D M) (.f64 d 2))
27.0ms	(/.f64 (.f64 D M) (.f64 d 2))

Compiler

Compiled 3622 to 2422 computations (33.1% saved)

simplify713.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

514×	`times-frac_binary64`
479×	`associate-l_binary64`
425×	`*-commutative_binary64`
406×	`associate-/l*_binary64`
375×	`associate-+l+_binary64`

Counts

683 → 632

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1063	29706
1	2223	27950
2	4157	22753
3	3575	22753
4	5275	22753

prune145.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	630	2	632
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	632	12	644

Error

3.0b

Counts

644 → 12

Alt Table

Status	Error	Program
	22.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (/.f64 (.f64 (*.f64 D D) h) l) (pow.f64 (/.f64 M d) 2))))))
	62.1b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	61.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
▶	10.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (.f64 (.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 h)))) (.f64 (.f64 d 2) (cbrt.f64 l))))))
	14.8b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	15.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2)) (/.f64 h l))))))
	15.9b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))))
	16.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 M M) 4)) (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))))))
	57.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 w0 (neg.f64 M)))
	14.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 -1/4 (/.f64 D (/.f64 (/.f64 (/.f64 (/.f64 l (pow.f64 (/.f64 M d) 2)) h) -1) D))))))
	57.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	59.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (pow.f64 (/.f64 M d) 2) (/.f64 h l)) -1/4))))

Compiler

Compiled 4562 to 1706 computations (62.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.9b	(.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
4.2b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (.f64 (.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 h)))) (.f64 (*.f64 d 2) (cbrt.f64 l)))))
5.9b	(/.f64 (.f64 D M) (.f64 d 2))
6.3b	(/.f64 (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (.f64 (.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 h)))) (.f64 (*.f64 d 2) (cbrt.f64 l)))

rewrite887.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

3.0b

Rules

1732×	`add-exp-log_binary64`
1122×	`add-cbrt-cube_binary64`
1051×	`cbrt-unprod_binary64`
1051×	`prod-exp_binary64`
480×	`cbrt-undiv_binary64`

Counts

4 → 497

Calls

4 calls:

46.0ms	(/.f64 (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (.f64 (.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 h)))) (.f64 (*.f64 d 2) (cbrt.f64 l)))
15.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (.f64 (.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 h)))) (.f64 (*.f64 d 2) (cbrt.f64 l)))))
11.0ms	(.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
5.0ms	(/.f64 (.f64 D M) (.f64 d 2))

Compiler

Compiled 30862 to 10674 computations (65.4% saved)

series363.0ms (2.3%)

Error

3.0b

Counts

4 → 51

Calls

4 calls:

134.0ms	(/.f64 (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (.f64 (.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 h)))) (.f64 (*.f64 d 2) (cbrt.f64 l)))
97.0ms	(.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
86.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (.f64 (.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 h)))) (.f64 (*.f64 d 2) (cbrt.f64 l)))))
27.0ms	(/.f64 (.f64 D M) (.f64 d 2))

Compiler

Compiled 4185 to 2897 computations (30.8% saved)

simplify454.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

630×	`associate-*r/_binary64`
561×	`associate-*l/_binary64`
438×	`associate-/l/_binary64`
228×	`associate-/r/_binary64`
223×	`sub-neg_binary64`

Counts

548 → 492

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	904	36799
1	2574	25933
2	5330	25933

prune316.0ms (2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	491	1	492
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	491	13	504

Error

3.0b

Counts

504 → 13

Alt Table

Status	Error	Program
	22.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (/.f64 (.f64 (*.f64 D D) h) l) (pow.f64 (/.f64 M d) 2))))))
	62.1b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	61.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	10.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (.f64 (.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 h)))) (.f64 (.f64 d 2) (cbrt.f64 l))))))
	11.2b	(.f64 w0 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (.f64 (.f64 (cbrt.f64 h) (/.f64 (.f64 D M) (.f64 2 d))) (.f64 (.f64 D M) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))) (.f64 (cbrt.f64 l) (.f64 2 d))))) 3)))
	57.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	14.8b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	15.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2)) (/.f64 h l))))))
	15.9b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)))))))
	16.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 M M) 4)) (.f64 (/.f64 (cbrt.f64 h) (cbrt.f64 l)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))))))
	57.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 w0 (neg.f64 M)))
	14.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 -1/4 (/.f64 D (/.f64 (/.f64 (/.f64 (/.f64 l (pow.f64 (/.f64 M d) 2)) h) -1) D))))))
	59.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (pow.f64 (/.f64 M d) 2) (/.f64 h l)) -1/4))))

Compiler

Compiled 9174 to 4880 computations (46.8% saved)

regimes3.1s (19.9%)

Accuracy

Total 4.2b remaining (51.6%)

Threshold costs 0b (0%)

Compiler

Compiled 79147 to 53103 computations (32.9% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 24 to 18 computations (25% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

46×	`*-commutative_binary64`
26×	`+-commutative_binary64`
26×	`sub-neg_binary64`
24×	`neg-sub0_binary64`
24×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	263
1	107	263
2	147	263
3	191	263
4	228	263
5	257	263
6	270	263
7	275	263
8	276	263
9	275	263

end14.0ms (0.1%)

Compiler: Compiled 531 to 312 computations (41.2% saved)

sample2.6s (16.3%)

Algorithm

1×

intervals

Results

808.0ms	8000×	body	128	valid
290.0ms	2978×	body	128	nan
128.0ms	1250×	body	128	invalid

Compiler

Compiled 647 to 422 computations (34.8% saved)

Iter	Nodes	Cost
0	67	263
1	107	263
2	147	263
3	191	263
4	228	263
5	257	263
6	270	263
7	275	263
8	276	263
9	275	263

Iter	Nodes	Cost
0	67	263
1	107	263
2	147	263
3	191	263
4	228	263
5	257	263
6	270	263
7	275	263
8	276	263
9	275	263

Details

analyze3.2s (20.7%)

sample80.0ms (0.5%)

simplify53.0ms (0.3%)

prune2.0ms (0%)

localize13.0ms (0.1%)

rewrite173.0ms (1.1%)

series334.0ms (2.1%)

simplify107.0ms (0.7%)

prune104.0ms (0.7%)

localize23.0ms (0.1%)

rewrite369.0ms (2.4%)

series564.0ms (3.6%)

simplify236.0ms (1.5%)

prune155.0ms (1%)

localize20.0ms (0.1%)

rewrite1.3s (8%)

series337.0ms (2.1%)

simplify713.0ms (4.5%)

prune145.0ms (0.9%)

localize24.0ms (0.2%)

rewrite887.0ms (5.7%)

series363.0ms (2.3%)

simplify454.0ms (2.9%)

prune316.0ms (2%)

regimes3.1s (19.9%)

bsearch9.0ms (0.1%)

simplify16.0ms (0.1%)

end14.0ms (0.1%)

sample2.6s (16.3%)

Profiling

Iter	Nodes	Cost
0	67	263
1	107	263
2	147	263
3	191	263
4	228	263
5	257	263
6	270	263
7	275	263
8	276	263
9	275	263