Details

analyze2.7s (21.6%)

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)

sample101.0ms (0.8%)

Algorithm

1×

intervals

Symmetry

(sort M D)

Results

23.0ms	256×	body	128	valid
10.0ms	104×	body	128	nan
3.0ms	40×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

645×	`distribute-neg-frac_binary64`
581×	`distribute-rgt-neg-in_binary64`
418×	`associate-/l*_binary64`
372×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	111	27
3	723	27
4	2855	27
5	4994	27

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

14.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Compiler

Compiled 72 to 54 computations (25% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	6.9b	(/.f64 (.f64 M D) (.f64 2 d))
✓	10.1b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series802.0ms (6.4%)

Counts

4 → 204

Calls

4 calls:

363.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
225.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
201.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
14.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

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 → 124

Calls

4 calls:

9.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
6.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0ms	(/.f64 (.f64 M D) (.f64 2 d))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

simplify158.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

517×	`times-frac_binary64`
399×	`associate-l_binary64`
365×	`associate-/l*_binary64`
342×	`associate-/r*_binary64`
258×	`associate-*r/_binary64`

Counts

328 → 314

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	516	11209
1	1262	10441
2	4988	10441

prune365.0ms (2.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	298	16	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	299	16	315

Error

4.0b

Counts

315 → 16

Alt Table

Status	Error	Program
	14.6b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.4b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	14.7b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	60.6b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	41.1b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
	59.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	14.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	60.3b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	22.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	42.2b	(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))) 3) (pow.f64 w0 3)))
	60.8b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	39.5b	(-.f64 w0 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 w0 (.f64 (pow.f64 M 2) h))) (*.f64 l (pow.f64 d 2)))))
	15.9b	w0
	38.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (sqrt.f64 h) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (sqrt.f64 h) (cbrt.f64 l))))))
▶	12.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
	61.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)

Compiler

Compiled 12560 to 7603 computations (39.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
✓	4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
	6.9b	(/.f64 (.f64 M D) (.f64 2 d))
✓	8.7b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

series603.0ms (4.8%)

Counts

3 → 168

Calls

3 calls:

356.0ms

(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))))))

174.0ms

(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l)))))

72.0ms

(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-cbrt-cube_binary64`
46×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
19×	`cbrt-unprod_binary64`

Counts

3 → 97

Calls

3 calls:

9.0ms

(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))

7.0ms

(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))))))

6.0ms

(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l)))))

simplify146.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

604×	`times-frac_binary64`
414×	`associate-/l*_binary64`
405×	`associate-/r*_binary64`
333×	`associate-*r/_binary64`
281×	`associate-*l/_binary64`

Counts

265 → 270

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	498	10374
1	1286	9786
2	4989	9786

prune473.0ms (3.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	345	3	348
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	347	17	364

Error

3.8b

Counts

364 → 17

Alt Table

Status	Error	Program
	14.6b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.4b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	14.7b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	60.6b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	41.1b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
	59.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
▶	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h) l)))))
	61.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	14.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	60.3b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	22.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	39.5b	(-.f64 w0 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 w0 (.f64 (pow.f64 M 2) h))) (*.f64 l (pow.f64 d 2)))))
	15.9b	w0
	38.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (sqrt.f64 h) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (sqrt.f64 h) (cbrt.f64 l))))))
	60.8b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	13.6b	(.f64 (.f64 (cbrt.f64 w0) (cbrt.f64 w0)) (.f64 (cbrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l)))))))
	42.2b	(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))) 3) (pow.f64 w0 3)))

Compiler

Compiled 15118 to 8260 computations (45.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) l))))
✓	4.3b	(/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h) l)
✓	4.5b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
	6.9b	(/.f64 (.f64 M D) (.f64 2 d))

series262.0ms (2.1%)

Counts

3 → 156

Calls

3 calls:

180.0ms

(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h) l))))

54.0ms

(/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h) l)

28.0ms

(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-cbrt-cube_binary64`
46×	`add-exp-log_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`
14×	`cbrt-undiv_binary64`

Counts

3 → 80

Calls

3 calls:

7.0ms

(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)

7.0ms

(/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h) l)

4.0ms

(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h) l))))

simplify162.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

445×	`times-frac_binary64`
410×	`fma-def_binary64`
335×	`associate-/l*_binary64`
275×	`associate-r_binary64`
263×	`associate-/r*_binary64`

Counts

236 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	6546
1	886	6024
2	4279	5984
3	4967	5984
4	4968	5984

prune467.0ms (3.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	258	3	261
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	261	17	278

Error

3.4b

Counts

278 → 17

Alt Table

Status	Error	Program
	41.1b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
	59.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	61.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	61.2b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 M (.f64 M h))) l) -1/4)) d))
	13.6b	(.f64 (.f64 (cbrt.f64 w0) (cbrt.f64 w0)) (.f64 (cbrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l)))))))
	58.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 d (*.f64 d l))) -1/4))))
	14.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	60.3b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	22.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
▶	11.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (pow.f64 (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 d 2))) l) 3))))))
	39.5b	(-.f64 w0 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 w0 (.f64 (pow.f64 M 2) h))) (*.f64 l (pow.f64 d 2)))))
	15.9b	w0
	14.6b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	38.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (sqrt.f64 h) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (sqrt.f64 h) (cbrt.f64 l))))))
	14.7b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	60.8b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	42.2b	(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))) 3) (pow.f64 w0 3)))

Compiler

Compiled 10487 to 5968 computations (43.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.5b	(.f64 h (/.f64 (.f64 D M) (*.f64 d 2)))
✓	6.9b	(/.f64 (.f64 D M) (.f64 d 2))
	6.9b	(/.f64 (.f64 M D) (.f64 2 d))
✓	19.9b	(cbrt.f64 (pow.f64 (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 d 2))) l) 3))

series170.0ms (1.4%)

Counts

3 → 144

Calls

3 calls:

128.0ms	(cbrt.f64 (pow.f64 (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 d 2))) l) 3))
26.0ms	(.f64 h (/.f64 (.f64 D M) (*.f64 d 2)))
15.0ms	(/.f64 (.f64 D M) (.f64 d 2))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-cbrt-cube_binary64`
33×	`add-exp-log_binary64`
20×	`cbrt-prod_binary64`
13×	`cbrt-unprod_binary64`
13×	`prod-exp_binary64`

Counts

3 → 86

Calls

3 calls:

6.0ms	(.f64 h (/.f64 (.f64 D M) (*.f64 d 2)))
6.0ms	(/.f64 (.f64 D M) (.f64 d 2))
2.0ms	(cbrt.f64 (pow.f64 (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 d 2))) l) 3))

simplify107.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

767×	`associate-/l/_binary64`
479×	`associate-/r/_binary64`
260×	`times-frac_binary64`
199×	`associate-/l*_binary64`
162×	`associate-l_binary64`

Counts

230 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	3701
1	456	3513
2	2169	3505
3	4649	3505
4	4981	3505

prune276.0ms (2.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	158	17	175

Error

3.4b

Counts

175 → 17

Alt Table

Status	Error	Program
	41.1b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
	59.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	61.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	61.2b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 M (.f64 M h))) l) -1/4)) d))
	13.6b	(.f64 (.f64 (cbrt.f64 w0) (cbrt.f64 w0)) (.f64 (cbrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l)))))))
	58.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 d (*.f64 d l))) -1/4))))
	14.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	60.3b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	22.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
✓	11.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (pow.f64 (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 d 2))) l) 3))))))
	39.5b	(-.f64 w0 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 w0 (.f64 (pow.f64 M 2) h))) (*.f64 l (pow.f64 d 2)))))
	15.9b	w0
	14.6b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	38.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (sqrt.f64 h) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (sqrt.f64 h) (cbrt.f64 l))))))
	14.7b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	60.8b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	42.2b	(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))) 3) (pow.f64 w0 3)))

Compiler

Compiled 5737 to 3420 computations (40.4% saved)

regimes3.5s (27.7%)

Accuracy

Total 3.1b remaining (34.8%)

Threshold costs 0b (0%)

Counts

175 → 1

Compiler

Compiled 92778 to 65827 computations (29% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	36
1	30	36
2	41	36
3	61	36
4	76	36
5	86	36
6	90	36
7	89	36

end6.0ms (0%)

Remove: (sort M D)
Compiler: Compiled 90 to 60 computations (33.3% saved)

sample2.0s (16.3%)

Algorithm

1×

intervals

Results

800.0ms	8000×	body	128	valid
299.0ms	3164×	body	128	nan
133.0ms	1336×	body	128	invalid

Compiler

Compiled 556 to 393 computations (29.3% saved)

Details

analyze2.7s (21.6%)

sample101.0ms (0.8%)

simplify26.0ms (0.2%)

prune2.0ms (0%)

localize12.0ms (0.1%)

series802.0ms (6.4%)

rewrite34.0ms (0.3%)

simplify158.0ms (1.3%)

prune365.0ms (2.9%)

localize14.0ms (0.1%)

series603.0ms (4.8%)

rewrite32.0ms (0.3%)

simplify146.0ms (1.2%)

prune473.0ms (3.8%)

localize14.0ms (0.1%)

series262.0ms (2.1%)

rewrite24.0ms (0.2%)

simplify162.0ms (1.3%)

prune467.0ms (3.7%)

localize20.0ms (0.2%)

series170.0ms (1.4%)

rewrite20.0ms (0.2%)

simplify107.0ms (0.9%)

prune276.0ms (2.2%)

regimes3.5s (27.7%)

simplify4.0ms (0%)

end6.0ms (0%)

sample2.0s (16.3%)

Profiling