Details

analyze2.8s (19.3%)

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
4.3%	95.4%	0.3%	13
6.6%	93.1%	0.3%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample2.6s (17.8%)

Symmetry

(sort M D)

Results

1.7s	8256×	body	128	valid
806.0ms	4672×	body	128	invalid

Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify27.0ms (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

17.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.3b	(.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)

localize13.0ms (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)))))
✓	4.3b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.6b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	12.8b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series824.0ms (5.7%)

Counts

4 → 204

Calls

4 calls:

362.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
273.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
173.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
16.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite35.0ms (0.2%)

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:

10.0ms	(.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)))))
4.0ms	(/.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))))

simplify193.0ms (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

prune393.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	301	13	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	302	13	315

Error

4.9b

Counts

315 → 13

Alt Table

Status	Error	Program
	61.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	14.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	16.5b	w0
	14.9b	(.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 (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2) (/.f64 h l))))))
	60.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
▶	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l)))))
	41.2b	(.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))))))
	14.3b	(.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))))))
	20.5b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 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)))))))
	58.7b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	59.9b	(.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)))
	17.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))))
	60.6b	(/.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 12466 to 7531 computations (39.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.3b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
✓	4.6b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (/.f64 1 l))))
✓	7.4b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (/.f64 1 l))

series591.0ms (4.1%)

Counts

3 → 156

Calls

3 calls:

257.0ms

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

186.0ms

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

148.0ms

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

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

152×	`add-exp-log_binary64`
87×	`prod-exp_binary64`
36×	`div-exp_binary64`
25×	`pow-exp_binary64`
21×	`add-sqr-sqrt_binary64`

Counts

3 → 115

Calls

3 calls:

9.0ms

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

8.0ms

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

4.0ms

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

simplify185.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary64`
322×	`unswap-sqr_binary64`
296×	`cancel-sign-sub-inv_binary64`
255×	`associate-l_binary64`
241×	`associate-r_binary64`

Counts

271 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	354	7915
1	795	7298
2	3026	7215
3	4877	7215
4	4990	7215

prune437.0ms (3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	259	2	261
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	260	14	274

Error

4.7b

Counts

274 → 14

Alt Table

Status	Error	Program
	58.7b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
▶	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) (/.f64 1 l)))))
	61.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	14.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	16.5b	w0
	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h) (/.f64 1 l)))))
	14.9b	(.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 (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2) (/.f64 h l))))))
	41.2b	(.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))))))
	14.3b	(.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))))))
	20.5b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 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)))))))
	59.9b	(.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)))
	60.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	17.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))))
	60.6b	(/.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 9522 to 6166 computations (35.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.3b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.6b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) (/.f64 1 l))))
✓	5.3b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
✓	7.4b	(.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) (/.f64 1 l))

series428.0ms (3%)

Counts

3 → 156

Calls

3 calls:

230.0ms

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

170.0ms

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

27.0ms

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

rewrite135.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

872×	`add-exp-log_binary64`
529×	`prod-exp_binary64`
462×	`add-cbrt-cube_binary64`
269×	`cbrt-unprod_binary64`
242×	`div-exp_binary64`

Counts

3 → 269

Calls

3 calls:

20.0ms

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

9.0ms

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

6.0ms

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

simplify288.0ms (2%)

Algorithm

1×	egg-herbie

Rules

716×	`associate-*l/_binary64`
514×	`times-frac_binary64`
383×	`associate-/r*_binary64`
311×	`associate-/l*_binary64`
279×	`sqr-pow_binary64`

Counts

425 → 378

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	564	12888
1	1402	11707
2	4269	11456
3	3823	10988
4	5189	10988

prune690.0ms (4.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	452	4	456
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	456	14	470

Error

4.0b

Counts

470 → 14

Alt Table

Status	Error	Program
	16.5b	w0
	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h) (/.f64 1 l)))))
	60.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	17.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))))
	41.2b	(.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))))))
	14.3b	(.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))))))
▶	8.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)))))
	60.6b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2) (cbrt.f64 (/.f64 (.f64 D M) (*.f64 2 d)))) h)) (/.f64 1 l)))))
	20.5b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 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)))))))
	58.7b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	61.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	60.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	11.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) (/.f64 1 l))) (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) (/.f64 1 l)))) (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) (/.f64 1 l)))))))

Compiler

Compiled 19540 to 10715 computations (45.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.3b	(/.f64 (.f64 D M) (.f64 2 d))
✓	4.6b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (.f64 2 d))) l))))
✓	5.3b	(.f64 h (/.f64 (.f64 D M) (*.f64 2 d)))
✓	6.0b	(/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)

series268.0ms (1.9%)

Counts

4 → 192

Calls

4 calls:

178.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (.f64 2 d))) l))))
47.0ms	(/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)
25.0ms	(.f64 h (/.f64 (.f64 D M) (*.f64 2 d)))
16.0ms	(/.f64 (.f64 D M) (.f64 2 d))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-cbrt-cube_binary64`
59×	`add-exp-log_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`
18×	`cbrt-undiv_binary64`

Counts

4 → 103

Calls

4 calls:

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

simplify151.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

462×	`times-frac_binary64`
363×	`associate-/l*_binary64`
341×	`fma-def_binary64`
300×	`associate-r_binary64`
278×	`associate-/r*_binary64`

Counts

295 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	357	7217
1	925	6698
2	4472	6696
3	4986	6696

prune353.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	224	12	236

Error

4.0b

Counts

236 → 12

Alt Table

Status	Error	Program
	16.5b	w0
	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h) (/.f64 1 l)))))
	60.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	17.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))))
	11.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2) (cbrt.f64 (/.f64 (.f64 D M) (*.f64 2 d)))) h)) (/.f64 1 l)))))
	20.5b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 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)))))))
	58.7b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	8.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 h (/.f64 (/.f64 (.f64 D M) (*.f64 d 2)) l))))))
	61.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	60.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	41.2b	(.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))))))
	60.6b	(/.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 8749 to 4930 computations (43.7% saved)

regimes3.7s (25.9%)

Accuracy

Total 4.0b remaining (47.2%)

Threshold costs 0b (0%)

Counts

188 → 1

Compiler

Compiled 104839 to 75179 computations (28.3% 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

end199.0ms (1.4%)

Remove: (sort M D)
Compiler: Compiled 496 to 345 computations (30.4% saved)

Details

analyze2.8s (19.3%)

sample2.6s (17.8%)

simplify27.0ms (0.2%)

prune2.0ms (0%)

localize13.0ms (0.1%)

series824.0ms (5.7%)

rewrite35.0ms (0.2%)

simplify193.0ms (1.3%)

prune393.0ms (2.7%)

localize16.0ms (0.1%)

series591.0ms (4.1%)

rewrite33.0ms (0.2%)

simplify185.0ms (1.3%)

prune437.0ms (3%)

localize15.0ms (0.1%)

series428.0ms (3%)

rewrite135.0ms (0.9%)

simplify288.0ms (2%)

prune690.0ms (4.8%)

localize16.0ms (0.1%)

series268.0ms (1.9%)

rewrite30.0ms (0.2%)

simplify151.0ms (1.1%)

prune353.0ms (2.5%)

regimes3.7s (25.9%)

simplify4.0ms (0%)

end199.0ms (1.4%)

Profiling