Details

analyze2.8s (13.2%)

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

Compiler

Compiled 25 to 19 computations (24% saved)

sample2.4s (11.3%)

Symmetry

(sort M D)

Results

1.5s	8256×	body	128	valid
814.0ms	4656×	body	128	invalid

Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify28.0ms (0.1%)

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

13.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.5b	(.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)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.9b	(.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))))
✓	5.4b	(/.f64 (.f64 M D) (.f64 2 d))
✓	10.9b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series811.0ms (3.8%)

Counts

4 → 204

Calls

4 calls:

341.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
261.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
193.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
15.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite36.0ms (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:

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

simplify165.0ms (0.8%)

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

prune376.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	300	14	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	301	14	315

Error

3.7b

Counts

315 → 14

Alt Table

Status	Error	Program
	12.1b	(.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))))))
	58.3b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	17.0b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 (.f64 1 1) (.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)))))) (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
	12.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	12.2b	w0
	61.7b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	61.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
▶	11.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.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))))))
	61.2b	(.f64 w0 (.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 l (pow.f64 d 2)))))) M)))
	62.2b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	13.5b	(.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))))))
	13.6b	(.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))))))
	61.0b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	60.8b	(-.f64 (.f64 1/8 (/.f64 w0 (.f64 (pow.f64 M 3) (pow.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) 3)))) (fma.f64 1/2 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))) (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (*.f64 M w0))))

Compiler

Compiled 12580 to 7591 computations (39.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.2b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.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)))
✓	4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.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)))))
	5.4b	(/.f64 (.f64 M D) (.f64 2 d))
✓	7.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

series3.1s (14.4%)

Counts

3 → 168

Calls

3 calls:

2.6s

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

273.0ms

(*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.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)))

181.0ms

(sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.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)))))

rewrite102.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

596×	`add-exp-log_binary64`
321×	`prod-exp_binary64`
180×	`div-exp_binary64`
75×	`pow-exp_binary64`
45×	`associate-r_binary64`

Counts

3 → 230

Calls

3 calls:

19.0ms

(*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.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)))

14.0ms

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

6.0ms

(sqrt.f64 (-.f64 1 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.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)))))

simplify269.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

588×	`associate-l_binary64`
361×	`associate-*r/_binary64`
355×	`associate-*l/_binary64`
346×	`times-frac_binary64`
316×	`fma-def_binary64`

Counts

398 → 364

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	589	16882
1	1313	12632
2	4928	12616
3	5095	12616

prune603.0ms (2.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	402	1	403
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	402	15	417

Error

3.2b

Counts

417 → 15

Alt Table

Status	Error	Program
▶	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	61.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	12.1b	(.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))))))
	58.3b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	17.0b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 (.f64 1 1) (.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)))))) (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
	12.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	12.2b	w0
	61.7b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
✓	11.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.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))))))
	61.2b	(.f64 w0 (.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 l (pow.f64 d 2)))))) M)))
	62.2b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	13.5b	(.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))))))
	13.6b	(.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))))))
	61.0b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	60.8b	(-.f64 (.f64 1/8 (/.f64 w0 (.f64 (pow.f64 M 3) (pow.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) 3)))) (fma.f64 1/2 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))) (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (*.f64 M w0))))

Compiler

Compiled 18370 to 8000 computations (56.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.2b	(.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
✓	4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
	5.4b	(/.f64 (.f64 M D) (.f64 2 d))
✓	7.1b	(.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

series2.9s (13.6%)

Counts

3 → 168

Calls

3 calls:

2.4s

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

269.0ms

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

188.0ms

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

rewrite535.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

2514×	`add-exp-log_binary64`
1812×	`add-cbrt-cube_binary64`
1445×	`cbrt-unprod_binary64`
1445×	`prod-exp_binary64`
779×	`cbrt-undiv_binary64`

Counts

3 → 686

Calls

3 calls:

36.0ms

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

15.0ms

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

10.0ms

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

simplify865.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

872×	`times-frac_binary64`
426×	`*-commutative_binary64`
334×	`associate-l_binary64`
290×	`fma-def_binary64`
225×	`associate-r_binary64`

Counts

854 → 840

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	1339	43446
1	2736	27934
2	3481	27259
3	4416	27162
4	4924	27162
5	4973	27162

prune1.3s (6.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	915	3	918
Fresh	1	12	13
Picked	1	0	1
Done	1	0	1
Total	918	15	933

Error

3.2b

Counts

933 → 15

Alt Table

Status	Error	Program
	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (cbrt.f64 (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))))) (cbrt.f64 (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	12.2b	w0
	12.1b	(.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))))))
	58.3b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	17.0b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 (.f64 1 1) (.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)))))) (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
	12.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	61.7b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	61.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	62.2b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
▶	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 h))) (cbrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 l)))))))
	13.5b	(.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))))))
	13.6b	(.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))))))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (.f64 M D) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (cbrt.f64 h)) (.f64 (.f64 (.f64 2 d) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l))))))
	61.0b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	60.8b	(-.f64 (.f64 1/8 (/.f64 w0 (.f64 (pow.f64 M 3) (pow.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) 3)))) (fma.f64 1/2 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))) (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (*.f64 M w0))))

Compiler

Compiled 55751 to 18969 computations (66% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 h))) (cbrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 l)))))))
✓	4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 h))) (cbrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 l))))))
	5.4b	(/.f64 (.f64 M D) (.f64 2 d))
	7.1b	(.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

series551.0ms (2.6%)

Counts

2 → 108

Calls

2 calls:

360.0ms

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

190.0ms

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

rewrite66.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
6×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

30.0ms

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

29.0ms

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

simplify202.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

360×	`associate-r_binary64`
336×	`times-frac_binary64`
293×	`associate-l_binary64`
264×	`associate-/r*_binary64`
256×	`fma-neg_binary64`

Counts

151 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	397	10916
1	986	10580
2	4493	10562
3	4999	10562

prune697.0ms (3.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	372	0	372
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	372	15	387

Error

3.2b

Counts

387 → 15

Alt Table

Status	Error	Program
	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (cbrt.f64 (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))))) (cbrt.f64 (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	12.2b	w0
	12.1b	(.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))))))
	58.3b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	17.0b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 (.f64 1 1) (.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)))))) (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
	12.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	61.7b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	61.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	62.2b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
✓	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 h))) (cbrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 l)))))))
	13.5b	(.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))))))
	13.6b	(.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))))))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (.f64 M D) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (cbrt.f64 h)) (.f64 (.f64 (.f64 2 d) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l))))))
	61.0b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	60.8b	(-.f64 (.f64 1/8 (/.f64 w0 (.f64 (pow.f64 M 3) (pow.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) 3)))) (fma.f64 1/2 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))) (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (*.f64 M w0))))

Compiler

Compiled 25400 to 9305 computations (63.4% saved)

regimes2.9s (13.7%)

Accuracy

Total 4.8b remaining (55.1%)

Threshold costs 0b (0%)

Counts

142 → 3

Compiler

Compiled 92170 to 60157 computations (34.7% saved)

bsearch9.0ms (0%)

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

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary64`
24×	`+-commutative_binary64`
24×	`sub-neg_binary64`
22×	`neg-sub0_binary64`
22×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	181
1	89	181
2	126	181
3	164	181
4	195	181
5	219	181
6	230	181
7	234	181
8	235	181
9	234	181

end494.0ms (2.3%)

Compiler: Compiled 1070 to 653 computations (39% saved)

Iter	Nodes	Cost
0	53	181
1	89	181
2	126	181
3	164	181
4	195	181
5	219	181
6	230	181
7	234	181
8	235	181
9	234	181

Iter	Nodes	Cost
0	53	181
1	89	181
2	126	181
3	164	181
4	195	181
5	219	181
6	230	181
7	234	181
8	235	181
9	234	181

Details

analyze2.8s (13.2%)

sample2.4s (11.3%)

simplify28.0ms (0.1%)

prune2.0ms (0%)

localize14.0ms (0.1%)

series811.0ms (3.8%)

rewrite36.0ms (0.2%)

simplify165.0ms (0.8%)

prune376.0ms (1.8%)

localize20.0ms (0.1%)

series3.1s (14.4%)

rewrite102.0ms (0.5%)

simplify269.0ms (1.3%)

prune603.0ms (2.8%)

localize20.0ms (0.1%)

series2.9s (13.6%)

rewrite535.0ms (2.5%)

simplify865.0ms (4.1%)

prune1.3s (6.2%)

localize25.0ms (0.1%)

series551.0ms (2.6%)

rewrite66.0ms (0.3%)

simplify202.0ms (0.9%)

prune697.0ms (3.3%)

regimes2.9s (13.7%)

bsearch9.0ms (0%)

simplify10.0ms (0%)

end494.0ms (2.3%)

Profiling

Iter	Nodes	Cost
0	53	181
1	89	181
2	126	181
3	164	181
4	195	181
5	219	181
6	230	181
7	234	181
8	235	181
9	234	181