Details

analyze3.0s (18.8%)

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 (16%)

Symmetry

(sort M D)

Results

1.6s	8256×	body	128	valid
852.0ms	4505×	body	128	invalid

Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify29.0ms (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

12.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.8b	(.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
✓	2.3b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	5.3b	(/.f64 (.f64 M D) (.f64 2 d))
✓	10.9b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series845.0ms (5.3%)

Counts

4 → 204

Calls

4 calls:

393.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
249.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
187.0ms	(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))

rewrite33.0ms (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:

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

simplify166.0ms (1%)

Algorithm

1×	egg-herbie

Rules

517×	`times-frac_binary64`
398×	`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

prune421.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	304	10	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	305	10	315

Error

4.3b

Counts

315 → 10

Alt Table

Status	Error	Program
	59.8b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	12.8b	(.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))))))
	60.9b	(.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)))
	10.9b	(.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))))))
	60.9b	(.f64 D (.f64 w0 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
▶	10.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l)))))
	60.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	13.0b	w0
	21.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	12.8b	(.f64 (.f64 w0 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))

Compiler

Compiled 12190 to 7340 computations (39.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l)))))
✓	4.0b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (/.f64 1 l))
✓	5.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
	5.3b	(/.f64 (.f64 M D) (.f64 2 d))

series749.0ms (4.7%)

Counts

3 → 168

Calls

3 calls:

343.0ms

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

242.0ms

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

164.0ms

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

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

154×	`add-exp-log_binary64`
88×	`prod-exp_binary64`
36×	`div-exp_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`pow-exp_binary64`

Counts

3 → 124

Calls

3 calls:

9.0ms

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

7.0ms

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

6.0ms

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

simplify173.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

462×	`fma-def_binary64`
352×	`associate-l_binary64`
343×	`associate-r_binary64`
306×	`unswap-sqr_binary64`
248×	`times-frac_binary64`

Counts

292 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	395	8873
1	888	8197
2	3761	8113
3	5180	8113

prune397.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	275	2	277
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	277	10	287

Error

3.9b

Counts

287 → 10

Alt Table

Status	Error	Program
	59.8b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	12.8b	(.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))))))
▶	7.8b	(.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)))))
	60.9b	(.f64 D (.f64 w0 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	60.9b	(.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)))
	10.9b	(.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))))))
	60.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	35.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (sqrt.f64 h))) (/.f64 1 l)))))
	13.0b	w0
	12.8b	(.f64 (.f64 w0 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))

Compiler

Compiled 9901 to 6326 computations (36.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(.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)))))
✓	4.0b	(.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 M D) (.f64 2 d))
✓	5.8b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)

series615.0ms (3.8%)

Counts

3 → 168

Calls

3 calls:

343.0ms

(*.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)))))

242.0ms

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

29.0ms

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

rewrite142.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

874×	`add-exp-log_binary64`
530×	`prod-exp_binary64`
464×	`add-cbrt-cube_binary64`
270×	`cbrt-unprod_binary64`
242×	`div-exp_binary64`

Counts

3 → 278

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 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)))))

7.0ms

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

simplify275.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

726×	`associate-*l/_binary64`
616×	`times-frac_binary64`
407×	`associate-/r*_binary64`
377×	`associate-/l*_binary64`
218×	`*-commutative_binary64`

Counts

446 → 418

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	605	16690
1	1495	13673
2	4727	13419
3	5001	13419

prune593.0ms (3.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	494	2	496
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	497	9	506

Error

3.7b

Counts

506 → 9

Alt Table

Status	Error	Program
	59.8b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	12.8b	(.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))))))
▶	6.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 d 2))) l)))))
	35.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (sqrt.f64 h))) (/.f64 1 l)))))
	60.9b	(.f64 D (.f64 w0 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	60.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	60.9b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	13.0b	w0
	12.8b	(.f64 (.f64 w0 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))

Compiler

Compiled 20802 to 11393 computations (45.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.3b	(/.f64 (.f64 D M) (.f64 d 2))
	5.3b	(/.f64 (.f64 M D) (.f64 2 d))
✓	5.8b	(.f64 h (/.f64 (.f64 D M) (*.f64 d 2)))
✓	6.6b	(/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 d 2))) l)

series103.0ms (0.6%)

Counts

3 → 144

Calls

3 calls:

56.0ms	(/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 d 2))) l)
31.0ms	(.f64 h (/.f64 (.f64 D M) (*.f64 d 2)))
15.0ms	(/.f64 (.f64 D M) (.f64 d 2))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 86

Calls

3 calls:

9.0ms	(.f64 h (/.f64 (.f64 D M) (*.f64 d 2)))
6.0ms	(/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 d 2))) l)
4.0ms	(/.f64 (.f64 D M) (.f64 d 2))

simplify123.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

553×	`*-commutative_binary64`
305×	`times-frac_binary64`
272×	`associate--l+_binary64`
260×	`fma-def_binary64`
241×	`associate-/l*_binary64`

Counts

230 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	3756
1	396	3253
2	2003	3253
3	2964	3252
4	4724	3252
5	5055	3252

prune216.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	154	9	163

Error

3.7b

Counts

163 → 9

Alt Table

Status	Error	Program
	59.8b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	12.8b	(.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))))))
✓	6.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 d 2))) l)))))
	35.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (sqrt.f64 h))) (/.f64 1 l)))))
	60.9b	(.f64 D (.f64 w0 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	60.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	60.9b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	13.0b	w0
	12.8b	(.f64 (.f64 w0 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))

Compiler

Compiled 4938 to 2659 computations (46.2% saved)

regimes5.3s (32.9%)

Accuracy

Total 2.7b remaining (31.1%)

Threshold costs 0b (0%)

Counts

267 → 1

Compiler

Compiled 137061 to 100526 computations (26.7% 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	57	36
4	74	36
5	84	36
6	89	36
7	90	36
8	89	36

end178.0ms (1.1%)

Remove: (sort M D)
Compiler: Compiled 374 to 259 computations (30.7% saved)

Details

analyze3.0s (18.8%)

sample2.6s (16%)

simplify29.0ms (0.2%)

prune2.0ms (0%)

localize14.0ms (0.1%)

series845.0ms (5.3%)

rewrite33.0ms (0.2%)

simplify166.0ms (1%)

prune421.0ms (2.6%)

localize16.0ms (0.1%)

series749.0ms (4.7%)

rewrite35.0ms (0.2%)

simplify173.0ms (1.1%)

prune397.0ms (2.5%)

localize15.0ms (0.1%)

series615.0ms (3.8%)

rewrite142.0ms (0.9%)

simplify275.0ms (1.7%)

prune593.0ms (3.7%)

localize17.0ms (0.1%)

series103.0ms (0.6%)

rewrite25.0ms (0.2%)

simplify123.0ms (0.8%)

prune216.0ms (1.3%)

regimes5.3s (32.9%)

simplify4.0ms (0%)

end178.0ms (1.1%)

Profiling