Details

analyze2.8s (22.8%)

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)

sample2.4s (20%)

Symmetry

(sort M D)

Results

1.5s	8256×	body	128	valid
835.0ms	4570×	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

12.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.4b	(.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
✓	2.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	3.1b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	4.0b	(/.f64 (.f64 M D) (.f64 2 d))
✓	9.6b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series850.0ms (7%)

Counts

4 → 204

Calls

4 calls:

391.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
242.0ms	(.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))))
15.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite33.0ms (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:

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

simplify219.0ms (1.8%)

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

prune342.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	305	9	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	306	9	315

Error

4.3b

Counts

315 → 9

Alt Table

Status	Error	Program
	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	59.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	12.4b	(.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))))))
	12.0b	w0
▶	9.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	61.1b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	61.6b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	61.5b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	11.6b	(.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))))))

Compiler

Compiled 12090 to 7275 computations (39.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
	4.0b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
✓	4.3b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)

series658.0ms (5.4%)

Counts

3 → 156

Calls

3 calls:

333.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
175.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
149.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary64`
22×	`prod-exp_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`div-exp_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 84

Calls

3 calls:

6.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
6.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
5.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

simplify136.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

315×	`fma-def_binary64`
298×	`unswap-sqr_binary64`
288×	`distribute-neg-frac_binary64`
241×	`cancel-sign-sub-inv_binary64`
191×	`times-frac_binary64`

Counts

240 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	7367
1	764	6748
2	2985	6661
3	4995	6661

prune289.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	229	9	238

Error

3.7b

Counts

238 → 9

Alt Table

Status	Error	Program
▶	8.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))
	61.6b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	59.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	12.4b	(.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))))))
	12.0b	w0
	61.1b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	61.5b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	11.6b	(.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))))))

Compiler

Compiled 7909 to 5003 computations (36.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)))
	4.0b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.3b	(/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)
✓	4.4b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)

series433.0ms (3.6%)

Counts

3 → 156

Calls

3 calls:

232.0ms

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

171.0ms

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

29.0ms

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

rewrite64.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

226×	`add-cbrt-cube_binary64`
226×	`add-exp-log_binary64`
108×	`cbrt-unprod_binary64`
108×	`prod-exp_binary64`
79×	`cbrt-undiv_binary64`

Counts

3 → 135

Calls

3 calls:

15.0ms

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

9.0ms

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

6.0ms

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

simplify175.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/l*_binary64`
484×	`associate-l_binary64`
455×	`associate-/r*_binary64`
414×	`associate-*l/_binary64`
390×	`associate-*r/_binary64`

Counts

291 → 254

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	458	9762
1	1205	8761
2	4703	8697
3	4996	8697

prune406.0ms (3.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	329	3	332
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	330	11	341

Error

3.0b

Counts

341 → 11

Alt Table

Status	Error	Program
	61.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
▶	7.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 l (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h))))))
✓	8.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))
	61.6b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	59.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	61.6b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 M (.f64 M h))) l) -1/4)) d))
	12.4b	(.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))))))
	12.0b	w0
	61.1b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	61.5b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))

Compiler

Compiled 13288 to 7224 computations (45.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(sqrt.f64 (-.f64 1 (/.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 l (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)))))
	4.0b	(/.f64 (.f64 M D) (.f64 2 d))
	4.4b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
✓	5.2b	(/.f64 l (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h))

series245.0ms (2%)

Counts

2 → 108

Calls

2 calls:

179.0ms	(sqrt.f64 (-.f64 1 (/.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 l (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)))))
65.0ms	(/.f64 l (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-cbrt-cube_binary64`
27×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`cbrt-undiv_binary64`
10×	`div-exp_binary64`

Counts

2 → 54

Calls

2 calls:

25.0ms	(sqrt.f64 (-.f64 1 (/.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 l (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)))))
6.0ms	(/.f64 l (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h))

simplify118.0ms (1%)

Algorithm

1×	egg-herbie

Rules

430×	`times-frac_binary64`
352×	`fma-def_binary64`
302×	`associate-/r*_binary64`
301×	`unswap-sqr_binary64`
300×	`associate-/l*_binary64`

Counts

162 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	5643
1	852	5268
2	3960	5223
3	5162	5223

prune337.0ms (2.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	270	11	281

Error

3.0b

Counts

281 → 11

Alt Table

Status	Error	Program
	61.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
✓	7.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 l (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h))))))
✓	8.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))
	61.6b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	59.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	61.6b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 M (.f64 M h))) l) -1/4)) d))
	12.4b	(.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))))))
	12.0b	w0
	61.1b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	61.5b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))

Compiler

Compiled 10169 to 5721 computations (43.7% saved)

regimes2.3s (19%)

Accuracy

Total 4.1b remaining (48.9%)

Threshold costs 0b (0%)

Counts

141 → 1

Compiler

Compiled 64631 to 46338 computations (28.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	39
1	29	39
2	35	39
3	45	39
4	60	39
5	69	39
6	75	39
7	77	39
8	75	39

end176.0ms (1.5%)

Remove: (sort M D)
Compiler: Compiled 404 to 283 computations (30% saved)

Details

analyze2.8s (22.8%)

sample2.4s (20%)

simplify27.0ms (0.2%)

prune2.0ms (0%)

localize14.0ms (0.1%)

series850.0ms (7%)

rewrite33.0ms (0.3%)

simplify219.0ms (1.8%)

prune342.0ms (2.8%)

localize12.0ms (0.1%)

series658.0ms (5.4%)

rewrite25.0ms (0.2%)

simplify136.0ms (1.1%)

prune289.0ms (2.4%)

localize13.0ms (0.1%)

series433.0ms (3.6%)

rewrite64.0ms (0.5%)

simplify175.0ms (1.5%)

prune406.0ms (3.4%)

localize12.0ms (0.1%)

series245.0ms (2%)

rewrite36.0ms (0.3%)

simplify118.0ms (1%)

prune337.0ms (2.8%)

regimes2.3s (19%)

simplify4.0ms (0%)

end176.0ms (1.5%)

Profiling