Details

analyze3.1s (28.6%)

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

Compiler

Compiled 25 to 19 computations (24% saved)

sample2.5s (22.8%)

Symmetry

(sort M D)

Results

1.6s	8256×	body	128	valid
790.0ms	4509×	body	128	invalid

Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify25.0ms (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

16.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.5b	(.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)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	6.1b	(/.f64 (.f64 M D) (.f64 2 d))
✓	6.7b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	9.9b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series506.0ms (4.7%)

Counts

4 → 204

Calls

4 calls:

209.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
168.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
108.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
19.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite89.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

593×	`prod-diff_binary64`
190×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`
177×	`add-log-exp_binary64`

Counts

4 → 119

Calls

4 calls:

87.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
87.0ms	(/.f64 (.f64 M D) (.f64 2 d))
87.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
87.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	80
1	384	80
2	4932	80
3	6086	80

simplify224.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
276×	`unswap-sqr_binary64`
262×	`times-frac_binary64`
248×	`associate-r_binary64`
246×	`associate-/r*_binary64`

Counts

323 → 238

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	310	8076
1	810	8010
2	3470	7948
3	4942	7780
4	4984	7780
5	4959	7780

prune357.0ms (3.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	228	10	238
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	229	10	239

Error

7.4b

Counts

239 → 10

Alt Table

Status	Error	Program
	16.6b	(.f64 w0 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) 3))
	61.8b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	14.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l)))))
	60.2b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	60.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	16.5b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) 1/4) 2))
▶	13.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) l))))
	37.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (sqrt.f64 l)) (sqrt.f64 l)))))
	62.6b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (.f64 d d))) -1/4)) (*.f64 M w0))
	15.3b	w0

Compiler

Compiled 9251 to 5611 computations (39.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.1b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
✓	4.7b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
	6.1b	(/.f64 (.f64 M D) (.f64 2 d))
✓	6.7b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))

series488.0ms (4.5%)

Counts

3 → 156

Calls

3 calls:

197.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
179.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
111.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

rewrite80.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

494×	`prod-diff_binary64`
168×	`add-sqr-sqrt_binary64`
159×	`log1p-expm1-u_binary64`
159×	`expm1-log1p-u_binary64`
157×	`add-log-exp_binary64`

Counts

3 → 82

Calls

3 calls:

77.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
77.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
77.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	59
1	342	59
2	4467	59
3	5458	59

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

587×	`associate-*l/_binary64`
267×	`associate-/r/_binary64`
264×	`fma-def_binary64`
231×	`unswap-sqr_binary64`
216×	`distribute-neg-frac_binary64`

Counts

238 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	5336
1	495	5302
2	2011	5284
3	5257	5284

prune254.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	202	10	212

Error

6.7b

Counts

212 → 10

Alt Table

Status	Error	Program
	39.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (sqrt.f64 h)) 2) l))))
	60.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	14.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l)))))
	60.2b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	16.5b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) 1/4) 2))
	61.8b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
▶	11.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 D d) (.f64 M 1/2)) 2)) l))))
	13.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (.f64 M D)) -1) 2)) l))))
	62.6b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (.f64 d d))) -1/4)) (*.f64 M w0))
	15.3b	w0

Compiler

Compiled 6866 to 4327 computations (37% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.7b	(.f64 (/.f64 D d) (.f64 M 1/2))
✓	4.1b	(.f64 h (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2))
✓	4.7b	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2)) l)
✓	6.7b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2)) l)))

series416.0ms (3.9%)

Counts

4 → 192

Calls

4 calls:

175.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2)) l)
117.0ms	(.f64 h (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2))
109.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2)) l)))
15.0ms	(.f64 (/.f64 D d) (.f64 M 1/2))

rewrite76.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

476×	`prod-diff_binary64`
174×	`add-sqr-sqrt_binary64`
167×	`log1p-expm1-u_binary64`
167×	`expm1-log1p-u_binary64`
164×	`add-cbrt-cube_binary64`

Counts

4 → 109

Calls

4 calls:

74.0ms	(.f64 (/.f64 D d) (.f64 M 1/2))
74.0ms	(.f64 h (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2))
74.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2)) l)
74.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2)) l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	362	69
2	4426	69
3	5343	69

simplify107.0ms (1%)

Algorithm

1×	egg-herbie

Rules

590×	`associate-*l/_binary64`
272×	`associate-/r/_binary64`
264×	`fma-def_binary64`
231×	`unswap-sqr_binary64`
216×	`distribute-neg-frac_binary64`

Counts

301 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	5696
1	504	5662
2	2032	5644
3	5287	5644

prune199.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	173	10	183

Error

6.7b

Counts

183 → 10

Alt Table

Status	Error	Program
	39.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (sqrt.f64 h)) 2) l))))
	60.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	14.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l)))))
	60.2b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	16.5b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) 1/4) 2))
	61.8b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
✓	11.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 D d) (.f64 M 1/2)) 2)) l))))
▶	13.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (.f64 M D)) -1) 2)) l))))
	62.6b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (.f64 d d))) -1/4)) (*.f64 M w0))
	15.3b	w0

Compiler

Compiled 6128 to 3867 computations (36.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.1b	(.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (*.f64 M D)) -1) 2))
✓	4.7b	(/.f64 (.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (*.f64 M D)) -1) 2)) l)
✓	5.8b	(/.f64 (.f64 2 d) (.f64 M D))
✓	6.7b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (*.f64 M D)) -1) 2)) l)))

series409.0ms (3.8%)

Counts

4 → 192

Calls

4 calls:

173.0ms	(/.f64 (.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (*.f64 M D)) -1) 2)) l)
112.0ms	(.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (*.f64 M D)) -1) 2))
106.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (*.f64 M D)) -1) 2)) l)))
18.0ms	(/.f64 (.f64 2 d) (.f64 M D))

rewrite87.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

536×	`prod-diff_binary64`
187×	`add-sqr-sqrt_binary64`
177×	`log1p-expm1-u_binary64`
177×	`expm1-log1p-u_binary64`
174×	`add-cbrt-cube_binary64`

Counts

4 → 133

Calls

4 calls:

84.0ms	(.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (*.f64 M D)) -1) 2))
84.0ms	(/.f64 (.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (*.f64 M D)) -1) 2)) l)
84.0ms	(/.f64 (.f64 2 d) (.f64 M D))
84.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (*.f64 M D)) -1) 2)) l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	69
1	386	69
2	4935	69
3	5984	69

simplify113.0ms (1%)

Algorithm

1×	egg-herbie

Rules

592×	`associate-*l/_binary64`
268×	`associate-/r/_binary64`
264×	`fma-def_binary64`
231×	`unswap-sqr_binary64`
216×	`distribute-neg-frac_binary64`

Counts

325 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	5696
1	504	5662
2	2036	5644
3	5287	5644

prune203.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	197	10	207

Error

6.7b

Counts

207 → 10

Alt Table

Status	Error	Program
	39.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (sqrt.f64 h)) 2) l))))
	60.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	14.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l)))))
	60.2b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	16.5b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) 1/4) 2))
	61.8b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
✓	11.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 D d) (.f64 M 1/2)) 2)) l))))
✓	13.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (pow.f64 (/.f64 (.f64 2 d) (.f64 M D)) -1) 2)) l))))
	62.6b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (.f64 d d))) -1/4)) (*.f64 M w0))
	15.3b	w0

Compiler

Compiled 6642 to 4210 computations (36.6% saved)

regimes1.2s (11.3%)

Accuracy

Total 3.0b remaining (32.1%)

Threshold costs 0b (0%)

Counts

63 → 2

Compiler

Compiled 30416 to 22894 computations (24.7% saved)

bsearch54.0ms (0.5%)

Steps

Iters	Range		Point
14	1.8632409427501411e+149	#hash((type . real) (value . +inf))	1.7832048700333877e+308

Compiler

Compiled 22 to 17 computations (22.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	57
1	33	57
2	42	57
3	50	57
4	56	57
5	59	57
6	60	57
7	59	57

end152.0ms (1.4%)

Remove: (sort M D)
Compiler: Compiled 406 to 287 computations (29.3% saved)

Details

analyze3.1s (28.6%)

sample2.5s (22.8%)

simplify25.0ms (0.2%)

prune2.0ms (0%)

localize20.0ms (0.2%)

series506.0ms (4.7%)

rewrite89.0ms (0.8%)

simplify224.0ms (2.1%)

prune357.0ms (3.3%)

localize12.0ms (0.1%)

series488.0ms (4.5%)

rewrite80.0ms (0.7%)

simplify102.0ms (0.9%)

prune254.0ms (2.4%)

localize12.0ms (0.1%)

series416.0ms (3.9%)

rewrite76.0ms (0.7%)

simplify107.0ms (1%)

prune199.0ms (1.8%)

localize13.0ms (0.1%)

series409.0ms (3.8%)

rewrite87.0ms (0.8%)

simplify113.0ms (1%)

prune203.0ms (1.9%)

regimes1.2s (11.3%)

bsearch54.0ms (0.5%)

simplify4.0ms (0%)

end152.0ms (1.4%)

Profiling