Details

analyze2.8s (24.5%)

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 (21.4%)

Symmetry

(sort M D)

Results

1.5s	8256×	body	128	valid
842.0ms	4577×	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

14.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.8b	(.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)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	4.4b	(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))
✓	13.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series576.0ms (5.1%)

Counts

4 → 204

Calls

4 calls:

226.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
184.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
152.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
14.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite94.0ms (0.8%)

Algorithm

2×	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:

92.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
92.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
92.0ms	(/.f64 (.f64 M D) (.f64 2 d))
92.0ms	(.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
0	0	0
1	0	0

simplify218.0ms (1.9%)

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

prune313.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	231	7	238
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	232	7	239

Error

5.6b

Counts

239 → 7

Alt Table

Status	Error	Program
	15.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (.f64 M (/.f64 1/2 d))) 2) (/.f64 h l)))))
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
▶	8.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	29.7b	(fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 (.f64 M M) h) w0)) (.f64 l (*.f64 d d))) -1/8 w0)
	11.0b	w0
	61.3b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	8.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 l)))))

Compiler

Compiled 9103 to 5499 computations (39.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.2b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
✓	4.4b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
	5.4b	(/.f64 (.f64 M D) (.f64 2 d))
✓	5.8b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

series503.0ms (4.4%)

Counts

3 → 156

Calls

3 calls:

274.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
119.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
110.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))

rewrite87.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

488×	`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:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	59
1	342	59
2	4468	59
3	5450	59
0	0	0
1	0	0

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

588×	`associate-*l/_binary64`
263×	`associate-/r/_binary64`
249×	`fma-def_binary64`
227×	`unswap-sqr_binary64`
207×	`distribute-neg-frac_binary64`

Counts

238 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	5336
1	496	5304
2	2005	5284
3	5169	5284

prune255.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	201	8	209

Error

4.9b

Counts

209 → 8

Alt Table

Status	Error	Program
	29.7b	(fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 (.f64 M M) h) w0)) (.f64 l (*.f64 d d))) -1/8 w0)
▶	8.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (.f64 M 1/2)) 2) h) l))))
	15.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (.f64 M (/.f64 1/2 d))) 2) (/.f64 h l)))))
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	37.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (sqrt.f64 h)) (.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (sqrt.f64 h)) (/.f64 1 l))))))
	11.0b	w0
	61.3b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	8.8b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l)) 1/4) 2))

Compiler

Compiled 6789 to 4264 computations (37.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.2b	(/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h) l)
✓	4.3b	(.f64 (/.f64 D d) (.f64 M 1/2))
✓	4.4b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h) l)))
✓	5.8b	(.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h)

series424.0ms (3.7%)

Counts

4 → 192

Calls

4 calls:

180.0ms	(/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h) l)
117.0ms	(.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h)
113.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h) l)))
14.0ms	(.f64 (/.f64 D d) (.f64 M 1/2))

rewrite86.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

470×	`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:

83.0ms	(/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h) l)
83.0ms	(.f64 (/.f64 D d) (.f64 M 1/2))
83.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h) l)))
83.0ms	(.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	362	69
2	4417	69
3	5324	69
0	0	0
1	0	0

simplify112.0ms (1%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-*l/_binary64`
268×	`associate-/r/_binary64`
249×	`fma-def_binary64`
227×	`unswap-sqr_binary64`
207×	`distribute-neg-frac_binary64`

Counts

301 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	5696
1	505	5664
2	2026	5644
3	5199	5644

prune227.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	174	7	181

Error

4.9b

Counts

181 → 7

Alt Table

Status	Error	Program
	15.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (.f64 M (/.f64 1/2 d))) 2) (/.f64 h l)))))
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	29.7b	(fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 (.f64 M M) h) w0)) (.f64 l (*.f64 d d))) -1/8 w0)
	37.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (sqrt.f64 h)) (.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (sqrt.f64 h)) (/.f64 1 l))))))
	11.0b	w0
	61.3b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
▶	8.5b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (.f64 M 1/2)) 2) h) l)) 1/4) 2))

Compiler

Compiled 6027 to 3786 computations (37.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.2b	(/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h) l)
	4.3b	(.f64 (/.f64 D d) (.f64 M 1/2))
✓	5.7b	(pow.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h) l)) 1/4)
	5.8b	(.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h)

series215.0ms (1.9%)

Counts

1 → 60

Calls

1 calls:

215.0ms

(pow.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h) l)) 1/4)

rewrite69.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

470×	`prod-diff_binary64`
183×	`add-sqr-sqrt_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`
173×	`add-cbrt-cube_binary64`

Counts

1 → 17

Calls

1 calls:

69.0ms

(pow.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 D d) (*.f64 M 1/2)) 2) h) l)) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	387	25
2	4588	25
3	5466	25
0	0	0
1	0	0

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

942×	`times-frac_binary64`
486×	`associate-/l*_binary64`
449×	`associate-/r*_binary64`
180×	`associate-l_binary64`
165×	`associate-*r/_binary64`

Counts

77 → 94

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	329	5764
1	992	5682
2	5206	5682

prune243.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	186	8	194

Error

4.7b

Counts

194 → 8

Alt Table

Status	Error	Program
	15.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (.f64 M (/.f64 1/2 d))) 2) (/.f64 h l)))))
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	29.7b	(fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 (.f64 M M) h) w0)) (.f64 l (*.f64 d d))) -1/8 w0)
	37.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (sqrt.f64 h)) (.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (sqrt.f64 h)) (/.f64 1 l))))))
	11.0b	w0
	62.4b	(.f64 w0 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (pow.f64 M 2)) (*.f64 l (pow.f64 d 2)))))) (log.f64 (/.f64 1 h))))) 2))
	61.3b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
✓	8.5b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 D d) (.f64 M 1/2)) 2) h) l)) 1/4) 2))

Compiler

Compiled 9802 to 6296 computations (35.8% saved)

regimes2.2s (19.7%)

Accuracy

Total 3.2b remaining (32.3%)

Threshold costs 0b (0%)

Counts

126 → 2

Compiler

Compiled 54354 to 41424 computations (23.8% saved)

bsearch62.0ms (0.5%)

Steps

Iters	Range		Point
11	2.0787274402888173e+170	1.2198741083688107e+190	1.2055921857439803e+190

Compiler

Compiled 15 to 12 computations (20% 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	24	50
1	32	50
2	38	50
3	48	50
4	55	50
5	60	50
6	62	50
7	61	50

end156.0ms (1.4%)

Remove: (sort M D)
Compiler: Compiled 364 to 263 computations (27.7% saved)

Details

analyze2.8s (24.5%)

sample2.4s (21.4%)

simplify27.0ms (0.2%)

prune2.0ms (0%)

localize12.0ms (0.1%)

series576.0ms (5.1%)

rewrite94.0ms (0.8%)

simplify218.0ms (1.9%)

prune313.0ms (2.7%)

localize12.0ms (0.1%)

series503.0ms (4.4%)

rewrite87.0ms (0.8%)

simplify105.0ms (0.9%)

prune255.0ms (2.2%)

localize13.0ms (0.1%)

series424.0ms (3.7%)

rewrite86.0ms (0.8%)

simplify112.0ms (1%)

prune227.0ms (2%)

localize15.0ms (0.1%)

series215.0ms (1.9%)

rewrite69.0ms (0.6%)

simplify88.0ms (0.8%)

prune243.0ms (2.1%)

regimes2.2s (19.7%)

bsearch62.0ms (0.5%)

simplify4.0ms (0%)

end156.0ms (1.4%)

Profiling