Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.5s (35%)

Results

763.0ms	6131×	body	128	valid
390.0ms	1053×	body	1024	valid
176.0ms	627×	body	512	valid
61.0ms	337×	body	256	valid
48.0ms	108×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

preprocess35.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

954×	`fma-neg_binary64`
549×	`div-sub_binary64`
376×	`times-frac_binary64`
249×	`cancel-sign-sub-inv_binary64`
246×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	38
1	39	38
2	64	38
3	109	38
4	201	38
5	404	34
6	859	34
7	2060	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

434×	`cancel-sign-sub-inv_binary64`
372×	`div-sub_binary64`
343×	`sub-neg_binary64`
331×	`fma-neg_binary64`
292×	`fma-def_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	40	19
3	67	19
4	118	19
5	238	17
6	445	17
7	753	17
8	1572	17
9	3643	17

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

15.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.4b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)

Compiler

Compiled 57 to 41 computations (28.1% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
✓	1.5b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series59.0ms (1.4%)

Counts

2 → 48

Calls

12 calls:

22.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))	alpha	inf
6.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)	alpha	inf
5.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)	alpha	-inf
4.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)	beta	inf
3.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)	beta	-inf

rewrite67.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

585×	`fma-def_binary64`
369×	`fma-neg_binary64`
219×	`log1p-udef_binary64`
218×	`expm1-udef_binary64`
127×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	243	29
2	3699	29

Stop Event

1×	node limit

Counts

2 → 127

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary64`
595×	`times-frac_binary64`
359×	`cancel-sign-sub-inv_binary64`
303×	`sub-neg_binary64`
160×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2372
1	564	2336
2	2232	2166

Stop Event

1×	node limit

Counts

175 → 188

prune173.0ms (4.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	184	4	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	4	189

Error

0.0b

Counts

189 → 4

Alt Table

Status	Error	Program
	46.8b	(/.f64 (-.f64 (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha)) (fma.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)) (fma.f64 (/.f64 6 alpha) (/.f64 beta alpha) (/.f64 (/.f64 4 alpha) alpha)))) 2)
▶	15.2b	(/.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2)) (/.f64 beta (cbrt.f64 (+.f64 (+.f64 2 alpha) beta))) (neg.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 2 alpha) beta)) 1))) 2)
	43.3b	(/.f64 (fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2) 2)
	15.5b	(/.f64 (log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1))) 2)

Compiler

Compiled 5571 to 3772 computations (32.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2)
✓	0.5b	(/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2))
✓	0.7b	(cbrt.f64 (+.f64 (+.f64 2 alpha) beta))
✓	1.5b	(-.f64 (/.f64 alpha (+.f64 (+.f64 2 alpha) beta)) 1)

series227.0ms (5.5%)

Counts

4 → 48

Calls

24 calls:

33.0ms	(/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2))	beta	inf
31.0ms	(/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2))	beta	0
29.0ms	(/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2))	alpha	inf
28.0ms	(/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2))	alpha	0
28.0ms	(/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2))	beta	-inf

rewrite63.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

889×	`prod-diff_binary64`
136×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`
133×	`expm1-log1p-u_binary64`
132×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	280	46
2	3843	46

Stop Event

1×	node limit

Counts

4 → 109

simplify60.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

567×	`associate-r_binary64`
504×	`fma-def_binary64`
398×	`associate-l_binary64`
235×	`associate-+l+_binary64`
145×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	426	4193
1	1386	3925

Stop Event

1×	node limit

Counts

157 → 186

prune338.0ms (8.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	225	2	227
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	226	5	231

Error

0.0b

Counts

231 → 5

Alt Table

Status	Error	Program
	16.0b	(/.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2)) (/.f64 beta (cbrt.f64 (+.f64 (+.f64 2 alpha) beta))) (neg.f64 (fma.f64 alpha (/.f64 1 (+.f64 alpha (+.f64 2 beta))) -1))) 2)
	46.8b	(/.f64 (-.f64 (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha)) (fma.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)) (fma.f64 (/.f64 6 alpha) (/.f64 beta alpha) (/.f64 (/.f64 4 alpha) alpha)))) 2)
	46.9b	(/.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2)) (/.f64 beta (cbrt.f64 (+.f64 (+.f64 2 alpha) beta))) (neg.f64 (+.f64 (/.f64 4 (.f64 alpha alpha)) (-.f64 (fma.f64 4 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))) (+.f64 (/.f64 2 alpha) (/.f64 beta alpha)))))) 2)
	43.3b	(/.f64 (fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2) 2)
▶	15.5b	(/.f64 (log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1))) 2)

Compiler

Compiled 12445 to 9609 computations (22.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta))
✓	0.0b	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1))
✓	1.5b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1)
✓	1.5b	(log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1)))

series99.0ms (2.4%)

Counts

4 → 96

Calls

24 calls:

8.0ms	(log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1)))	alpha	-inf
7.0ms	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1))	beta	-inf
6.0ms	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1))	alpha	0
6.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1)	alpha	-inf
6.0ms	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1))	beta	0

rewrite79.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

364×	`fma-neg_binary64`
235×	`log1p-udef_binary64`
234×	`expm1-udef_binary64`
182×	`egg-rr`
132×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	63
1	265	63
2	3928	63

Stop Event

1×	node limit

Counts

4 → 182

simplify108.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

460×	`sub-neg_binary64`
267×	`+-commutative_binary64`
258×	`times-frac_binary64`
244×	`fma-def_binary64`
240×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	320	5433
1	1079	5358
2	4617	5272

Stop Event

1×	node limit

Counts

278 → 225

prune227.0ms (5.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	225	5	230

Error

0.0b

Counts

230 → 5

Alt Table

Status	Error	Program
▶	16.0b	(/.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2)) (/.f64 beta (cbrt.f64 (+.f64 (+.f64 2 alpha) beta))) (neg.f64 (fma.f64 alpha (/.f64 1 (+.f64 alpha (+.f64 2 beta))) -1))) 2)
	46.8b	(/.f64 (-.f64 (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha)) (fma.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)) (fma.f64 (/.f64 6 alpha) (/.f64 beta alpha) (/.f64 (/.f64 4 alpha) alpha)))) 2)
	46.9b	(/.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2)) (/.f64 beta (cbrt.f64 (+.f64 (+.f64 2 alpha) beta))) (neg.f64 (+.f64 (/.f64 4 (.f64 alpha alpha)) (-.f64 (fma.f64 4 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))) (+.f64 (/.f64 2 alpha) (/.f64 beta alpha)))))) 2)
	43.3b	(/.f64 (fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2) 2)
✓	15.5b	(/.f64 (log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1))) 2)

Compiler

Compiled 7987 to 5440 computations (31.9% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2)
	0.5b	(/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2))
	0.7b	(cbrt.f64 (+.f64 (+.f64 2 alpha) beta))
✓	15.7b	(fma.f64 alpha (/.f64 1 (+.f64 alpha (+.f64 2 beta))) -1)

series17.0ms (0.4%)

Counts

1 → 24

Calls

6 calls:

5.0ms	(fma.f64 alpha (/.f64 1 (+.f64 alpha (+.f64 2 beta))) -1)	alpha	-inf
4.0ms	(fma.f64 alpha (/.f64 1 (+.f64 alpha (+.f64 2 beta))) -1)	alpha	inf
2.0ms	(fma.f64 alpha (/.f64 1 (+.f64 alpha (+.f64 2 beta))) -1)	beta	0
2.0ms	(fma.f64 alpha (/.f64 1 (+.f64 alpha (+.f64 2 beta))) -1)	beta	-inf
2.0ms	(fma.f64 alpha (/.f64 1 (+.f64 alpha (+.f64 2 beta))) -1)	alpha	0

rewrite41.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

581×	`prod-diff_binary64`
290×	`fma-def_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
168×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	216	13
2	2794	13

Stop Event

1×	node limit

Counts

1 → 23

simplify32.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

463×	`fma-def_binary64`
387×	`associate--r+_binary64`
364×	`times-frac_binary64`
323×	`associate--l+_binary64`
271×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	987
1	322	979
2	1206	894

Stop Event

1×	node limit

Counts

47 → 52

prune329.0ms (7.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	216	5	221

Error

Counts

221 → 5

Alt Table

Status	Error	Program
	46.8b	(/.f64 (-.f64 (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha)) (fma.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)) (fma.f64 (/.f64 6 alpha) (/.f64 beta alpha) (/.f64 (/.f64 4 alpha) alpha)))) 2)
	16.9b	(/.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2)) (/.f64 beta (pow.f64 (+.f64 alpha (+.f64 2 beta)) 1/3)) (neg.f64 (fma.f64 alpha (/.f64 1 (+.f64 alpha (+.f64 2 beta))) -1))) 2)
	43.3b	(/.f64 (fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2) 2)
	46.5b	(/.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (+.f64 2 alpha) beta)) 2)) (/.f64 beta (cbrt.f64 (+.f64 (+.f64 2 alpha) beta))) (neg.f64 (+.f64 (/.f64 4 (.f64 alpha alpha)) (-.f64 (+.f64 (.f64 (/.f64 beta alpha) (+.f64 (/.f64 4 alpha) (/.f64 beta alpha))) (/.f64 -2 alpha)) (+.f64 (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 6 (/.f64 beta (/.f64 (pow.f64 alpha 3) beta)) (fma.f64 12 (/.f64 beta (pow.f64 alpha 3)) (/.f64 beta alpha)))) (pow.f64 (/.f64 beta alpha) 3)))))) 2)
✓	15.5b	(/.f64 (log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1))) 2)

Compiler

Compiled 11947 to 9299 computations (22.2% saved)

regimes440.0ms (10.6%)

Accuracy

Total 0.1b remaining (60.2%)

Threshold costs 0.1b (60.2%)

Counts

60 → 2

Compiler

Compiled 6740 to 5071 computations (24.8% saved)

bsearch5.0ms (0.1%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Steps

Iters	Point		Range
-0.9999997731697953	∈ [	-0.9999997731697953	,	-0.9696724805405891	]

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	87
1	44	87
2	51	87
3	55	87
4	57	87

Stop Event

1×

saturated

end139.0ms (3.3%)

Stop Event

1×

fuel

Compiler

Compiled 299 to 195 computations (34.8% saved)

Details

analyze2.0ms (0%)

sample1.5s (35%)

preprocess35.0ms (0.9%)

simplify30.0ms (0.7%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series59.0ms (1.4%)

rewrite67.0ms (1.6%)

simplify71.0ms (1.7%)

prune173.0ms (4.2%)

localize13.0ms (0.3%)

series227.0ms (5.5%)

rewrite63.0ms (1.5%)

simplify60.0ms (1.4%)

prune338.0ms (8.1%)

localize11.0ms (0.3%)

series99.0ms (2.4%)

rewrite79.0ms (1.9%)

simplify108.0ms (2.6%)

prune227.0ms (5.5%)

localize17.0ms (0.4%)

series17.0ms (0.4%)

rewrite41.0ms (1%)

simplify32.0ms (0.8%)

prune329.0ms (7.9%)

regimes440.0ms (10.6%)

bsearch5.0ms (0.1%)

simplify4.0ms (0.1%)

end139.0ms (3.3%)

Profiling