Details

analyze710.0ms (9.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
34.7%	55.4%	9.9%	9
36.1%	51.1%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.0s (26.7%)

Results

636.0ms	5304×	body	128	valid
554.0ms	1225×	body	2048	valid
284.0ms	759×	body	1024	valid
234.0ms	425×	body	4096	valid
122.0ms	1077×	body	128	invalid
106.0ms	366×	body	512	valid
36.0ms	177×	body	256	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess94.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

508×	`times-frac_binary64`
390×	`div-sub_binary64`
354×	`fma-def_binary64`
351×	`fma-neg_binary64`
312×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	80
1	65	72
2	112	72
3	222	72
4	365	72
5	620	72
6	1057	72
7	1768	72
8	4025	72
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
361×	`div-sub_binary64`
341×	`fma-def_binary64`
313×	`associate-/l*_binary64`
224×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	23	18
2	42	18
3	77	18
4	123	18
5	218	18
6	370	18
7	586	18
8	948	18
9	1471	18
10	2000	18
11	3220	18
12	4095	18
13	4427	18
14	4435	18
15	4443	18
16	4469	18
17	4485	18
18	4521	18
19	4553	18
20	4565	18

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

35.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Compiler

Compiled 58 to 30 computations (48.3% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	26.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series116.0ms (1.6%)

Counts

4 → 96

Calls

36 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)	a	-inf
8.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)	a	inf
7.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)	c	-inf
7.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)	c	inf
5.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)	c	-inf

rewrite91.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
338×	`fma-neg_binary64`
313×	`egg-rr`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	55
1	239	55
2	3605	55

Stop Event

1×	node limit

Counts

4 → 313

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

738×	`times-frac_binary64`
490×	`associate-/l*_binary64`
401×	`associate-/r*_binary64`
360×	`fma-def_binary64`
133×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2203
1	392	2175
2	1383	2133

Stop Event

1×	node limit

Counts

409 → 388

prune244.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	379	9	388
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	379	10	389

Error

6.1b

Counts

389 → 10

Alt Table

Status	Error	Program
	41.9b	(/.f64 (*.f64 -2 b_2) a)
	51.0b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)) 2)
	41.9b	(/.f64 (*.f64 c -1/2) b_2)
	46.3b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
▶	35.3b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
✓	35.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	41.9b	(*.f64 (/.f64 -2 a) b_2)
	56.2b	(/.f64 (-.f64 b_2 b_2) a)
	36.5b	(fma.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (/.f64 1 a) (neg.f64 (/.f64 b_2 a)))
	42.2b	(/.f64 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 b_2 -2)) a)

Compiler

Compiled 9506 to 2913 computations (69.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	26.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series691.0ms (9.3%)

Counts

1 → 20

Calls

9 calls:

192.0ms	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)	c	-inf
185.0ms	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)	c	inf
155.0ms	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)	a	-inf
136.0ms	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)	a	inf
6.0ms	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)	b_2	inf

rewrite52.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

323×	`fma-neg_binary64`
238×	`expm1-udef_binary64`
238×	`log1p-udef_binary64`
137×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	277	18
2	3912	18

Stop Event

1×	node limit

Counts

1 → 46

simplify37.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-neg_binary64`
363×	`times-frac_binary64`
239×	`associate-/l*_binary64`
212×	`associate-r_binary64`
206×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	654
1	207	642
2	703	624
3	3907	624

Stop Event

1×	node limit

Counts

66 → 69

prune236.0ms (3.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	382	4	386
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	384	12	396

Error

6.1b

Counts

396 → 12

Alt Table

Status	Error	Program
	41.9b	(*.f64 (/.f64 -2 a) b_2)
	42.3b	(pow.f64 (/.f64 a (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 b_2 -2))) -1)
	41.9b	(/.f64 (*.f64 c -1/2) b_2)
▶	35.3b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
	46.3b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
✓	35.3b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	41.9b	(/.f64 (*.f64 -2 b_2) a)
✓	35.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	41.9b	(pow.f64 (/.f64 a (*.f64 b_2 -2)) -1)
	56.2b	(/.f64 (-.f64 b_2 b_2) a)
	35.5b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))))
	42.2b	(/.f64 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 b_2 -2)) a)

Compiler

Compiled 10153 to 3561 computations (64.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
	0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	26.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series48.0ms (0.6%)

Counts

1 → 20

Calls

9 calls:

11.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))	a	-inf
8.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))	a	inf
7.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))	c	inf
6.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))	c	-inf
4.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))	b_2	inf

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`
149×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`
144×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	303	18
2	4325	18

Stop Event

1×	node limit

Counts

1 → 38

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-neg_binary64`
363×	`times-frac_binary64`
239×	`associate-/l*_binary64`
212×	`associate-r_binary64`
206×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	654
1	207	642
2	703	624
3	3907	624

Stop Event

1×	node limit

Counts

58 → 61

prune222.0ms (3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	376	2	378
Fresh	1	8	9
Picked	1	0	1
Done	0	2	2
Total	378	12	390

Error

6.1b

Counts

390 → 12

Alt Table

Status	Error	Program
✓	35.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
▶	35.3b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)))
	41.9b	(*.f64 (/.f64 -2 a) b_2)
	42.3b	(pow.f64 (/.f64 a (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 b_2 -2))) -1)
	41.9b	(/.f64 (*.f64 c -1/2) b_2)
	44.8b	(/.f64 (/.f64 1 a) (/.f64 1 (.f64 (/.f64 (.f64 c -1/2) b_2) a)))
	46.3b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
✓	35.3b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	41.9b	(/.f64 (*.f64 -2 b_2) a)
	41.9b	(pow.f64 (/.f64 a (*.f64 b_2 -2)) -1)
	56.2b	(/.f64 (-.f64 b_2 b_2) a)
	42.2b	(/.f64 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 b_2 -2)) a)

Compiler

Compiled 10602 to 4235 computations (60.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))
✓	1.2b	(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)
✓	26.2b	(sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c)))))
✓	52.2b	(fma.f64 a (neg.f64 c) (*.f64 a c))

series89.0ms (1.2%)

Counts

4 → 100

Calls

33 calls:

7.0ms	(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)	c	-inf
5.0ms	(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)	c	inf
5.0ms	(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)	a	inf
5.0ms	(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)	a	-inf
5.0ms	(sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c)))))	c	inf

rewrite77.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

514×	`log-prod_binary64`
367×	`fma-def_binary64`
217×	`fma-neg_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	77
1	233	57
2	3092	57

Stop Event

1×	node limit

Counts

4 → 191

simplify61.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

416×	`times-frac_binary64`
278×	`associate-/l*_binary64`
264×	`associate-r_binary64`
235×	`associate-/r*_binary64`
224×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	1573
1	272	1557
2	879	1533
3	4612	1533

Stop Event

1×	node limit

Counts

291 → 243

prune133.0ms (1.8%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	242	1	243
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	242	13	255

Error

6.1b

Counts

255 → 13

Alt Table

Status	Error	Program
✓	35.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	35.3b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)))
	41.9b	(*.f64 (/.f64 -2 a) b_2)
	42.3b	(pow.f64 (/.f64 a (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 b_2 -2))) -1)
	41.9b	(/.f64 (*.f64 c -1/2) b_2)
	44.8b	(/.f64 (/.f64 1 a) (/.f64 1 (.f64 (/.f64 (.f64 c -1/2) b_2) a)))
	46.3b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	42.2b	(/.f64 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 b_2 -2)) a)
	47.0b	(/.f64 (/.f64 1 a) (/.f64 1 (exp.f64 (log.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (fma.f64 a c (*.f64 a (+.f64 c c))))) b_2)))))
✓	35.3b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	41.9b	(/.f64 (*.f64 -2 b_2) a)
	41.9b	(pow.f64 (/.f64 a (*.f64 b_2 -2)) -1)
	56.2b	(/.f64 (-.f64 b_2 b_2) a)

Compiler

Compiled 7272 to 2815 computations (61.3% saved)

regimes2.1s (27.9%)

Accuracy

Total 4.8b remaining (47.1%)

Threshold costs 0b (0%)

Counts

136 → 3

Compiler

Compiled 10700 to 6862 computations (35.9% saved)

bsearch57.0ms (0.8%)

Algorithm

2×	binary-search

Calls

2 calls:

34.0ms	b_2
18.0ms	b_2

Steps

Iters	Point		Range
3.5516450204745413e-95	∈ [	2.4336191574493255e-95	,	7.555548468790224e-94	]
-2.3813446637561993e+60	∈ [	-2.414460495428899e+60	,	-6.160930651602259e+58	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	57
1	43	57
2	57	57
3	66	57
4	71	57
5	72	57

Stop Event

1×

saturated

end147.0ms (2%)

Stop Event

1×

fuel

Compiler

Compiled 282 to 182 computations (35.5% saved)

Details

analyze710.0ms (9.5%)

sample2.0s (26.7%)

preprocess94.0ms (1.3%)

simplify60.0ms (0.8%)

prune3.0ms (0%)

localize28.0ms (0.4%)

series116.0ms (1.6%)

rewrite91.0ms (1.2%)

simplify54.0ms (0.7%)

prune244.0ms (3.3%)

localize10.0ms (0.1%)

series691.0ms (9.3%)

rewrite52.0ms (0.7%)

simplify37.0ms (0.5%)

prune236.0ms (3.2%)

localize12.0ms (0.2%)

series48.0ms (0.6%)

rewrite57.0ms (0.8%)

simplify38.0ms (0.5%)

prune222.0ms (3%)

localize14.0ms (0.2%)

series89.0ms (1.2%)

rewrite77.0ms (1%)

simplify61.0ms (0.8%)

prune133.0ms (1.8%)

regimes2.1s (27.9%)

bsearch57.0ms (0.8%)

simplify4.0ms (0%)

end147.0ms (2%)

Profiling