Details

analyze1.0s (19.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.2s (22.8%)

Results

1.2s	8256×	body	128	valid
44.0ms	308×	body	128	invalid

Compiler

Compiled 44 to 28 computations (36.4% saved)

preprocess39.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

513×	`distribute-rgt-in_binary64`
482×	`fma-def_binary64`
472×	`div-sub_binary64`
360×	`fma-neg_binary64`
312×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	175
1	123	175
2	214	175
3	436	175
4	1062	175
5	2449	175
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

507×	`times-frac_binary64`
351×	`fma-def_binary64`
333×	`associate-/l*_binary64`
262×	`div-sub_binary64`
250×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	202	25
5	448	25
6	1376	25

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

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

7.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.1b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.5b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.7b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series121.0ms (2.3%)

Counts

4 → 114

Calls

42 calls:

7.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	x	inf
7.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	z	0
7.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	y	-inf
6.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	y	inf
6.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	x	0

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

169×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
160×	`add-cbrt-cube_binary64`
156×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	325	55

Stop Event

1×	node limit

Counts

4 → 149

simplify99.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

933×	`cancel-sign-sub-inv_binary64`
447×	`sub-neg_binary64`
341×	`times-frac_binary64`
261×	`+-commutative_binary64`
255×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	5495
1	876	5208
2	4054	5103

Stop Event

1×	node limit

Counts

263 → 238

prune224.0ms (4.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	232	6	238
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	233	6	239

Error

0.0b

Counts

239 → 6

Alt Table

Status	Error	Program
	35.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (fma.f64 (sqrt.f64 (.f64 z t)) (sqrt.f64 (*.f64 z t)) (neg.f64 x)))) (+.f64 x 1))
	26.6b	(-.f64 (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (.f64 (+.f64 1 x) t))) (/.f64 x (.f64 (+.f64 1 x) (*.f64 t z))))
▶	7.1b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 z t) x)))) (+.f64 x 1))
	7.1b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (/.f64 1 (+.f64 x 1)))
	26.2b	(-.f64 1 (/.f64 y (*.f64 (+.f64 x 1) (/.f64 x z))))
	28.3b	(+.f64 1 (*.f64 (/.f64 z x) (-.f64 (/.f64 t (+.f64 x 1)) (/.f64 y (+.f64 x 1)))))

Compiler

Compiled 8008 to 3422 computations (57.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.4b	(/.f64 1 (-.f64 (*.f64 z t) x))
✓	0.5b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 z t) x)))) (+.f64 x 1))
✓	9.5b	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 z t) x)))

series129.0ms (2.4%)

Counts

3 → 132

Calls

33 calls:

9.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 z t) x)))) (+.f64 x 1))	x	inf
8.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 z t) x)))) (+.f64 x 1))	t	0
7.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 z t) x)))) (+.f64 x 1))	y	-inf
7.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 z t) x)))) (+.f64 x 1))	y	inf
6.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 z t) x)))) (+.f64 x 1))	x	0

rewrite43.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

177×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`
167×	`add-cbrt-cube_binary64`
163×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	51
1	345	51

Stop Event

1×	node limit

Counts

3 → 97

simplify102.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

457×	`sub-neg_binary64`
355×	`times-frac_binary64`
279×	`+-commutative_binary64`
272×	`associate-+r+_binary64`
258×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	6514
1	932	6203
2	4260	6098

Stop Event

1×	node limit

Counts

229 → 195

prune214.0ms (4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	239	5	244

Error

0.0b

Counts

244 → 5

Alt Table

Status	Error	Program
	35.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (fma.f64 (sqrt.f64 (.f64 z t)) (sqrt.f64 (*.f64 z t)) (neg.f64 x)))) (+.f64 x 1))
	26.6b	(-.f64 (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (.f64 (+.f64 1 x) t))) (/.f64 x (.f64 (+.f64 1 x) (*.f64 t z))))
	7.1b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (/.f64 1 (+.f64 x 1)))
	26.2b	(-.f64 1 (/.f64 y (*.f64 (+.f64 x 1) (/.f64 x z))))
▶	7.1b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))

Compiler

Compiled 8228 to 3672 computations (55.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.2b	(/.f64 1 (/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x)))
✓	0.5b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	9.7b	(/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x))

series151.0ms (2.8%)

Counts

3 → 144

Calls

36 calls:

10.0ms	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))	x	inf
8.0ms	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))	y	-inf
8.0ms	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))	t	0
7.0ms	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))	y	inf
6.0ms	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))	x	0

rewrite44.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

183×	`add-sqr-sqrt_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`
173×	`add-cbrt-cube_binary64`
169×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	353	57

Stop Event

1×	node limit

Counts

3 → 107

simplify94.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

424×	`times-frac_binary64`
317×	`+-commutative_binary64`
306×	`associate-/l*_binary64`
287×	`associate-+r+_binary64`
271×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	306	7592
1	1104	7245

Stop Event

1×	node limit

Counts

251 → 225

prune249.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	268	5	273

Error

0.0b

Counts

273 → 5

Alt Table

Status	Error	Program
	35.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (fma.f64 (sqrt.f64 (.f64 z t)) (sqrt.f64 (*.f64 z t)) (neg.f64 x)))) (+.f64 x 1))
	26.6b	(-.f64 (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (.f64 (+.f64 1 x) t))) (/.f64 x (.f64 (+.f64 1 x) (*.f64 t z))))
▶	7.1b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (/.f64 1 (+.f64 x 1)))
	26.2b	(-.f64 1 (/.f64 y (*.f64 (+.f64 x 1) (/.f64 x z))))
✓	7.1b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))

Compiler

Compiled 9541 to 4257 computations (55.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 z t) x)
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.5b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (/.f64 1 (+.f64 x 1)))
✓	9.7b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))

series114.0ms (2.1%)

Counts

3 → 132

Calls

33 calls:

9.0ms	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (/.f64 1 (+.f64 x 1)))	x	0
7.0ms	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (/.f64 1 (+.f64 x 1)))	y	-inf
6.0ms	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (/.f64 1 (+.f64 x 1)))	y	inf
6.0ms	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (/.f64 1 (+.f64 x 1)))	y	0
6.0ms	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (/.f64 1 (+.f64 x 1)))	t	0

rewrite45.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

179×	`add-sqr-sqrt_binary64`
170×	`log1p-expm1-u_binary64`
170×	`expm1-log1p-u_binary64`
169×	`add-cbrt-cube_binary64`
165×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	348	48

Stop Event

1×	node limit

Counts

3 → 114

simplify98.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

933×	`cancel-sign-sub-inv_binary64`
447×	`sub-neg_binary64`
341×	`times-frac_binary64`
261×	`+-commutative_binary64`
255×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	5652
1	876	5365
2	4054	5260

Stop Event

1×	node limit

Counts

246 → 202

prune308.0ms (5.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	245	5	250

Error

0.0b

Counts

250 → 5

Alt Table

Status	Error	Program
	35.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (fma.f64 (sqrt.f64 (.f64 z t)) (sqrt.f64 (*.f64 z t)) (neg.f64 x)))) (+.f64 x 1))
	26.6b	(-.f64 (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (.f64 (+.f64 1 x) t))) (/.f64 x (.f64 (+.f64 1 x) (*.f64 t z))))
✓	7.1b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (/.f64 1 (+.f64 x 1)))
	26.2b	(-.f64 1 (/.f64 y (*.f64 (+.f64 x 1) (/.f64 x z))))
✓	7.1b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 z t) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))

Compiler

Compiled 8452 to 3706 computations (56.2% saved)

regimes794.0ms (14.9%)

Accuracy

Total 1.0b remaining (93.8%)

Threshold costs 1.0b (93.8%)

Counts

145 → 2

Compiler

Compiled 15582 to 10393 computations (33.3% saved)

bsearch8.0ms (0.2%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

Steps

Iters	Point		Range
#hash((type . real) (value . +inf))	∈ [	#hash((type . real) (value . +inf))	,	#hash((type . real) (value . NaN))	]

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	77
1	41	77
2	50	77
3	54	77
4	56	77

Stop Event

1×

saturated

end96.0ms (1.8%)

Stop Event

1×

fuel

Compiler

Compiled 227 to 132 computations (41.9% saved)

Details

analyze1.0s (19.3%)

sample1.2s (22.8%)

preprocess39.0ms (0.7%)

simplify21.0ms (0.4%)

prune2.0ms (0%)

localize10.0ms (0.2%)

series121.0ms (2.3%)

rewrite50.0ms (0.9%)

simplify99.0ms (1.8%)

prune224.0ms (4.2%)

localize11.0ms (0.2%)

series129.0ms (2.4%)

rewrite43.0ms (0.8%)

simplify102.0ms (1.9%)

prune214.0ms (4%)

localize13.0ms (0.2%)

series151.0ms (2.8%)

rewrite44.0ms (0.8%)

simplify94.0ms (1.8%)

prune249.0ms (4.7%)

localize11.0ms (0.2%)

series114.0ms (2.1%)

rewrite45.0ms (0.9%)

simplify98.0ms (1.8%)

prune308.0ms (5.8%)

regimes794.0ms (14.9%)

bsearch8.0ms (0.2%)

simplify4.0ms (0.1%)

end96.0ms (1.8%)

Profiling