Details

analyze623.0ms (14.6%)

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
0%	99.8%	0.2%	7
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
41.7%	58.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample970.0ms (22.8%)

Results

903.0ms	8256×	body	128	valid
51.0ms	425×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess38.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

672×	`unsub-neg_binary64`
506×	`fma-neg_binary64`
322×	`distribute-rgt-in_binary64`
248×	`associate-+l+_binary64`
211×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	91
1	60	91
2	155	91
3	440	91
4	1449	91
5	2806	91
0	4	4
1	4	4

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort y t)

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify58.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

930×	`fma-neg_binary64`
752×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
200×	`unsub-neg_binary64`
135×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	35	13
3	94	13
4	299	13
5	905	13
6	1777	13
7	3115	13
8	3878	13
9	3900	13
10	3900	13
11	4061	13
12	4061	13

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.5b	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))
	9.5b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 74 to 44 computations (40.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 z y))
✓	2.4b	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))

series109.0ms (2.6%)

Counts

2 → 72

Calls

21 calls:

18.0ms	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))	x	-inf
16.0ms	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))	x	inf
12.0ms	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))	y	inf
10.0ms	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))	t	inf
7.0ms	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))	y	-inf

rewrite55.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

754×	`prod-diff_binary64`
210×	`log1p-udef_binary64`
114×	`add-sqr-sqrt_binary64`
109×	`log1p-expm1-u_binary64`
109×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	212	20
2	3378	20

Stop Event

1×	node limit

Counts

2 → 77

simplify62.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

676×	`times-frac_binary64`
513×	`associate-/l*_binary64`
415×	`associate-/r*_binary64`
245×	`associate-r_binary64`
201×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	297	4390
1	1125	4194

Stop Event

1×	node limit

Counts

149 → 143

prune125.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	139	6	145

Error

Counts

145 → 6

Alt Table

Status	Error	Program
▶	1.8b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 z t)) (/.f64 (cbrt.f64 x) (-.f64 z y)))
✓	2.5b	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))
	9.5b	(.f64 (/.f64 x (.f64 (-.f64 z y) (-.f64 z t))) 1)
	9.1b	(.f64 x (.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (-.f64 z t))))
	1.8b	(/.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))
	2.9b	(pow.f64 (*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x)) -1)

Compiler

Compiled 4813 to 2128 computations (55.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cbrt.f64 x) (-.f64 z y))
✓	0.5b	(pow.f64 (cbrt.f64 x) 2)
✓	0.6b	(cbrt.f64 x)
✓	1.1b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 z t)) (/.f64 (cbrt.f64 x) (-.f64 z y)))

series227.0ms (5.3%)

Counts

4 → 72

Calls

27 calls:

82.0ms	(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 z t)) (/.f64 (cbrt.f64 x) (-.f64 z y)))	x	-inf
19.0ms	(pow.f64 (cbrt.f64 x) 2)	x	-inf
16.0ms	(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 z t)) (/.f64 (cbrt.f64 x) (-.f64 z y)))	x	inf
13.0ms	(/.f64 (cbrt.f64 x) (-.f64 z y))	x	-inf
9.0ms	(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 z t)) (/.f64 (cbrt.f64 x) (-.f64 z y)))	t	0

rewrite75.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

772×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`
145×	`expm1-log1p-u_binary64`
144×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	297	31
2	4399	31

Stop Event

1×	node limit

Counts

4 → 131

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

682×	`times-frac_binary64`
504×	`associate-/l*_binary64`
425×	`associate-/r*_binary64`
264×	`associate-r_binary64`
224×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	308	4453
1	1174	4197

Stop Event

1×	node limit

Counts

203 → 197

prune177.0ms (4.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	220	6	226

Error

Counts

226 → 6

Alt Table

Status	Error	Program
	9.1b	(.f64 x (.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (-.f64 z t))))
	9.5b	(/.f64 x (*.f64 (-.f64 z y) (-.f64 z t)))
✓	1.8b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 z t)) (/.f64 (cbrt.f64 x) (-.f64 z y)))
✓	2.5b	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))
▶	1.8b	(/.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))
	2.9b	(pow.f64 (*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x)) -1)

Compiler

Compiled 6473 to 2863 computations (55.8% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 z t))
✓	1.7b	(/.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))

series106.0ms (2.5%)

Counts

2 → 72

Calls

21 calls:

19.0ms	(/.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))	x	inf
18.0ms	(/.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))	x	-inf
9.0ms	(/.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))	y	-inf
8.0ms	(/.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))	t	-inf
7.0ms	(/.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))	y	inf

rewrite59.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

754×	`prod-diff_binary64`
210×	`log1p-udef_binary64`
114×	`add-sqr-sqrt_binary64`
109×	`log1p-expm1-u_binary64`
109×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	212	20
2	3378	20

Stop Event

1×	node limit

Counts

2 → 77

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

666×	`times-frac_binary64`
507×	`associate-/l*_binary64`
410×	`associate-/r*_binary64`
245×	`associate-r_binary64`
201×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	298	4390
1	1125	4194

Stop Event

1×	node limit

Counts

149 → 143

prune114.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	143	6	149

Error

Counts

149 → 6

Alt Table

Status	Error	Program
✓	1.8b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 z t)) (/.f64 (cbrt.f64 x) (-.f64 z y)))
	9.0b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 (-.f64 z t)) (-.f64 z y)))
✓	2.5b	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))
	9.5b	(/.f64 x (*.f64 (-.f64 z y) (-.f64 z t)))
✓	1.8b	(/.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))
▶	2.9b	(pow.f64 (*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x)) -1)

Compiler

Compiled 4777 to 2096 computations (56.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z y) x)
✓	0.6b	(pow.f64 (*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x)) -1)
✓	2.4b	(*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x))

series132.0ms (3.1%)

Counts

3 → 124

Calls

33 calls:

19.0ms	(pow.f64 (*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x)) -1)	x	-inf
18.0ms	(pow.f64 (*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x)) -1)	x	inf
10.0ms	(pow.f64 (*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x)) -1)	y	-inf
8.0ms	(pow.f64 (*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x)) -1)	t	-inf
7.0ms	(pow.f64 (*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x)) -1)	t	inf

rewrite103.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

900×	`prod-diff_binary64`
247×	`egg-rr`
133×	`add-sqr-sqrt_binary64`
127×	`log1p-expm1-u_binary64`
127×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	254	33
2	3820	33

Stop Event

1×	node limit

Counts

3 → 247

simplify79.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

666×	`times-frac_binary64`
516×	`associate-/l*_binary64`
410×	`associate-/r*_binary64`
250×	`associate-r_binary64`
202×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	304	5254
1	1149	4878

Stop Event

1×	node limit

Counts

371 → 328

prune271.0ms (6.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	327	1	328
Fresh	1	1	2
Picked	0	1	1
Done	0	3	3
Total	328	6	334

Error

Counts

334 → 6

Alt Table

Status	Error	Program
✓	1.8b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 z t)) (/.f64 (cbrt.f64 x) (-.f64 z y)))
✓	2.5b	(/.f64 (/.f64 x (-.f64 z y)) (-.f64 z t))
	2.6b	(/.f64 (/.f64 1 (-.f64 z t)) (/.f64 (-.f64 z y) x))
	9.5b	(/.f64 x (*.f64 (-.f64 z y) (-.f64 z t)))
✓	1.8b	(/.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))
✓	2.9b	(pow.f64 (*.f64 (-.f64 z t) (/.f64 (-.f64 z y) x)) -1)

Compiler

Compiled 12275 to 4745 computations (61.3% saved)

regimes476.0ms (11.2%)

Accuracy

Total 1.4b remaining (98.9%)

Threshold costs 0b (0%)

Counts

75 → 3

Compiler

Compiled 6874 to 4496 computations (34.6% saved)

bsearch2.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
0.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Steps

Iters	Point		Range
2.351325104598589e+147	∈ [	2.351325104598589e+147	,	1.1630724595946072e+148	]
-0.0	∈ [	-0.0	,	3.755e-321	]

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	82
1	41	82
2	60	82
3	72	82
4	80	82
5	81	82

Stop Event

1×

saturated

end219.0ms (5.1%)

Stop Event

1×

fuel

Compiler

Compiled 328 to 152 computations (53.7% saved)

Details

analyze623.0ms (14.6%)

sample970.0ms (22.8%)

preprocess38.0ms (0.9%)

simplify58.0ms (1.4%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series109.0ms (2.6%)

rewrite55.0ms (1.3%)

simplify62.0ms (1.5%)

prune125.0ms (2.9%)

localize12.0ms (0.3%)

series227.0ms (5.3%)

rewrite75.0ms (1.8%)

simplify68.0ms (1.6%)

prune177.0ms (4.2%)

localize8.0ms (0.2%)

series106.0ms (2.5%)

rewrite59.0ms (1.4%)

simplify66.0ms (1.5%)

prune114.0ms (2.7%)

localize9.0ms (0.2%)

series132.0ms (3.1%)

rewrite103.0ms (2.4%)

simplify79.0ms (1.9%)

prune271.0ms (6.4%)

regimes476.0ms (11.2%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end219.0ms (5.1%)

Profiling