Details

analyze1.3s (26.4%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.4s (28.2%)

Results

939.0ms	7022×	body	128	valid
136.0ms	457×	body	512	valid
130.0ms	350×	body	1024	valid
98.0ms	789×	body	128	invalid
76.0ms	362×	body	256	valid
29.0ms	65×	body	2048	valid

Compiler

Compiled 38 to 24 computations (36.8% saved)

preprocess48.0ms (1%)

Algorithm

2×	egg-herbie

Rules

769×	`fma-neg_binary64`
745×	`times-frac_binary64`
335×	`fma-def_binary64`
254×	`sub-neg_binary64`
193×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	209
1	158	209
2	465	209
3	1322	187
4	4018	187
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify25.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

744×	`div-sub_binary64`
641×	`fma-def_binary64`
283×	`fma-neg_binary64`
233×	`times-frac_binary64`
164×	`unsub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	158	17
4	424	17
5	1286	17
6	3985	17

Stop Event

1×	node limit

Counts

1 → 2

prune7.0ms (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

6.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	8.6b	(+.f64 x (fma.f64 y (/.f64 (-.f64 z t) (-.f64 t a)) y))
	17.2b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 57 computations (43% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 t a))
✓	4.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 t a)) y)

series58.0ms (1.1%)

Counts

2 → 84

Calls

21 calls:

6.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 t a)) y)	t	inf
5.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 t a)) y)	y	inf
4.0ms	(/.f64 (-.f64 z t) (-.f64 t a))	z	0
4.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 t a)) y)	t	-inf
3.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 t a)) y)	a	0

rewrite64.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

370×	`fma-def_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
197×	`fma-neg_binary64`
176×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	208	24
2	3197	24

Stop Event

1×	node limit

Counts

2 → 77

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

679×	`times-frac_binary64`
577×	`cancel-sign-sub-inv_binary64`
402×	`sub-neg_binary64`
251×	`fma-neg_binary64`
160×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	177	2841
1	598	2781
2	2064	2341

Stop Event

1×	node limit

Counts

161 → 157

prune177.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	150	7	157
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	152	7	159

Error

0.1b

Counts

159 → 7

Alt Table

Status	Error	Program
	29.6b	(+.f64 x (pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 t a)) y)) 2))
	31.1b	(+.f64 x (-.f64 (+.f64 (.f64 (+.f64 1 (/.f64 a t)) (.f64 (/.f64 y t) z)) (.f64 (/.f64 a (/.f64 (.f64 t t) a)) (-.f64 (.f64 (/.f64 y t) z) y))) (.f64 (/.f64 a t) y)))
	30.1b	(+.f64 x (/.f64 (*.f64 y (neg.f64 (-.f64 a z))) t))
	26.2b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	23.5b	(+.f64 x (-.f64 y (/.f64 (*.f64 y z) a)))
	17.2b	(+.f64 x (*.f64 (/.f64 y (-.f64 t a)) z))
▶	8.7b	(+.f64 x (fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 t a))) y))

Compiler

Compiled 4106 to 1563 computations (61.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 t a))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 t a)))
✓	8.2b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 t a))) y)

series60.0ms (1.2%)

Counts

3 → 108

Calls

27 calls:

4.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 t a))) y)	z	inf
4.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 t a))) y)	t	-inf
3.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 t a))) y)	t	inf
3.0ms	(/.f64 1 (-.f64 t a))	t	0
3.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 t a))) y)	t	0

rewrite54.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`prod-diff_binary64`
124×	`add-sqr-sqrt_binary64`
117×	`add-cbrt-cube_binary64`
117×	`log1p-expm1-u_binary64`
117×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	241	31
2	3377	31

Stop Event

1×	node limit

Counts

3 → 89

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

695×	`times-frac_binary64`
580×	`cancel-sign-sub-inv_binary64`
410×	`sub-neg_binary64`
259×	`fma-neg_binary64`
165×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	3333
1	654	3261
2	2253	2791

Stop Event

1×	node limit

Counts

197 → 183

prune152.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	183	7	190

Error

0.1b

Counts

190 → 7

Alt Table

Status	Error	Program
	29.6b	(+.f64 x (pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 t a)) y)) 2))
	31.1b	(+.f64 x (-.f64 (+.f64 (.f64 (+.f64 1 (/.f64 a t)) (.f64 (/.f64 y t) z)) (.f64 (/.f64 a (/.f64 (.f64 t t) a)) (-.f64 (.f64 (/.f64 y t) z) y))) (.f64 (/.f64 a t) y)))
	30.1b	(+.f64 x (/.f64 (*.f64 y (neg.f64 (-.f64 a z))) t))
	26.2b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	23.5b	(+.f64 x (-.f64 y (/.f64 (*.f64 y z) a)))
▶	17.2b	(+.f64 x (*.f64 (/.f64 y (-.f64 t a)) z))
✓	8.7b	(+.f64 x (fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 t a))) y))

Compiler

Compiled 4567 to 1866 computations (59.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 t a))
✓	5.9b	(*.f64 (/.f64 y (-.f64 t a)) z)

series39.0ms (0.8%)

Counts

2 → 72

Calls

21 calls:

3.0ms	(/.f64 y (-.f64 t a))	y	-inf
3.0ms	(*.f64 (/.f64 y (-.f64 t a)) z)	t	-inf
2.0ms	(*.f64 (/.f64 y (-.f64 t a)) z)	y	-inf
2.0ms	(*.f64 (/.f64 y (-.f64 t a)) z)	z	-inf
2.0ms	(*.f64 (/.f64 y (-.f64 t a)) z)	y	0

rewrite50.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

487×	`log-prod_binary64`
377×	`prod-diff_binary64`
182×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	176	17
2	2529	17

Stop Event

1×	node limit

Counts

2 → 66

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-neg_binary64`
576×	`times-frac_binary64`
472×	`associate-/l*_binary64`
462×	`fma-def_binary64`
255×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	1632
1	309	1632
2	943	1380
3	4829	1380

Stop Event

1×	node limit

Counts

138 → 107

prune105.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	106	8	114

Error

0.0b

Counts

114 → 8

Alt Table

Status	Error	Program
	20.2b	(+.f64 x (/.f64 1 (/.f64 (-.f64 t a) (*.f64 y z))))
▶	17.3b	(+.f64 x (/.f64 y (/.f64 (-.f64 t a) z)))
	31.1b	(+.f64 x (-.f64 (+.f64 (.f64 (+.f64 1 (/.f64 a t)) (.f64 (/.f64 y t) z)) (.f64 (/.f64 a (/.f64 (.f64 t t) a)) (-.f64 (.f64 (/.f64 y t) z) y))) (.f64 (/.f64 a t) y)))
	30.1b	(+.f64 x (/.f64 (*.f64 y (neg.f64 (-.f64 a z))) t))
	26.2b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	17.2b	(+.f64 x (*.f64 (/.f64 y (-.f64 t a)) z))
	25.0b	(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 t a)) 3)) z))
✓	8.7b	(+.f64 x (fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 t a))) y))

Compiler

Compiled 2154 to 922 computations (57.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t a) z)
✓	5.8b	(/.f64 y (/.f64 (-.f64 t a) z))

series35.0ms (0.7%)

Counts

2 → 76

Calls

21 calls:

3.0ms	(/.f64 y (/.f64 (-.f64 t a) z))	z	-inf
2.0ms	(/.f64 y (/.f64 (-.f64 t a) z))	z	inf
2.0ms	(/.f64 y (/.f64 (-.f64 t a) z))	y	-inf
2.0ms	(/.f64 y (/.f64 (-.f64 t a) z))	z	0
2.0ms	(/.f64 y (/.f64 (-.f64 t a) z))	y	0

rewrite92.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

568×	`prod-diff_binary64`
212×	`egg-rr`
190×	`fma-def_binary64`
180×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	185	17
2	2910	17

Stop Event

1×	node limit

Counts

2 → 212

simplify49.0ms (1%)

Algorithm

1×	egg-herbie

Rules

657×	`cancel-sign-sub-inv_binary64`
555×	`fma-neg_binary64`
449×	`times-frac_binary64`
371×	`associate-/l*_binary64`
266×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	1276
1	208	1210
2	746	1066
3	3546	1066

Stop Event

1×	node limit

Counts

288 → 239

prune255.0ms (5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	239	8	247

Error

0.0b

Counts

247 → 8

Alt Table

Status	Error	Program
	17.3b	(+.f64 x (/.f64 y (*.f64 (-.f64 t a) (/.f64 1 z))))
	26.2b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	20.2b	(+.f64 x (/.f64 1 (/.f64 (-.f64 t a) (*.f64 y z))))
✓	17.3b	(+.f64 x (/.f64 y (/.f64 (-.f64 t a) z)))
	31.1b	(+.f64 x (-.f64 (+.f64 (.f64 (+.f64 1 (/.f64 a t)) (.f64 (/.f64 y t) z)) (.f64 (/.f64 a (/.f64 (.f64 t t) a)) (-.f64 (.f64 (/.f64 y t) z) y))) (.f64 (/.f64 a t) y)))
	30.1b	(+.f64 x (/.f64 (*.f64 y (neg.f64 (-.f64 a z))) t))
✓	17.2b	(+.f64 x (*.f64 (/.f64 y (-.f64 t a)) z))
✓	8.7b	(+.f64 x (fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 t a))) y))

Compiler

Compiled 7949 to 2947 computations (62.9% saved)

regimes667.0ms (13.2%)

Accuracy

Total 5.3b remaining (98.8%)

Threshold costs 0b (0%)

Counts

62 → 3

Compiler

Compiled 6312 to 3978 computations (37% saved)

bsearch2.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

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

Steps

Iters	Point		Range
1.865968207475801e-234	∈ [	1.865968207475801e-234	,	2.684397514278662e-227	]
-1.0228914215450133e-231	∈ [	-1.0228914215450133e-231	,	-3.120765088145568e-259	]

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

63×	`distribute-rgt-neg-in_binary64`
60×	`cancel-sign-sub-inv_binary64`
45×	`distribute-lft-neg-in_binary64`
40×	`neg-sub0_binary64`
40×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	102
1	59	102
2	86	100
3	117	100
4	151	100
5	194	100
6	252	100
7	309	100
8	365	100
9	420	100
10	457	100
11	490	100
12	507	100
13	515	100
14	521	100

Stop Event

1×

saturated

end113.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 294 to 153 computations (48% saved)

Iter	Nodes	Cost
0	34	102
1	59	102
2	86	100
3	117	100
4	151	100
5	194	100
6	252	100
7	309	100
8	365	100
9	420	100
10	457	100
11	490	100
12	507	100
13	515	100
14	521	100

Iter	Nodes	Cost
0	34	102
1	59	102
2	86	100
3	117	100
4	151	100
5	194	100
6	252	100
7	309	100
8	365	100
9	420	100
10	457	100
11	490	100
12	507	100
13	515	100
14	521	100

Details

analyze1.3s (26.4%)

sample1.4s (28.2%)

preprocess48.0ms (1%)

simplify25.0ms (0.5%)

prune7.0ms (0.1%)

localize8.0ms (0.2%)

series58.0ms (1.1%)

rewrite64.0ms (1.3%)

simplify64.0ms (1.3%)

prune177.0ms (3.5%)

localize9.0ms (0.2%)

series60.0ms (1.2%)

rewrite54.0ms (1.1%)

simplify65.0ms (1.3%)

prune152.0ms (3%)

localize8.0ms (0.1%)

series39.0ms (0.8%)

rewrite50.0ms (1%)

simplify56.0ms (1.1%)

prune105.0ms (2.1%)

localize7.0ms (0.1%)

series35.0ms (0.7%)

rewrite92.0ms (1.8%)

simplify49.0ms (1%)

prune255.0ms (5%)

regimes667.0ms (13.2%)

bsearch2.0ms (0%)

simplify16.0ms (0.3%)

end113.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	34	102
1	59	102
2	86	100
3	117	100
4	151	100
5	194	100
6	252	100
7	309	100
8	365	100
9	420	100
10	457	100
11	490	100
12	507	100
13	515	100
14	521	100