Details

analyze954.0ms (16.3%)

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
0%	99.8%	0.2%	7
7.8%	92%	0.2%	8
15.6%	84.2%	0.2%	9
23.4%	76.4%	0.2%	10
25%	74.9%	0.2%	11
37.9%	59.6%	2.5%	12
41.4%	55.7%	2.9%	13
46.3%	50.6%	3.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (20.6%)

Results

967.0ms	8256×	body	128	valid
220.0ms	1864×	body	128	invalid

Compiler

Compiled 32 to 22 computations (31.3% saved)

preprocess39.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

1016×	`fma-def_binary64`
487×	`div-sub_binary64`
327×	`sub-neg_binary64`
288×	`times-frac_binary64`
246×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	112
1	66	112
2	146	112
3	373	112
4	742	112
5	1408	112
6	3058	112
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary64`
547×	`fma-neg_binary64`
454×	`div-sub_binary64`
251×	`distribute-rgt-in_binary64`
229×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	33	16
3	68	16
4	130	16
5	233	16
6	479	16
7	1128	16
8	2572	16

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

4.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.1b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 56 to 35 computations (37.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 1 z))
✓	0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
✓	3.9b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series55.0ms (0.9%)

Counts

3 → 78

Calls

27 calls:

5.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))	y	-inf
4.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))	x	-inf
4.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))	x	0
3.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))	x	inf
3.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))	y	0

rewrite99.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

408×	`fma-def_binary64`
234×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
209×	`fma-neg_binary64`
187×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	248	36
2	3758	36

Stop Event

1×	node limit

Counts

3 → 187

simplify47.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

396×	`cancel-sign-sub-inv_binary64`
301×	`fma-neg_binary64`
292×	`fma-def_binary64`
233×	`times-frac_binary64`
228×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1328
1	235	1302
2	699	1241
3	2286	1195

Stop Event

1×	node limit

Counts

265 → 237

prune177.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	232	5	237
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	232	6	238

Error

0.0b

Counts

238 → 6

Alt Table

Status	Error	Program
	6.8b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	4.1b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
▶	5.1b	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))) 3)
	22.4b	(/.f64 (.f64 (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t)) x) (.f64 z (-.f64 1 z)))
	22.9b	(.f64 x (/.f64 1 (/.f64 (.f64 z (-.f64 1 z)) (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t)))))
	19.9b	(*.f64 (/.f64 x z) (+.f64 y t))

Compiler

Compiled 5110 to 2724 computations (46.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))) 3)
	3.9b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
✓	6.1b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))

series771.0ms (13.2%)

Counts

2 → 16

Calls

24 calls:

362.0ms	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))) 3)	t	0
117.0ms	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))) 3)	y	0
47.0ms	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))) 3)	z	-inf
35.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))	t	0
34.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))	y	0

rewrite66.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

263×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
147×	`add-sqr-sqrt_binary64`
142×	`log1p-expm1-u_binary64`
142×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	309	34
2	4251	34

Stop Event

1×	node limit

Counts

2 → 67

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

844×	`associate-/l*_binary64`
646×	`fma-def_binary64`
264×	`cancel-sign-sub-inv_binary64`
255×	`unswap-sqr_binary64`
148×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	1559
1	613	1471
2	2145	1443

Stop Event

1×	node limit

Counts

83 → 94

prune255.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	280	2	282
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	282	6	288

Error

0.0b

Counts

288 → 6

Alt Table

Status	Error	Program
	22.4b	(/.f64 (.f64 (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t)) x) (.f64 z (-.f64 1 z)))
	20.5b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 x z) (+.f64 y t))) 3)
▶	6.8b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	4.1b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	26.8b	(/.f64 x (/.f64 z y))
	19.9b	(*.f64 (/.f64 x z) (+.f64 y t))

Compiler

Compiled 7950 to 4894 computations (38.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	2.4b	(/.f64 (*.f64 t x) (-.f64 1 z))
✓	7.0b	(/.f64 (*.f64 y x) z)

series110.0ms (1.9%)

Counts

3 → 42

Calls

30 calls:

25.0ms	(/.f64 (*.f64 y x) z)	x	inf
23.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))	y	0
4.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))	x	inf
4.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))	t	inf
3.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))	y	inf

rewrite86.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`expm1-udef_binary64`
255×	`log1p-udef_binary64`
145×	`egg-rr`
141×	`add-sqr-sqrt_binary64`
133×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	272	36
2	4341	36

Stop Event

1×	node limit

Counts

3 → 145

simplify43.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

635×	`cancel-sign-sub-inv_binary64`
593×	`fma-neg_binary64`
462×	`times-frac_binary64`
364×	`fma-def_binary64`
153×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	857
1	198	845
2	633	717
3	2372	710

Stop Event

1×	node limit

Counts

187 → 181

prune140.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	182	5	187

Error

Counts

187 → 5

Alt Table

Status	Error	Program
	26.8b	(/.f64 x (/.f64 z y))
	22.4b	(/.f64 (.f64 (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t)) x) (.f64 z (-.f64 1 z)))
✓	4.1b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
▶	8.1b	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))
	19.9b	(*.f64 (/.f64 x z) (+.f64 y t))

Compiler

Compiled 3783 to 1657 computations (56.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))
✓	2.4b	(/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z))
✓	6.9b	(/.f64 y (/.f64 z x))

series69.0ms (1.2%)

Counts

3 → 120

Calls

30 calls:

5.0ms	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))	x	inf
4.0ms	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))	t	-inf
4.0ms	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))	y	-inf
3.0ms	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))	x	-inf
3.0ms	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))	x	0

rewrite56.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

167×	`egg-rr`
155×	`add-sqr-sqrt_binary64`
146×	`add-cbrt-cube_binary64`
146×	`log1p-expm1-u_binary64`
146×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	300	34

Stop Event

1×	node limit

Counts

3 → 167

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-neg_binary64`
584×	`cancel-sign-sub-inv_binary64`
396×	`fma-def_binary64`
269×	`distribute-rgt-out_binary64`
186×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1767
1	198	1755
2	638	1537
3	2332	1498

Stop Event

1×	node limit

Counts

287 → 204

prune142.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	204	5	209

Error

Counts

209 → 5

Alt Table

Status	Error	Program
	26.8b	(/.f64 x (/.f64 z y))
	22.4b	(/.f64 (.f64 (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t)) x) (.f64 z (-.f64 1 z)))
✓	4.1b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
✓	8.1b	(+.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t (neg.f64 x)) (-.f64 1 z)))
	19.9b	(*.f64 (/.f64 x z) (+.f64 y t))

Compiler

Compiled 4220 to 1781 computations (57.8% saved)

regimes1.3s (21.4%)

Accuracy

Total 1.2b remaining (97.7%)

Threshold costs 0b (0%)

Counts

108 → 3

Compiler

Compiled 11428 to 7807 computations (31.7% saved)

bsearch3.0ms (0.1%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
0.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

Steps

Iters	Point		Range
8.332972841835484e+202	∈ [	8.332972841835484e+202	,	8.93142159330437e+202	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-4.8292843950205685e+300	]

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	90
1	43	90
2	56	90
3	65	90
4	70	90
5	71	90

Stop Event

1×

saturated

end83.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 204 to 125 computations (38.7% saved)

Details

analyze954.0ms (16.3%)

sample1.2s (20.6%)

preprocess39.0ms (0.7%)

simplify26.0ms (0.4%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series55.0ms (0.9%)

rewrite99.0ms (1.7%)

simplify47.0ms (0.8%)

prune177.0ms (3%)

localize10.0ms (0.2%)

series771.0ms (13.2%)

rewrite66.0ms (1.1%)

simplify65.0ms (1.1%)

prune255.0ms (4.4%)

localize9.0ms (0.2%)

series110.0ms (1.9%)

rewrite86.0ms (1.5%)

simplify43.0ms (0.7%)

prune140.0ms (2.4%)

localize10.0ms (0.2%)

series69.0ms (1.2%)

rewrite56.0ms (1%)

simplify58.0ms (1%)

prune142.0ms (2.4%)

regimes1.3s (21.4%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end83.0ms (1.4%)

Profiling