Details

analyze1.5s (25.6%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
3.1%	96.6%	0.2%	11
4.7%	95.1%	0.2%	12
7%	92.7%	0.2%	13
14%	85.7%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (20%)

Results

1.1s	8253×	body	128	valid
99.0ms	798×	body	128	invalid
0.0ms	1×	body	2048	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess41.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

758×	`div-sub_binary64`
354×	`fma-def_binary64`
338×	`fma-neg_binary64`
287×	`distribute-rgt-in_binary64`
252×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	176
1	109	176
2	277	154
3	623	154
4	1429	154
5	3919	154
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify23.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

726×	`fma-def_binary64`
585×	`fma-neg_binary64`
512×	`div-sub_binary64`
345×	`times-frac_binary64`
287×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	84	14
4	185	14
5	371	14
6	871	14
7	2142	14

Stop Event

1×	node limit

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	8.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series51.0ms (0.9%)

Counts

2 → 84

Calls

24 calls:

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

rewrite54.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
218×	`log1p-udef_binary64`
119×	`add-sqr-sqrt_binary64`
113×	`log1p-expm1-u_binary64`
113×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	223	21
2	3231	21

Stop Event

1×	node limit

Counts

2 → 58

simplify51.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

636×	`times-frac_binary64`
600×	`fma-def_binary64`
499×	`associate-/l*_binary64`
262×	`cancel-sign-sub-inv_binary64`
247×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2438
1	374	2438
2	1413	2037

Stop Event

1×	node limit

Counts

142 → 115

prune95.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	112	5	117

Error

Counts

117 → 5

Alt Table

Status	Error	Program
	27.0b	(fma.f64 (-.f64 y z) (pow.f64 (sqrt.f64 (/.f64 t (-.f64 a z))) 2) x)
▶	1.4b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
	8.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
✓	2.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	2.8b	(fma.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2)) x)

Compiler

Compiled 2490 to 815 computations (67.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (-.f64 a z))
✓	0.0b	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
✓	0.0b	(/.f64 y (-.f64 a z))
✓	2.0b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series89.0ms (1.5%)

Counts

4 → 111

Calls

36 calls:

7.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	t	-inf
6.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	t	0
4.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	z	inf
4.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	t	inf
4.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	y	-inf

rewrite95.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

534×	`fma-def_binary64`
283×	`fma-neg_binary64`
254×	`egg-rr`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	234	37
2	3802	37

Stop Event

1×	node limit

Counts

4 → 254

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
757×	`times-frac_binary64`
495×	`cancel-sign-sub-inv_binary64`
330×	`sub-neg_binary64`
170×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	3449
1	582	3422
2	2035	3023

Stop Event

1×	node limit

Counts

365 → 361

prune307.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	361	0	361
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	361	5	366

Error

Counts

366 → 5

Alt Table

Status	Error	Program
	27.0b	(fma.f64 (-.f64 y z) (pow.f64 (sqrt.f64 (/.f64 t (-.f64 a z))) 2) x)
✓	1.4b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
	8.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
✓	2.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	2.8b	(fma.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2)) x)

Compiler

Compiled 9558 to 3090 computations (67.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2)
✓	2.4b	(fma.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2)) x)
✓	16.8b	(cbrt.f64 (/.f64 t (-.f64 a z)))

series367.0ms (6.2%)

Counts

4 → 112

Calls

42 calls:

53.0ms	(*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2))	t	-inf
48.0ms	(pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2)	a	0
41.0ms	(pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2)	a	-inf
30.0ms	(cbrt.f64 (/.f64 t (-.f64 a z)))	a	0
28.0ms	(fma.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2)) x)	t	-inf

rewrite70.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`prod-diff_binary64`
145×	`add-sqr-sqrt_binary64`
139×	`log1p-expm1-u_binary64`
139×	`expm1-log1p-u_binary64`
138×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	308	42
2	3878	42

Stop Event

1×	node limit

Counts

4 → 104

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

294×	`associate-r_binary64`
294×	`fma-neg_binary64`
262×	`sub-neg_binary64`
214×	`associate-l_binary64`
192×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	362	4246
1	1110	4229
2	4213	4211

Stop Event

1×	node limit

Counts

216 → 193

prune214.0ms (3.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	240	5	245

Error

Counts

245 → 5

Alt Table

Status	Error	Program
	27.0b	(fma.f64 (-.f64 y z) (pow.f64 (sqrt.f64 (/.f64 t (-.f64 a z))) 2) x)
✓	1.4b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
▶	8.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
✓	2.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	2.8b	(fma.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2)) x)

Compiler

Compiled 8084 to 3768 computations (53.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
✓	5.1b	(/.f64 (*.f64 y t) (-.f64 a z))
✓	9.6b	(/.f64 (*.f64 t z) (-.f64 a z))

series80.0ms (1.4%)

Counts

3 → 96

Calls

36 calls:

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

rewrite81.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

294×	`log1p-udef_binary64`
160×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`
153×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	304	45
2	4988	45

Stop Event

1×	node limit

Counts

3 → 145

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-def_binary64`
629×	`times-frac_binary64`
483×	`associate-/l*_binary64`
374×	`cancel-sign-sub-inv_binary64`
164×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	2924
1	451	2924
2	1784	2338

Stop Event

1×	node limit

Counts

241 → 221

prune159.0ms (2.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	221	5	226

Error

Counts

226 → 5

Alt Table

Status	Error	Program
	27.0b	(fma.f64 (-.f64 y z) (pow.f64 (sqrt.f64 (/.f64 t (-.f64 a z))) 2) x)
✓	1.4b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
✓	8.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
✓	2.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	2.8b	(fma.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (pow.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) 2)) x)

Compiler

Compiled 6198 to 1470 computations (76.3% saved)

regimes1.1s (18.1%)

Accuracy

Total 0.8b remaining (98.1%)

Threshold costs 0.8b (98.1%)

Counts

118 → 3

Compiler

Compiled 14318 to 9230 computations (35.5% saved)

bsearch3.0ms (0.1%)

Algorithm

2×	left-value

Calls

2 calls:

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

Steps

Iters	Point		Range
-1.794658762741621e-119	∈ [	-1.794658762741621e-119	,	-2.676622720842355e-126	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-5.5265165988201535e+305	]

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	96
1	46	96
2	55	96
3	59	96
4	61	96

Stop Event

1×

saturated

end93.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 240 to 105 computations (56.3% saved)

Details

analyze1.5s (25.6%)

sample1.2s (20%)

preprocess41.0ms (0.7%)

simplify23.0ms (0.4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series51.0ms (0.9%)

rewrite54.0ms (0.9%)

simplify51.0ms (0.9%)

prune95.0ms (1.6%)

localize9.0ms (0.1%)

series89.0ms (1.5%)

rewrite95.0ms (1.6%)

simplify74.0ms (1.3%)

prune307.0ms (5.2%)

localize12.0ms (0.2%)

series367.0ms (6.2%)

rewrite70.0ms (1.2%)

simplify91.0ms (1.5%)

prune214.0ms (3.6%)

localize10.0ms (0.2%)

series80.0ms (1.4%)

rewrite81.0ms (1.4%)

simplify57.0ms (1%)

prune159.0ms (2.7%)

regimes1.1s (18.1%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end93.0ms (1.6%)

Profiling