Details

analyze17.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample1.2s (35.3%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 44 to 26 computations (40.9% saved)

preprocess43.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

968×	`fma-def_binary64`
834×	`fma-neg_binary64`
302×	`cancel-sign-sub-inv_binary64`
287×	`div-sub_binary64`
232×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
1	44	48
2	102	48
3	217	48
4	462	48
5	889	48
6	1477	48
7	2476	48
8	4351	48
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 12 computations (42.9% saved)

simplify28.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
456×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`
358×	`div-sub_binary64`
252×	`distribute-frac-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	24	24
2	56	24
3	114	24
4	240	24
5	457	24
6	723	24
7	987	24
8	1607	24
9	3745	24

Stop Event

1×	node limit

Counts

1 → 2

prune7.0ms (0.2%)

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

32.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 80 to 45 computations (43.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	4.0b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	32.1b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series37.0ms (1.1%)

Counts

3 → 72

Calls

18 calls:

10.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))	x	inf
3.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))	x	0
2.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))	y	0
2.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))	x	inf
2.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))	x	-inf

rewrite87.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

450×	`fma-def_binary64`
279×	`egg-rr`
230×	`fma-neg_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	50
1	237	46
2	3393	46

Stop Event

1×	node limit

Counts

3 → 279

simplify42.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-*l/_binary64`
439×	`associate-*r/_binary64`
378×	`fma-def_binary64`
318×	`associate-/r/_binary64`
311×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	1038
1	124	984
2	352	972
3	1389	954

Stop Event

1×	node limit

Counts

351 → 301

prune252.0ms (7.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	298	3	301
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	298	4	302

Error

0.2b

Counts

302 → 4

Alt Table

Status	Error	Program
	32.8b	(log.f64 (exp.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	32.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
▶	30.0b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
	32.9b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)

Compiler

Compiled 9347 to 5340 computations (42.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
✓	0.2b	(*.f64 (/.f64 y x) (/.f64 y x))

series52.0ms (1.6%)

Counts

2 → 48

Calls

12 calls:

10.0ms	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)	y	0
10.0ms	(*.f64 (/.f64 y x) (/.f64 y x))	y	inf
6.0ms	(*.f64 (/.f64 y x) (/.f64 y x))	y	-inf
6.0ms	(*.f64 (/.f64 y x) (/.f64 y x))	y	0
5.0ms	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)	y	-inf

rewrite48.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

739×	`log1p-expm1-u_binary64`
739×	`expm1-log1p-u_binary64`
136×	`log1p-udef_binary64`
79×	`add-sqr-sqrt_binary64`
74×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	164	18
2	2054	18

Stop Event

1×	node limit

Counts

2 → 59

simplify31.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

740×	`associate-/r*_binary64`
623×	`associate-*l/_binary64`
535×	`associate-/l/_binary64`
377×	`associate-/r/_binary64`
156×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	570
1	32	570
2	74	534
3	242	534
4	1326	534

Stop Event

1×	node limit

Counts

107 → 65

prune43.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	65	4	69

Error

0.2b

Counts

69 → 4

Alt Table

Status	Error	Program
▶	32.8b	(log.f64 (exp.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	32.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
✓	30.0b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
	32.9b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)

Compiler

Compiled 874 to 545 computations (37.6% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
✓	0.0b	(log.f64 (exp.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	3.0b	(fma.f64 y (.f64 y -4) (.f64 x x))
✓	32.1b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series61.0ms (1.8%)

Counts

4 → 96

Calls

24 calls:

6.0ms	(exp.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))	y	0
6.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))	x	-inf
5.0ms	(exp.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))	x	0
4.0ms	(exp.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))	y	inf
3.0ms	(exp.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))	y	-inf

rewrite74.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

930×	`expm1-log1p-u_binary64`
565×	`prod-diff_binary64`
126×	`add-sqr-sqrt_binary64`
125×	`egg-rr`
120×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	85
1	268	69
2	3322	69

Stop Event

1×	node limit

Counts

4 → 125

simplify90.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

536×	`fma-neg_binary64`
376×	`times-frac_binary64`
362×	`distribute-rgt-neg-in_binary64`
280×	`distribute-neg-frac_binary64`
242×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	2085
1	225	2001
2	731	1947
3	3589	1923

Stop Event

1×	node limit

Counts

221 → 126

prune98.0ms (2.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	125	5	130

Error

0.2b

Counts

130 → 5

Alt Table

Status	Error	Program
✓	32.8b	(log.f64 (exp.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	32.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
✓	30.0b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
	32.9b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
▶	31.8b	(log.f64 (fma.f64 1/2 (*.f64 (/.f64 (exp.f64 -1) (/.f64 y (/.f64 x y))) x) (exp.f64 -1)))

Compiler

Compiled 2867 to 2092 computations (27% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 y (/.f64 x y))
✓	0.2b	(/.f64 (exp.f64 -1) (/.f64 y (/.f64 x y)))
✓	3.7b	(*.f64 (/.f64 (exp.f64 -1) (/.f64 y (/.f64 x y))) x)
✓	18.7b	(log.f64 (fma.f64 1/2 (*.f64 (/.f64 (exp.f64 -1) (/.f64 y (/.f64 x y))) x) (exp.f64 -1)))

series110.0ms (3.3%)

Counts

4 → 96

Calls

24 calls:

14.0ms	(/.f64 (exp.f64 -1) (/.f64 y (/.f64 x y)))	x	-inf
9.0ms	(*.f64 (/.f64 (exp.f64 -1) (/.f64 y (/.f64 x y))) x)	x	-inf
9.0ms	(log.f64 (fma.f64 1/2 (*.f64 (/.f64 (exp.f64 -1) (/.f64 y (/.f64 x y))) x) (exp.f64 -1)))	y	inf
9.0ms	(*.f64 (/.f64 (exp.f64 -1) (/.f64 y (/.f64 x y))) x)	x	0
8.0ms	(log.f64 (fma.f64 1/2 (*.f64 (/.f64 (exp.f64 -1) (/.f64 y (/.f64 x y))) x) (exp.f64 -1)))	x	-inf

rewrite68.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
193×	`log-div_binary64`
190×	`log-pow_binary64`
138×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	57
1	250	57
2	3478	57

Stop Event

1×	node limit

Counts

4 → 138

simplify165.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

434×	`fma-neg_binary64`
345×	`associate-/r/_binary64`
287×	`sub-neg_binary64`
202×	`associate-/l/_binary64`
198×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	1584
1	231	1578
2	732	1538
3	2859	1502

Stop Event

1×	node limit

Counts

234 → 169

prune115.0ms (3.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	169	5	174

Error

0.2b

Counts

174 → 5

Alt Table

Status	Error	Program
✓	32.8b	(log.f64 (exp.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	32.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
✓	30.0b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
	32.9b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
✓	31.8b	(log.f64 (fma.f64 1/2 (*.f64 (/.f64 (exp.f64 -1) (/.f64 y (/.f64 x y))) x) (exp.f64 -1)))

Compiler

Compiled 3590 to 2340 computations (34.8% saved)

regimes367.0ms (11%)

Accuracy

Total 13.8b remaining (98.9%)

Threshold costs 0b (0%)

Counts

28 → 9

Compiler

Compiled 2437 to 1600 computations (34.3% saved)

bsearch161.0ms (4.8%)

Algorithm

8×	binary-search

Calls

8 calls:

30.0ms	y
21.0ms	y
21.0ms	y
20.0ms	y
19.0ms	y

Steps

Iters	Point		Range
2.4640601155356646e+62	∈ [	2.122333170605815e+62	,	1.1474753309664864e+63	]
24356890242677384.0	∈ [	4159622120860769.5	,	234066370442816670.0	]
2.965025937488653e-115	∈ [	3.4493095959545627e-119	,	3.011416380072901e-113	]
-1.9158754988432684e-140	∈ [	-6.071698387776014e-140	,	-1.80155958082887e-143	]
-5.0558409145486e-114	∈ [	-1.0647964215118965e-113	,	-1.212094595332846e-115	]
-1.1545087867875005e-10	∈ [	-3.7875015163591027e-6	,	-1.0334643143294579e-10	]
-2.8779396213703784e+94	∈ [	-2.926883090087508e+94	,	-1.6238548446833534e+92	]
-3.68300159984312e+122	∈ [	-8.67077198964372e+127	,	-3.62521110853202e+122	]

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
5×	`+-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	199
1	76	199
2	90	199
3	96	199
4	100	199
5	101	199

Stop Event

1×

saturated

end123.0ms (3.7%)

Stop Event

1×

fuel

Compiler

Compiled 351 to 214 computations (39% saved)

Details

analyze17.0ms (0.5%)

sample1.2s (35.3%)

preprocess43.0ms (1.3%)

simplify28.0ms (0.8%)

prune7.0ms (0.2%)

localize7.0ms (0.2%)

series37.0ms (1.1%)

rewrite87.0ms (2.6%)

simplify42.0ms (1.2%)

prune252.0ms (7.5%)

localize5.0ms (0.1%)

series52.0ms (1.6%)

rewrite48.0ms (1.4%)

simplify31.0ms (0.9%)

prune43.0ms (1.3%)

localize16.0ms (0.5%)

series61.0ms (1.8%)

rewrite74.0ms (2.2%)

simplify90.0ms (2.7%)

prune98.0ms (2.9%)

localize10.0ms (0.3%)

series110.0ms (3.3%)

rewrite68.0ms (2%)

simplify165.0ms (4.9%)

prune115.0ms (3.4%)

regimes367.0ms (11%)

bsearch161.0ms (4.8%)

simplify8.0ms (0.2%)

end123.0ms (3.7%)

Profiling