Details

analyze115.0ms (3.8%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
37.5%	40.6%	22%	7
43.7%	32.8%	23.5%	8
43.7%	21.1%	35.2%	9
46.8%	16.8%	36.4%	10
46.8%	10.7%	42.4%	11
48.4%	8.5%	43.1%	12
48.4%	5.4%	46.2%	13
49.2%	4.3%	46.6%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample850.0ms (27.7%)

Symmetry

(sort x y)

Results

752.0ms	8256×	body	128	valid
50.0ms	535×	body	128	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify27.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

274×	`fma-neg_binary64`
192×	`rules-42_binary64`
190×	`rules-41_binary64`
190×	`rules-43_binary64`
188×	`rules-40_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	36	9
2	106	9
3	294	7
4	656	7
5	6	7

prune2.0ms (0.1%)

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

31.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.5b	(.f64 x (exp.f64 (.f64 y y)))

Compiler

Compiled 29 to 19 computations (34.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (exp.f64 (.f64 y y)))

series12.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(*.f64 x (exp.f64 (*.f64 y y)))

rewrite58.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

528×	`log1p-expm1-u_binary64`
528×	`expm1-log1p-u_binary64`
453×	`fma-neg_binary64`
298×	`fma-def_binary64`
140×	`prod-diff_binary64`

Counts

1 → 133

Calls

1 calls:

55.0ms

(*.f64 x (exp.f64 (*.f64 y y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	135	9
2	1609	9
3	4972	9
0	0	0
1	0	0

simplify92.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1344×	`rules-43_binary64`
762×	`rules-21_binary64`
760×	`rules-40_binary64`
760×	`rules-42_binary64`
754×	`rules-41_binary64`

Counts

157 → 142

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	243
1	142	243
2	529	234
3	2841	234
4	4629	66
5	4566	66
6	5145	66

prune102.0ms (3.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	130	12	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	12	143

Error

30.5b

Counts

143 → 12

Alt Table

Status	Error	Program
	60.8b	(pow.f64 (sqrt.f64 (.f64 x (exp.f64 (.f64 y y)))) 2)
	31.4b	(+.f64 (.f64 1/6 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x)))
	62.7b	(pow.f64 (pow.f64 (.f64 x (exp.f64 (.f64 y y))) 3) 1/3)
	31.4b	(+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x))
	61.1b	(exp.f64 (fma.f64 y y (log.f64 x)))
	31.5b	x
	31.5b	(fma.f64 (sqrt.f64 (exp.f64 (.f64 y y))) (.f64 (sqrt.f64 (exp.f64 (*.f64 y y))) x) 0)
	52.6b	(cbrt.f64 (pow.f64 (.f64 x (exp.f64 (.f64 y y))) 3))
	61.4b	(log.f64 (pow.f64 (exp.f64 x) (exp.f64 (*.f64 y y))))
	59.6b	(fabs.f64 (.f64 x (exp.f64 (.f64 y y))))
	32.2b	(pow.f64 (cbrt.f64 (.f64 x (exp.f64 (.f64 y y)))) 3)
▶	31.3b	(fma.f64 (*.f64 y y) x x)

Compiler

Compiled 2687 to 978 computations (63.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.7b	(fma.f64 (*.f64 y y) x x)

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(fma.f64 (*.f64 y y) x x)

rewrite83.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

902×	`log1p-udef_binary64`
467×	`log1p-expm1-u_binary64`
467×	`expm1-log1p-u_binary64`
368×	`fma-neg_binary64`
237×	`fma-def_binary64`

Counts

1 → 39

Calls

1 calls:

82.0ms

(fma.f64 (*.f64 y y) x x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	116	8
2	1392	8
3	4973	8
4	6535	8
0	0	0
1	0	0

simplify23.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

289×	`fma-neg_binary64`
199×	`fma-def_binary64`
163×	`rules-11_binary64`
137×	`rules-40_binary64`
137×	`rules-41_binary64`

Counts

63 → 43

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	58	24
2	156	24
3	524	24
4	174	24

prune39.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	37	6	43
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	42	13	55

Error

30.4b

Counts

55 → 13

Alt Table

Status	Error	Program
	47.2b	(expm1.f64 (log1p.f64 (fma.f64 (*.f64 y y) x x)))
	31.4b	(+.f64 (.f64 1/6 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x)))
	59.2b	(fabs.f64 (fma.f64 (*.f64 y y) x x))
	62.7b	(pow.f64 (pow.f64 (.f64 x (exp.f64 (.f64 y y))) 3) 1/3)
▶	31.4b	(+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x))
	32.0b	(pow.f64 (cbrt.f64 (fma.f64 (*.f64 y y) x x)) 3)
	61.1b	(exp.f64 (fma.f64 y y (log.f64 x)))
	31.5b	x
	31.5b	(fma.f64 (sqrt.f64 (exp.f64 (.f64 y y))) (.f64 (sqrt.f64 (exp.f64 (*.f64 y y))) x) 0)
	61.3b	(*.f64 (pow.f64 y 2) x)
	61.4b	(log.f64 (pow.f64 (exp.f64 x) (exp.f64 (*.f64 y y))))
	52.4b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y y) x x) 3))
	60.5b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 y y) x x)) 2)

Compiler

Compiled 788 to 351 computations (55.5% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x))
✓	3.2b	(*.f64 (pow.f64 y 4) x)
✓	8.6b	(*.f64 (pow.f64 y 2) x)

series49.0ms (1.6%)

Counts

3 → 18

Calls

3 calls:

23.0ms	(+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x))
14.0ms	(*.f64 (pow.f64 y 2) x)
12.0ms	(*.f64 (pow.f64 y 4) x)

rewrite85.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
201×	`log-pow_binary64`
146×	`egg-rr`
135×	`log1p-expm1-u_binary64`

Counts

3 → 146

Calls

3 calls:

80.0ms	(+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x))
80.0ms	(*.f64 (pow.f64 y 4) x)
80.0ms	(*.f64 (pow.f64 y 2) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	326	32
2	3962	32
3	4843	32
0	0	0
1	0	0

simplify66.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1401×	`rules-42_binary64`
1099×	`rules-43_binary64`
462×	`rules-40_binary64`
462×	`rules-41_binary64`
454×	`rules-15-rev_binary64`

Counts

164 → 151

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	18
1	117	18
2	409	18
3	1764	18
4	4238	18
5	20	18

prune152.0ms (5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	145	6	151
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	149	15	164

Error

30.4b

Counts

164 → 15

Alt Table

Status	Error	Program
	60.9b	(exp.f64 (log.f64 (fma.f64 (.f64 y y) x (fma.f64 (.f64 x (pow.f64 y 4)) 1/2 x))))
	31.5b	(fma.f64 (sqrt.f64 (exp.f64 (.f64 y y))) (.f64 (sqrt.f64 (exp.f64 (*.f64 y y))) x) 0)
	47.2b	(expm1.f64 (log1p.f64 (fma.f64 (*.f64 y y) x x)))
▶	31.4b	(+.f64 (.f64 1/6 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x)))
	59.2b	(fabs.f64 (fma.f64 (*.f64 y y) x x))
	35.6b	(+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (pow.f64 (pow.f64 (*.f64 x (pow.f64 y 4)) 3) 1/3)) x))
	61.6b	(.f64 1/2 (.f64 (pow.f64 y 4) x))
	60.5b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 y y) x x)) 2)
	62.6b	(pow.f64 (pow.f64 (fma.f64 (.f64 y y) x (fma.f64 (.f64 x (pow.f64 y 4)) 1/2 x)) 3) 1/3)
	32.0b	(pow.f64 (cbrt.f64 (fma.f64 (*.f64 y y) x x)) 3)
	31.5b	x
	47.3b	(expm1.f64 (log1p.f64 (fma.f64 (.f64 y y) x (fma.f64 (.f64 x (pow.f64 y 4)) 1/2 x))))
	61.4b	(log.f64 (pow.f64 (exp.f64 x) (exp.f64 (*.f64 y y))))
	31.4b	(+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (fabs.f64 (*.f64 x (pow.f64 y 4)))) x))
	52.4b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y y) x x) 3))

Compiler

Compiled 3599 to 2081 computations (42.2% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 1/6 (.f64 (pow.f64 y 6) x))
✓	2.6b	(*.f64 (pow.f64 y 6) x)
	3.2b	(*.f64 (pow.f64 y 4) x)
	8.6b	(*.f64 (pow.f64 y 2) x)

series33.0ms (1.1%)

Counts

2 → 0

Calls

2 calls:

17.0ms	(.f64 1/6 (.f64 (pow.f64 y 6) x))
15.0ms	(*.f64 (pow.f64 y 6) x)

rewrite63.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

721×	`log1p-expm1-u_binary64`
721×	`expm1-log1p-u_binary64`
158×	`prod-diff_binary64`
91×	`egg-rr`
81×	`add-sqr-sqrt_binary64`

Counts

2 → 91

Calls

2 calls:

61.0ms	(.f64 1/6 (.f64 (pow.f64 y 6) x))
61.0ms	(*.f64 (pow.f64 y 6) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	190	17
2	2178	17
3	4955	17
0	0	0
1	0	0

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune213.0ms (6.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	150	5	155
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	152	18	170

Error

30.4b

Counts

170 → 18

Alt Table

Status	Error	Program
	60.9b	(exp.f64 (log.f64 (fma.f64 (.f64 y y) x (fma.f64 (.f64 x (pow.f64 y 4)) 1/2 x))))
	31.5b	(fma.f64 (sqrt.f64 (exp.f64 (.f64 y y))) (.f64 (sqrt.f64 (exp.f64 (*.f64 y y))) x) 0)
	31.4b	(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 (pow.f64 y 6) x) 1/6)) 2) (cbrt.f64 (.f64 (.f64 (pow.f64 y 6) x) 1/6)) 0) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x)))
	47.3b	(expm1.f64 (log1p.f64 (fma.f64 (.f64 y y) x (fma.f64 (.f64 x (pow.f64 y 4)) 1/2 x))))
	47.2b	(expm1.f64 (log1p.f64 (fma.f64 (*.f64 y y) x x)))
	31.3b	(+.f64 (.f64 1/6 (pow.f64 (.f64 (.f64 y y) (cbrt.f64 x)) 3)) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 4) x)) x)))
	59.2b	(fabs.f64 (fma.f64 (*.f64 y y) x x))
	61.9b	(+.f64 (.f64 1/6 (/.f64 (pow.f64 (.f64 (pow.f64 y 6) x) 3) (+.f64 (pow.f64 (.f64 (pow.f64 y 6) x) 2) (+.f64 0 (.f64 (.f64 (pow.f64 y 6) x) 0))))) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 4) x)) x)))
	35.6b	(+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (pow.f64 (pow.f64 (*.f64 x (pow.f64 y 4)) 3) 1/3)) x))
	61.6b	(.f64 1/2 (.f64 (pow.f64 y 4) x))
	60.5b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 y y) x x)) 2)
	62.6b	(pow.f64 (pow.f64 (fma.f64 (.f64 y y) x (fma.f64 (.f64 x (pow.f64 y 4)) 1/2 x)) 3) 1/3)
	32.0b	(pow.f64 (cbrt.f64 (fma.f64 (*.f64 y y) x x)) 3)
	31.5b	x
	34.1b	(+.f64 (pow.f64 (pow.f64 (.f64 (.f64 (pow.f64 y 6) x) 1/6) 3) 1/3) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x)))
	61.4b	(log.f64 (pow.f64 (exp.f64 x) (exp.f64 (*.f64 y y))))
	31.4b	(+.f64 (.f64 1/6 (fabs.f64 (.f64 (pow.f64 y 6) x))) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x)))
	52.4b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y y) x x) 3))

Compiler

Compiled 5005 to 3458 computations (30.9% saved)

regimes683.0ms (22.3%)

Accuracy

Total 0.3b remaining (92.2%)

Threshold costs 0.3b (92.2%)

Counts

137 → 1

Compiler

Compiled 14282 to 9776 computations (31.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	66
1	26	66

end274.0ms (8.9%)

Remove: (sort x y)
Compiler: Compiled 514 to 347 computations (32.5% saved)

Details

analyze115.0ms (3.8%)

sample850.0ms (27.7%)

simplify27.0ms (0.9%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series12.0ms (0.4%)

rewrite58.0ms (1.9%)

simplify92.0ms (3%)

prune102.0ms (3.3%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite83.0ms (2.7%)

simplify23.0ms (0.7%)

prune39.0ms (1.3%)

localize8.0ms (0.3%)

series49.0ms (1.6%)

rewrite85.0ms (2.8%)

simplify66.0ms (2.1%)

prune152.0ms (5%)

localize13.0ms (0.4%)

series33.0ms (1.1%)

rewrite63.0ms (2.1%)

simplify8.0ms (0.3%)

prune213.0ms (6.9%)

regimes683.0ms (22.3%)

simplify2.0ms (0.1%)

end274.0ms (8.9%)

Profiling