Details

analyze193.0ms (5.5%)

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
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
46.8%	53.1%	0.1%	7
60.9%	39%	0.1%	8
67.9%	31.2%	0.9%	9
74.5%	22.2%	3.2%	10
77.9%	17.2%	5%	11
81.1%	11.8%	7.1%	12
82.7%	9%	8.3%	13
84.3%	6.1%	9.7%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.2s (35.6%)

Results

1.1s	8256×	body	128	valid
25.0ms	276×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify83.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1151×	`distribute-rgt-in_binary64`
1143×	`distribute-lft-in_binary64`
971×	`fma-def_binary64`
653×	`associate-/l*_binary64`
535×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	22	14
2	30	14
3	75	14
4	112	14
5	222	14
6	406	14
7	419	14
8	783	14
9	937	14
10	1259	14
11	1611	14
12	1778	14
13	2015	14
14	2939	14
15	3245	14
16	5075	14

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

9.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.6b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Compiler

Compiled 47 to 27 computations (42.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (/.f64 x y) x)
✓	8.9b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

series28.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
7.0ms	(fma.f64 x (/.f64 x y) x)

rewrite88.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

447×	`log-prod_binary64`
385×	`prod-diff_binary64`
164×	`pow1/3_binary64`
158×	`log1p-udef_binary64`
157×	`expm1-udef_binary64`

Counts

2 → 71

Calls

2 calls:

87.0ms	(fma.f64 x (/.f64 x y) x)
87.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	175	22
2	2336	22
3	4876	22
4	5326	22
0	0	0
1	0	0

simplify80.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
530×	`associate-+l-_binary64`
372×	`cancel-sign-sub-inv_binary64`
370×	`associate--r+_binary64`
317×	`sub-neg_binary64`

Counts

119 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	711
1	130	707
2	408	649
3	1548	585
4	4387	585
5	4864	585
6	4963	585

prune85.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	92	4	96

Error

0.0b

Counts

96 → 4

Alt Table

Status	Error	Program
	13.8b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
✓	9.6b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
	39.7b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
▶	10.7b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2)) (+.f64 x 1))

Compiler

Compiled 1626 to 738 computations (54.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2)
✓	8.9b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2)) (+.f64 x 1))
✓	9.6b	(cbrt.f64 (fma.f64 x (/.f64 x y) x))

series73.0ms (2.1%)

Counts

4 → 96

Calls

4 calls:

28.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2)
22.0ms	(cbrt.f64 (fma.f64 x (/.f64 x y) x))
12.0ms	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2)) (+.f64 x 1))
9.0ms	(*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2))

rewrite76.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

557×	`log-prod_binary64`
214×	`prod-diff_binary64`
196×	`log1p-udef_binary64`
195×	`expm1-udef_binary64`
173×	`log-pow_binary64`

Counts

4 → 137

Calls

4 calls:

73.0ms	(*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2))
73.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2)
73.0ms	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2)) (+.f64 x 1))
73.0ms	(cbrt.f64 (fma.f64 x (/.f64 x y) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	240	45
2	2926	45
3	5499	45
0	0	0
1	0	0

simplify78.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1022×	`times-frac_binary64`
631×	`associate-/l*_binary64`
509×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
163×	`associate-/r/_binary64`

Counts

233 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	3237
1	639	2935
2	1836	2647
3	5132	2647

prune174.0ms (5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	269	2	271
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	270	5	275

Error

0.0b

Counts

275 → 5

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (+.f64 1 (/.f64 x y)) (/.f64 x (+.f64 x 1)))
	13.8b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
✓	9.6b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
✓	10.7b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2)) (+.f64 x 1))
	31.3b	(/.f64 (fma.f64 (*.f64 x (sqrt.f64 (/.f64 x y))) (sqrt.f64 (/.f64 x y)) x) (+.f64 x 1))

Compiler

Compiled 8171 to 4066 computations (50.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 x y))
✓	0.1b	(*.f64 (+.f64 1 (/.f64 x y)) (/.f64 x (+.f64 x 1)))

series14.0ms (0.4%)

Counts

2 → 39

Calls

2 calls:

10.0ms	(*.f64 (+.f64 1 (/.f64 x y)) (/.f64 x (+.f64 x 1)))
4.0ms	(+.f64 1 (/.f64 x y))

rewrite105.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

511×	`prod-diff_binary64`
339×	`fma-def_binary64`
182×	`log1p-udef_binary64`
181×	`expm1-udef_binary64`
161×	`fma-neg_binary64`

Counts

2 → 132

Calls

2 calls:

102.0ms	(+.f64 1 (/.f64 x y))
102.0ms	(*.f64 (+.f64 1 (/.f64 x y)) (/.f64 x (+.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	203	23
2	2838	23
3	4855	23
4	5117	23
0	0	0
1	0	0

simplify78.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
530×	`associate-+l-_binary64`
372×	`cancel-sign-sub-inv_binary64`
370×	`associate--r+_binary64`
317×	`sub-neg_binary64`

Counts

171 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	585
1	130	581
2	408	523
3	1548	495
4	4387	495
5	4864	495
6	4963	495

prune138.0ms (4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	155	4	159

Error

Counts

159 → 4

Alt Table

Status	Error	Program
	13.8b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
▶	13.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x y) 2)) x) (.f64 (-.f64 1 (/.f64 x y)) (+.f64 1 x)))
✓	0.1b	(*.f64 (+.f64 1 (/.f64 x y)) (/.f64 x (+.f64 x 1)))
✓	10.7b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2)) (+.f64 x 1))

Compiler

Compiled 2824 to 1619 computations (42.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 (/.f64 x y)) (+.f64 1 x))
✓	0.2b	(pow.f64 (/.f64 x y) 2)
✓	0.8b	(*.f64 (-.f64 1 (pow.f64 (/.f64 x y) 2)) x)
✓	12.3b	(/.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x y) 2)) x) (.f64 (-.f64 1 (/.f64 x y)) (+.f64 1 x)))

series179.0ms (5.1%)

Counts

4 → 96

Calls

4 calls:

134.0ms	(*.f64 (-.f64 1 (pow.f64 (/.f64 x y) 2)) x)
26.0ms	(/.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x y) 2)) x) (.f64 (-.f64 1 (/.f64 x y)) (+.f64 1 x)))
12.0ms	(pow.f64 (/.f64 x y) 2)
6.0ms	(*.f64 (-.f64 1 (/.f64 x y)) (+.f64 1 x))

rewrite92.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

264×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
161×	`egg-rr`
151×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`

Counts

4 → 161

Calls

4 calls:

85.0ms	(*.f64 (-.f64 1 (/.f64 x y)) (+.f64 1 x))
85.0ms	(pow.f64 (/.f64 x y) 2)
85.0ms	(*.f64 (-.f64 1 (pow.f64 (/.f64 x y) 2)) x)
85.0ms	(/.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x y) 2)) x) (.f64 (-.f64 1 (/.f64 x y)) (+.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	61
1	305	49
2	4340	49
3	5051	49
0	0	0
1	0	0

simplify86.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

535×	`associate-/l*_binary64`
485×	`associate-/r*_binary64`
468×	`fma-def_binary64`
190×	`associate-r_binary64`
182×	`fma-neg_binary64`

Counts

257 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	2096
1	366	2092
2	1412	1994
3	4888	1994
4	4994	1994

prune171.0ms (4.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	206	4	210

Error

Counts

210 → 4

Alt Table

Status	Error	Program
	13.8b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
✓	13.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 x y) 2)) x) (.f64 (-.f64 1 (/.f64 x y)) (+.f64 1 x)))
✓	0.1b	(*.f64 (+.f64 1 (/.f64 x y)) (/.f64 x (+.f64 x 1)))
✓	10.7b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) 2)) (+.f64 x 1))

Compiler

Compiled 5352 to 3239 computations (39.5% saved)

regimes287.0ms (8.2%)

Accuracy

Total 0.0b remaining (68.4%)

Threshold costs 0.0b (68.4%)

Counts

84 → 1

Compiler

Compiled 4073 to 2687 computations (34% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	11	20
2	10	20

end98.0ms (2.8%)

Compiler: Compiled 106 to 66 computations (37.7% saved)

Details

analyze193.0ms (5.5%)

sample1.2s (35.6%)

simplify83.0ms (2.4%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series28.0ms (0.8%)

rewrite88.0ms (2.5%)

simplify80.0ms (2.3%)

prune85.0ms (2.4%)

localize10.0ms (0.3%)

series73.0ms (2.1%)

rewrite76.0ms (2.2%)

simplify78.0ms (2.2%)

prune174.0ms (5%)

localize8.0ms (0.2%)

series14.0ms (0.4%)

rewrite105.0ms (3%)

simplify78.0ms (2.2%)

prune138.0ms (4%)

localize10.0ms (0.3%)

series179.0ms (5.1%)

rewrite92.0ms (2.6%)

simplify86.0ms (2.5%)

prune171.0ms (4.9%)

regimes287.0ms (8.2%)

simplify2.0ms (0.1%)

end98.0ms (2.8%)

Profiling