Details

analyze95.0ms (3.1%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
18.7%	43.7%	37.6%	6
28.1%	34.3%	37.6%	7
32.8%	23.4%	43.8%	8
36.7%	18.3%	45%	9
39.4%	12.3%	48.3%	10
41.6%	9.5%	49%	11
43%	6.3%	50.7%	12
44.1%	4.8%	51%	13
44.9%	3.2%	51.9%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample805.0ms (26.5%)

Results

772.0ms	8256×	body	128	valid
20.0ms	218×	body	128	invalid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess29.0ms (1%)

Algorithm

2×	egg-herbie

Rules

262×	`fma-neg_binary64`
254×	`fma-def_binary64`
74×	`cancel-sign-sub-inv_binary64`
60×	`sub-neg_binary64`
40×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	26	20
2	65	20
3	130	20
4	285	20
5	593	20
6	977	20
7	1145	20
8	1205	20
9	1217	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 7 computations (30% saved)

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

151×	`fma-def_binary64`
131×	`fma-neg_binary64`
46×	`cancel-sign-sub-inv_binary64`
36×	`sub-neg_binary64`
30×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	72	10
4	150	10
5	312	10
6	502	10
7	626	10
8	708	10
9	722	10

Stop Event

1×

saturated

Counts

1 → 2

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)

Compiler

Compiled 35 to 22 computations (37.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
✓	0.1b	(fma.f64 y (sqrt.f64 x) 1)

series16.0ms (0.5%)

Counts

2 → 28

Calls

12 calls:

2.0ms	(fma.f64 y (sqrt.f64 x) 1)	x	-inf
2.0ms	(fma.f64 y (sqrt.f64 x) 1)	x	inf
1.0ms	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)	x	-inf
1.0ms	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)	x	inf
1.0ms	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)	x	0

rewrite48.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

690×	`log1p-expm1-u_binary64`
690×	`expm1-log1p-u_binary64`
373×	`prod-diff_binary64`
94×	`egg-rr`
71×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	144	17
2	1819	17

Stop Event

1×	node limit

Counts

2 → 94

simplify26.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

189×	`fma-def_binary64`
157×	`fma-neg_binary64`
55×	`cancel-sign-sub-inv_binary64`
34×	`associate--r+_binary64`
34×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	190
1	25	190
2	36	190
3	56	190
4	92	190
5	151	190
6	287	190
7	441	190
8	612	190
9	750	190
10	842	190
11	848	190

Stop Event

1×

saturated

Counts

122 → 103

prune82.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	5	104

Error

0.1b

Counts

104 → 5

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))
	22.6b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 3)) x)
	0.5b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
	33.3b	(.f64 (-.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 3) (pow.f64 x 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 2) (.f64 x (+.f64 x (fma.f64 y (sqrt.f64 x) 1))))))
	1.0b	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) 2))

Compiler

Compiled 2205 to 1090 computations (50.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
	0.1b	(fma.f64 y (sqrt.f64 x) 1)
✓	60.6b	(fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x)

series7.0ms (0.2%)

Counts

1 → 3

Calls

3 calls:

3.0ms	(fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x)	x	0
2.0ms	(fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x)	x	-inf
2.0ms	(fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x)	x	inf

rewrite32.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

348×	`log1p-expm1-u_binary64`
348×	`expm1-log1p-u_binary64`
295×	`pow1_binary64`
280×	`unpow-prod-down_binary64`
184×	`log-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	103	4
2	1281	4

Stop Event

1×	node limit

Counts

1 → 59

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	3

Stop Event

1×

saturated

Counts

62 → 60

prune151.0ms (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	163	5	168

Error

0.1b

Counts

168 → 5

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))
	22.6b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 3)) x)
▶	0.5b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
	33.3b	(.f64 (-.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 3) (pow.f64 x 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 2) (.f64 x (+.f64 x (fma.f64 y (sqrt.f64 x) 1))))))
	1.0b	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)) 2))

Compiler

Compiled 4268 to 1870 computations (56.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
	0.1b	(fma.f64 y (sqrt.f64 x) 1)
✓	0.3b	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))
✓	0.4b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3)

series167.0ms (5.5%)

Counts

3 → 25

Calls

18 calls:

71.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3)	y	0
20.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3)	x	-inf
20.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3)	x	inf
12.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))	x	-inf
10.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))	x	inf

rewrite76.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

847×	`log1p-expm1-u_binary64`
847×	`expm1-log1p-u_binary64`
568×	`prod-diff_binary64`
179×	`egg-rr`
89×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	205	26
2	2320	26

Stop Event

1×	node limit

Counts

3 → 179

simplify27.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-neg_binary64`
486×	`cancel-sign-sub-inv_binary64`
449×	`fma-def_binary64`
313×	`*-commutative_binary64`
290×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	209
1	89	207
2	219	201
3	639	201
4	2255	198

Stop Event

1×	node limit

Counts

204 → 193

prune258.0ms (8.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	216	3	219
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	218	6	224

Error

0.0b

Counts

224 → 6

Alt Table

Status	Error	Program
▶	0.5b	(-.f64 (pow.f64 (cbrt.f64 (+.f64 1 (*.f64 y (sqrt.f64 x)))) 3) x)
	0.5b	(-.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3)) 3) x)
	0.6b	(-.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))) x)
✓	0.3b	(+.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))
	22.6b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 3)) x)
	33.3b	(.f64 (-.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 3) (pow.f64 x 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 2) (.f64 x (+.f64 x (fma.f64 y (sqrt.f64 x) 1))))))

Compiler

Compiled 5678 to 2998 computations (47.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (pow.f64 (cbrt.f64 (+.f64 1 (*.f64 y (sqrt.f64 x)))) 3) x)
✓	0.2b	(*.f64 y (sqrt.f64 x))
✓	0.3b	(cbrt.f64 (+.f64 1 (*.f64 y (sqrt.f64 x))))
✓	0.4b	(pow.f64 (cbrt.f64 (+.f64 1 (*.f64 y (sqrt.f64 x)))) 3)

series168.0ms (5.5%)

Counts

4 → 25

Calls

24 calls:

49.0ms	(pow.f64 (cbrt.f64 (+.f64 1 (*.f64 y (sqrt.f64 x)))) 3)	y	0
36.0ms	(pow.f64 (cbrt.f64 (+.f64 1 (*.f64 y (sqrt.f64 x)))) 3)	x	-inf
20.0ms	(pow.f64 (cbrt.f64 (+.f64 1 (*.f64 y (sqrt.f64 x)))) 3)	x	inf
11.0ms	(cbrt.f64 (+.f64 1 (*.f64 y (sqrt.f64 x))))	x	inf
10.0ms	(cbrt.f64 (+.f64 1 (*.f64 y (sqrt.f64 x))))	x	-inf

rewrite72.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

518×	`fma-def_binary64`
461×	`log-prod_binary64`
250×	`egg-rr`
213×	`fma-neg_binary64`
179×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	234	32
2	2801	32

Stop Event

1×	node limit

Counts

4 → 250

simplify28.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-neg_binary64`
486×	`cancel-sign-sub-inv_binary64`
449×	`fma-def_binary64`
313×	`*-commutative_binary64`
290×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	209
1	89	207
2	219	201
3	639	201
4	2255	198

Stop Event

1×	node limit

Counts

275 → 263

prune237.0ms (7.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	258	5	263
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	261	8	269

Error

0.0b

Counts

269 → 8

Alt Table

Status	Error	Program
	0.5b	(-.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3)) 3) x)
	31.0b	(-.f64 (/.f64 (fma.f64 (pow.f64 x 3/2) (pow.f64 y 3) 1) (fma.f64 x (.f64 y y) (-.f64 1 (.f64 y (sqrt.f64 x))))) x)
	0.3b	(-.f64 (fma.f64 (*.f64 y (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)) 1) x)
	0.6b	(-.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))) x)
✓	0.5b	(-.f64 (pow.f64 (cbrt.f64 (+.f64 1 (*.f64 y (sqrt.f64 x)))) 3) x)
	0.2b	(fma.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y) (-.f64 1 x))
	32.4b	(-.f64 (fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 x)) 1) x)
✓	0.3b	(+.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))

Compiler

Compiled 4483 to 2457 computations (45.2% saved)

regimes521.0ms (17.2%)

Accuracy

Total 0.1b remaining (74.8%)

Threshold costs 0.1b (74.8%)

Counts

164 → 1

Compiler

Compiled 7427 to 5179 computations (30.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11

Stop Event

1×

saturated

end136.0ms (4.5%)

Stop Event

1×

fuel

Compiler

Compiled 159 to 109 computations (31.4% saved)

Iter	Nodes	Cost
0	13	190
1	25	190
2	36	190
3	56	190
4	92	190
5	151	190
6	287	190
7	441	190
8	612	190
9	750	190
10	842	190
11	848	190

Iter	Nodes	Cost
0	13	190
1	25	190
2	36	190
3	56	190
4	92	190
5	151	190
6	287	190
7	441	190
8	612	190
9	750	190
10	842	190
11	848	190

Details

analyze95.0ms (3.1%)

sample805.0ms (26.5%)

preprocess29.0ms (1%)

simplify14.0ms (0.5%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series16.0ms (0.5%)

rewrite48.0ms (1.6%)

simplify26.0ms (0.8%)

prune82.0ms (2.7%)

localize8.0ms (0.3%)

series7.0ms (0.2%)

rewrite32.0ms (1%)

simplify7.0ms (0.2%)

prune151.0ms (5%)

localize9.0ms (0.3%)

series167.0ms (5.5%)

rewrite76.0ms (2.5%)

simplify27.0ms (0.9%)

prune258.0ms (8.5%)

localize7.0ms (0.2%)

series168.0ms (5.5%)

rewrite72.0ms (2.4%)

simplify28.0ms (0.9%)

prune237.0ms (7.8%)

regimes521.0ms (17.2%)

simplify2.0ms (0.1%)

end136.0ms (4.5%)

Profiling

Iter	Nodes	Cost
0	13	190
1	25	190
2	36	190
3	56	190
4	92	190
5	151	190
6	287	190
7	441	190
8	612	190
9	750	190
10	842	190
11	848	190