Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.3s (52.1%)

Results

480.0ms	2042×	body	512	valid
453.0ms	4739×	body	128	valid
170.0ms	1030×	body	256	valid
135.0ms	445×	body	1024	valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
13×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16

Stop Event

1×

saturated

Counts

1 → 2

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

14.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.6b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 47 to 39 computations (17% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	2.8b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite73.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

867×	`prod-diff_binary64`
180×	`egg-rr`
162×	`expm1-udef_binary64`
162×	`log1p-udef_binary64`
97×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	193	30
2	2924	30

Stop Event

1×	node limit

Counts

3 → 180

Calls

3 calls:

69.0ms	(/.f64 1 (+.f64 x 1))
69.0ms	(/.f64 1 (-.f64 x 1))
69.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

simplify31.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

429×	`associate-l_binary64`
355×	`fma-neg_binary64`
346×	`associate-/r*_binary64`
286×	`cancel-sign-sub-inv_binary64`
218×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	575
1	198	543
2	594	540
3	1925	537

Stop Event

1×	node limit

Counts

216 → 221

prune232.0ms (9.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	218	3	221
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	219	3	222

Error

0.2b

Counts

222 → 3

Alt Table

Status	Error	Program
	29.9b	(-.f64 (pow.f64 (pow.f64 (+.f64 1 x) -3) 1/3) (/.f64 1 (-.f64 x 1)))
	32.8b	(+.f64 (/.f64 -2 (pow.f64 x 4)) (/.f64 -2 (*.f64 x x)))
▶	13.6b	(/.f64 (/.f64 (+.f64 x (-.f64 -1 (+.f64 1 x))) (+.f64 1 x)) (+.f64 x -1))

Compiler

Compiled 5768 to 4659 computations (19.2% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (+.f64 x (-.f64 -1 (+.f64 1 x))) (+.f64 1 x)) (+.f64 x -1))
✓	0.0b	(/.f64 (+.f64 x (-.f64 -1 (+.f64 1 x))) (+.f64 1 x))
✓	0.0b	(-.f64 -1 (+.f64 1 x))
✓	1.7b	(+.f64 x (-.f64 -1 (+.f64 1 x)))

series8.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.f64 (/.f64 (+.f64 x (-.f64 -1 (+.f64 1 x))) (+.f64 1 x)) (+.f64 x -1))
2.0ms	(/.f64 (+.f64 x (-.f64 -1 (+.f64 1 x))) (+.f64 1 x))
1.0ms	(-.f64 -1 (+.f64 1 x))
1.0ms	(+.f64 x (-.f64 -1 (+.f64 1 x)))

rewrite100.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`fma-def_binary64`
277×	`fma-neg_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
212×	`egg-rr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	243	43
2	3885	38

Stop Event

1×	node limit

Counts

4 → 212

Calls

4 calls:

97.0ms	(/.f64 (/.f64 (+.f64 x (-.f64 -1 (+.f64 1 x))) (+.f64 1 x)) (+.f64 x -1))
97.0ms	(/.f64 (+.f64 x (-.f64 -1 (+.f64 1 x))) (+.f64 1 x))
97.0ms	(-.f64 -1 (+.f64 1 x))
97.0ms	(+.f64 x (-.f64 -1 (+.f64 1 x)))

simplify34.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

460×	`fma-neg_binary64`
453×	`times-frac_binary64`
336×	`associate-/r*_binary64`
303×	`cancel-sign-sub-inv_binary64`
238×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	482
1	188	444
2	554	435
3	1852	430

Stop Event

1×	node limit

Counts

260 → 245

prune167.0ms (6.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	245	3	248

Error

0.0b

Counts

248 → 3

Alt Table

Status	Error	Program
	29.9b	(-.f64 (pow.f64 (pow.f64 (+.f64 1 x) -3) 1/3) (/.f64 1 (-.f64 x 1)))
▶	0.1b	(/.f64 (/.f64 -2 (+.f64 1 x)) (+.f64 x -1))
	32.8b	(+.f64 (/.f64 -2 (pow.f64 x 4)) (/.f64 -2 (*.f64 x x)))

Compiler

Compiled 5118 to 3766 computations (26.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 -2 (+.f64 1 x))
✓	0.1b	(/.f64 (/.f64 -2 (+.f64 1 x)) (+.f64 x -1))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 (/.f64 -2 (+.f64 1 x)) (+.f64 x -1))
2.0ms	(/.f64 -2 (+.f64 1 x))

rewrite50.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

440×	`log-prod_binary64`
196×	`fma-def_binary64`
195×	`log-div_binary64`
177×	`prod-diff_binary64`
170×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	203	20
2	2753	15

Stop Event

1×	node limit

Counts

2 → 70

Calls

2 calls:

48.0ms	(/.f64 -2 (+.f64 1 x))
48.0ms	(/.f64 (/.f64 -2 (+.f64 1 x)) (+.f64 x -1))

simplify28.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

453×	`times-frac_binary64`
453×	`fma-neg_binary64`
349×	`associate-/r*_binary64`
302×	`cancel-sign-sub-inv_binary64`
241×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	409
1	179	389
2	539	380
3	1814	375

Stop Event

1×	node limit

Counts

94 → 99

prune77.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	99	3	102

Error

0.0b

Counts

102 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (/.f64 -2 (+.f64 1 x)) (+.f64 x -1))
▶	0.2b	(+.f64 0 (/.f64 -2 (fma.f64 x x -1)))
	21.0b	(/.f64 (*.f64 (/.f64 -2 (+.f64 1 (pow.f64 x 3))) (fma.f64 x (+.f64 x -1) 1)) (+.f64 x -1))

Compiler

Compiled 1455 to 1167 computations (19.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 -2 (fma.f64 x x -1))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 -2 (fma.f64 x x -1))

rewrite36.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

502×	`log1p-expm1-u_binary64`
502×	`expm1-log1p-u_binary64`
262×	`unpow-prod-down_binary64`
229×	`log-prod_binary64`
145×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	122	8
2	1361	8

Stop Event

1×	node limit

Counts

1 → 38

Calls

1 calls:

35.0ms

(/.f64 -2 (fma.f64 x x -1))

simplify30.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary64`
413×	`unswap-sqr_binary64`
236×	`associate-l_binary64`
235×	`associate-/r*_binary64`
220×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	227
1	116	209
2	340	206
3	1122	203
4	4483	203

Stop Event

1×	node limit

Counts

50 → 53

prune44.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	53	3	56

Error

0.0b

Counts

56 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (/.f64 -2 (+.f64 1 x)) (+.f64 x -1))
✓	0.2b	(+.f64 0 (/.f64 -2 (fma.f64 x x -1)))
	21.0b	(/.f64 (*.f64 (/.f64 -2 (+.f64 1 (pow.f64 x 3))) (fma.f64 x (+.f64 x -1) 1)) (+.f64 x -1))

Compiler

Compiled 830 to 676 computations (18.6% saved)

regimes149.0ms (6.1%)

Accuracy

Total 0.1b remaining (74.9%)

Threshold costs 0.1b (74.9%)

Counts

92 → 1

Compiler

Compiled 2732 to 2194 computations (19.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13

Stop Event

1×

saturated

end53.0ms (2.2%)

Compiler: Compiled 58 to 46 computations (20.7% saved)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16

Details

analyze5.0ms (0.2%)

sample1.3s (52.1%)

simplify9.0ms (0.4%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series7.0ms (0.3%)

rewrite73.0ms (3%)

simplify31.0ms (1.3%)

prune232.0ms (9.5%)

localize7.0ms (0.3%)

series8.0ms (0.3%)

rewrite100.0ms (4.1%)

simplify34.0ms (1.4%)

prune167.0ms (6.8%)

localize6.0ms (0.2%)

series6.0ms (0.2%)

rewrite50.0ms (2%)

simplify28.0ms (1.1%)

prune77.0ms (3.1%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite36.0ms (1.5%)

simplify30.0ms (1.2%)

prune44.0ms (1.8%)

regimes149.0ms (6.1%)

simplify2.0ms (0.1%)

end53.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16