Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.4s (56.2%)

Results

577.0ms	2065×	body	1024	valid
399.0ms	4402×	body	128	valid
245.0ms	1071×	body	512	valid
80.0ms	214×	body	2048	valid
79.0ms	504×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify12.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series10.0ms (0.4%)

Counts

1 → 1

Calls

1 calls:

10.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite48.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

832×	`prod-diff_binary64`
742×	`log1p-expm1-u_binary64`
742×	`expm1-log1p-u_binary64`
88×	`egg-rr`
72×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	153	11
2	2027	11

Stop Event

1×	node limit

Counts

1 → 88

Calls

1 calls:

46.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1

Stop Event

1×

saturated

Counts

89 → 89

prune111.0ms (4.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	7	90

Error

27.0b

Counts

90 → 7

Alt Table

Status	Error	Program
▶	27.9b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	28.6b	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))
	28.4b	(+.f64 (fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
	28.5b	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
	29.5b	1
	28.5b	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
	28.4b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) (fma.f64 -1 (sqrt.f64 x) (sqrt.f64 x)))

Compiler

Compiled 2291 to 1437 computations (37.3% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	0.0b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓	2.7b	(+.f64 x (-.f64 1 x))

series17.0ms (0.7%)

Counts

3 → 14

Calls

3 calls:

10.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
1.0ms	(+.f64 x (-.f64 1 x))

rewrite74.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`fma-def_binary64`
347×	`fma-neg_binary64`
275×	`egg-rr`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	237	29
2	3535	29

Stop Event

1×	node limit

Counts

3 → 275

Calls

3 calls:

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

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	14
1	4	14

Stop Event

1×

saturated

Counts

289 → 276

prune186.0ms (7.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	273	3	276
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	280	3	283

Error

0.1b

Counts

283 → 3

Alt Table

Status	Error	Program
	27.9b	(/.f64 (+.f64 x (-.f64 1 x)) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3)))
	28.4b	(+.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))
▶	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Compiler

Compiled 6070 to 3825 computations (37% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.4%)

Counts

1 → 1

Calls

1 calls:

9.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite42.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
84×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`
79×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	178	14
2	2385	14

Stop Event

1×	node limit

Counts

1 → 25

Calls

1 calls:

41.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1

Stop Event

1×

saturated

Counts

26 → 26

prune76.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	70	5	75
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	73	5	78

Error

0.0b

Counts

78 → 5

Alt Table

Status	Error	Program
	0.3b	(/.f64 1 (fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1))))
	13.6b	(.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (.f64 (+.f64 1 x) x))))
	7.9b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
▶	0.2b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
	0.3b	(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)

Compiler

Compiled 1280 to 926 computations (27.7% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.1b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
✓	0.3b	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)

series27.0ms (1.1%)

Counts

3 → 3

Calls

3 calls:

13.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
9.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite48.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`fma-def_binary64`
414×	`log-prod_binary64`
218×	`fma-neg_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	217	39
2	2675	39

Stop Event

1×	node limit

Counts

3 → 105

Calls

3 calls:

46.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
46.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
46.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	3
1	4	3

Stop Event

1×

saturated

Counts

108 → 106

prune106.0ms (4.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	105	6	111

Error

0.0b

Counts

111 → 6

Alt Table

Status	Error	Program
	0.3b	(/.f64 1 (fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1))))
	13.6b	(.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (.f64 (+.f64 1 x) x))))
	0.4b	(sqrt.f64 (*.f64 (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -2) (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -2)))
✓	0.2b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
	0.3b	(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
	7.9b	(cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3))

Compiler

Compiled 1834 to 1369 computations (25.4% saved)

regimes163.0ms (6.5%)

Accuracy

Total 0.1b remaining (82.3%)

Threshold costs 0.1b (82.3%)

Counts

93 → 1

Compiler

Compiled 3061 to 2389 computations (22% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`fabs-div_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	16	16

Stop Event

1×

saturated

end106.0ms (4.2%)

Compiler: Compiled 119 to 96 computations (19.3% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Details

analyze3.0ms (0.1%)

sample1.4s (56.2%)

simplify12.0ms (0.5%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series10.0ms (0.4%)

rewrite48.0ms (1.9%)

simplify6.0ms (0.3%)

prune111.0ms (4.4%)

localize7.0ms (0.3%)

series17.0ms (0.7%)

rewrite74.0ms (3%)

simplify13.0ms (0.5%)

prune186.0ms (7.4%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite42.0ms (1.7%)

simplify6.0ms (0.2%)

prune76.0ms (3%)

localize8.0ms (0.3%)

series27.0ms (1.1%)

rewrite48.0ms (1.9%)

simplify9.0ms (0.4%)

prune106.0ms (4.2%)

regimes163.0ms (6.5%)

simplify2.0ms (0.1%)

end106.0ms (4.2%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11