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)

sample1.5s (48.4%)

Results

662.0ms	2093×	body	1024	valid
376.0ms	4402×	body	128	valid
305.0ms	1035×	body	512	valid
81.0ms	233×	body	2048	valid
72.0ms	493×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify47.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

prune2.0ms (0%)

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

28.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series15.0ms (0.5%)

Counts

1 → 1

Calls

1 calls:

15.0ms

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

rewrite53.0ms (1.7%)

Algorithm

2×	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`

Counts

1 → 88

Calls

1 calls:

51.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	151	11
2	1841	11
3	6015	11
0	0	0
1	0	0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

89 → 89

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1
2	3	1

prune173.0ms (5.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	6	90

Error

27.1b

Counts

90 → 6

Alt Table

Status	Error	Program
	28.5b	(+.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)))
	29.1b	1
	29.0b	(/.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))
▶	27.9b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	28.7b	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
	28.7b	(+.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)))

Compiler

Compiled 2273 to 1275 computations (43.9% saved)

localize10.0ms (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)))
✓	1.2b	(+.f64 x (-.f64 1 x))

series22.0ms (0.7%)

Counts

3 → 14

Calls

3 calls:

12.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
1.0ms	(+.f64 x (-.f64 1 x))

rewrite104.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 275

Calls

3 calls:

84.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
84.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
84.0ms	(+.f64 x (-.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	232	29
2	3194	29
3	4955	29
0	0	0
1	0	0

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

289 → 276

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	14
1	4	14
2	3	14

prune301.0ms (9.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	273	3	276
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	279	3	282

Error

0.1b

Counts

282 → 3

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	27.9b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (/.f64 (+.f64 x (-.f64 1 x)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))
	28.5b	(+.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))

Compiler

Compiled 6075 to 3791 computations (37.6% 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)))

series14.0ms (0.4%)

Counts

1 → 1

Calls

1 calls:

14.0ms

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

rewrite47.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

1 → 25

Calls

1 calls:

46.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	176	14
2	2142	14
3	5096	14
0	0	0
1	0	0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

26 → 26

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1
2	3	1

prune86.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	70	8	78

Error

0.0b

Counts

78 → 8

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
	0.4b	(*.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	10.5b	(/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3)))
	0.3b	(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
	0.7b	(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
	17.6b	(.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (.f64 (+.f64 1 x) x)))))
	0.3b	(*.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))

Compiler

Compiled 1385 to 1005 computations (27.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))
✓	0.1b	(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
✓	0.2b	(pow.f64 (cbrt.f64 (+.f64 x 1)) 2)
✓	0.3b	(cbrt.f64 (+.f64 x 1))

series101.0ms (3.2%)

Counts

4 → 37

Calls

4 calls:

83.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
9.0ms	(pow.f64 (cbrt.f64 (+.f64 x 1)) 2)
4.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))
4.0ms	(cbrt.f64 (+.f64 x 1))

rewrite59.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

876×	`log1p-expm1-u_binary64`
876×	`expm1-log1p-u_binary64`
267×	`prod-diff_binary64`
103×	`egg-rr`
102×	`add-sqr-sqrt_binary64`

Counts

4 → 103

Calls

4 calls:

55.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))
55.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
55.0ms	(pow.f64 (cbrt.f64 (+.f64 x 1)) 2)
55.0ms	(cbrt.f64 (+.f64 x 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	227	33
2	2298	33
3	5737	33
0	0	0
1	0	0

simplify95.0ms (3%)

Algorithm

1×	egg-herbie

Rules

641×	`associate-/l*_binary64`
514×	`fma-neg_binary64`
354×	`div-exp_binary64`
339×	`fma-def_binary64`
297×	`cancel-sign-sub-inv_binary64`

Counts

140 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1050
1	277	1030
2	698	730
3	2184	559
4	4612	559
5	4548	559
6	4830	559
7	5466	559

prune190.0ms (6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	170	8	178

Error

0.0b

Counts

178 → 8

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
	0.4b	(*.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	10.5b	(/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3)))
	0.3b	(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
	0.7b	(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
	17.6b	(.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (.f64 (+.f64 1 x) x)))))
	0.3b	(*.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))

Compiler

Compiled 4166 to 3242 computations (22.2% saved)

regimes136.0ms (4.3%)

Accuracy

Total 0.1b remaining (81.1%)

Threshold costs 0.1b (81.1%)

Counts

76 → 1

Compiler

Compiled 2714 to 2037 computations (24.9% 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	10	16
1	14	16
2	13	16

end129.0ms (4.1%)

Compiler: Compiled 157 to 126 computations (19.7% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze3.0ms (0.1%)

sample1.5s (48.4%)

simplify47.0ms (1.5%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series15.0ms (0.5%)

rewrite53.0ms (1.7%)

simplify6.0ms (0.2%)

prune173.0ms (5.5%)

localize10.0ms (0.3%)

series22.0ms (0.7%)

rewrite104.0ms (3.3%)

simplify11.0ms (0.3%)

prune301.0ms (9.5%)

localize5.0ms (0.2%)

series14.0ms (0.4%)

rewrite47.0ms (1.5%)

simplify6.0ms (0.2%)

prune86.0ms (2.7%)

localize9.0ms (0.3%)

series101.0ms (3.2%)

rewrite59.0ms (1.9%)

simplify95.0ms (3%)

prune190.0ms (6%)

regimes136.0ms (4.3%)

simplify2.0ms (0.1%)

end129.0ms (4.1%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11