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)

sample1.6s (44%)

Results

699.0ms	2061×	body	1024	valid
459.0ms	4403×	body	128	valid
250.0ms	1014×	body	512	valid
90.0ms	560×	body	256	valid
77.0ms	218×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify12.0ms (0.3%)

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

29.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	2.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series26.0ms (0.7%)

Counts

2 → 5

Calls

2 calls:

19.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 x 1))

rewrite66.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

114× egg-rr

Counts

2 → 114

Calls

2 calls:

63.0ms	((-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	151	17
2	1841	17
3	6015	17
0	0	0
1	0	0

simplify73.0ms (2%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
635×	`associate-l_binary64`
538×	`unswap-sqr_binary64`
518×	`distribute-rgt-neg-in_binary64`
478×	`distribute-lft-neg-in_binary64`

Counts

119 → 121

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	48
1	50	44
2	113	38
3	305	34
4	801	29
5	2479	29
6	4718	29
7	4924	29
8	5130	29

prune145.0ms (4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	113	8	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	8	122

Error

28.5b

Counts

122 → 8

Alt Table

Status	Error	Program
	29.5b	(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
	30.1b	(+.f64 (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))
	29.7b	(+.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)))
	29.6b	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
	29.4b	(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
▶	29.4b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	30.3b	1
	29.6b	(+.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 2674 to 1533 computations (42.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓	2.4b	(+.f64 x (-.f64 1 x))

series26.0ms (0.7%)

Counts

3 → 14

Calls

3 calls:

16.0ms	(/.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))

rewrite100.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

275× egg-rr

Counts

3 → 275

Calls

2 calls:

95.0ms	((+.f64 x (-.f64 1 x)) (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.0ms	()

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

simplify13.0ms (0.4%)

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

prune237.0ms (6.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	313	3	316

Error

0.1b

Counts

316 → 3

Alt Table

Status	Error	Program
	29.5b	(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
	29.7b	(+.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (neg.f64 (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x))))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Compiler

Compiled 6594 to 4139 computations (37.2% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
	0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series13.0ms (0.3%)

Counts

1 → 1

Calls

1 calls:

13.0ms

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

rewrite48.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

25× egg-rr

Counts

1 → 25

Calls

2 calls:

46.0ms	((/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
0.0ms	()

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

simplify7.0ms (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

prune144.0ms (3.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	97	10	107
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	100	10	110

Error

0.0b

Counts

110 → 10

Alt Table

Status	Error	Program
	0.7b	(/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3))
	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
	17.1b	(.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)))))
	0.4b	(*.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))
	0.3b	(/.f64 1 (+.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
	0.5b	(*.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)))
	10.0b	(/.f64 1 (/.f64 1 (/.f64 (+.f64 (+.f64 x 1) (-.f64 x (hypot.f64 x (sqrt.f64 x)))) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))
	0.2b	(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
	9.6b	(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))

Compiler

Compiled 1898 to 1381 computations (27.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series53.0ms (1.4%)

Counts

4 → 7

Calls

4 calls:

23.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
14.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 1 x))

rewrite74.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

136× egg-rr

Counts

4 → 136

Calls

2 calls:

72.0ms	((pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) (sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	213	45
2	2442	45
3	4940	45
0	0	0
1	0	0

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
635×	`associate-l_binary64`
538×	`unswap-sqr_binary64`
518×	`distribute-rgt-neg-in_binary64`
478×	`distribute-lft-neg-in_binary64`

Counts

143 → 143

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	50
1	50	46
2	113	40
3	305	36
4	801	31
5	2479	31
6	4718	31
7	4924	31
8	5130	31

prune334.0ms (9.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	145	8	153

Error

0.0b

Counts

153 → 8

Alt Table

Status	Error	Program
	17.1b	(.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)))))
	0.7b	(sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) -2))
	10.0b	(/.f64 1 (/.f64 1 (/.f64 (+.f64 (+.f64 x 1) (-.f64 x (hypot.f64 x (sqrt.f64 x)))) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))
	0.2b	(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
	0.3b	(sqrt.f64 (*.f64 (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 3) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)))
	0.3b	(sqrt.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2)))
	9.6b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
	0.4b	(sqrt.f64 (.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))

Compiler

Compiled 2445 to 1823 computations (25.4% saved)

regimes404.0ms (11.1%)

Accuracy

Total 0.1b remaining (86.3%)

Threshold costs 0.1b (86.3%)

Counts

216 → 1

Compiler

Compiled 6675 to 5305 computations (20.5% 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	18
1	14	18
2	13	18

end156.0ms (4.3%)

Compiler: Compiled 194 to 153 computations (21.1% 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%)

sample1.6s (44%)

simplify12.0ms (0.3%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series26.0ms (0.7%)

rewrite66.0ms (1.8%)

simplify73.0ms (2%)

prune145.0ms (4%)

localize9.0ms (0.2%)

series26.0ms (0.7%)

rewrite100.0ms (2.7%)

simplify13.0ms (0.4%)

prune237.0ms (6.5%)

localize11.0ms (0.3%)

series13.0ms (0.3%)

rewrite48.0ms (1.3%)

simplify7.0ms (0.2%)

prune144.0ms (3.9%)

localize11.0ms (0.3%)

series53.0ms (1.4%)

rewrite74.0ms (2%)

simplify74.0ms (2%)

prune334.0ms (9.1%)

regimes404.0ms (11.1%)

simplify2.0ms (0.1%)

end156.0ms (4.3%)

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