Details

analyze2.0ms (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)

sample1.3s (49%)

Results

544.0ms	1997×	body	1024	valid
376.0ms	4448×	body	128	valid
221.0ms	1051×	body	512	valid
76.0ms	236×	body	2048	valid
72.0ms	524×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess17.0ms (0.7%)

Algorithm

2×	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
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 8 to 6 computations (25% 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

prune1.0ms (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

30.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series20.0ms (0.8%)

Counts

2 → 5

Calls

6 calls:

6.0ms	(sqrt.f64 (+.f64 x 1))	x	-inf
5.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))	x	-inf
4.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))	x	inf
2.0ms	(sqrt.f64 (+.f64 x 1))	x	inf
1.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))	x	0

rewrite45.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

794×	`pow1_binary64`
742×	`log1p-expm1-u_binary64`
742×	`expm1-log1p-u_binary64`
78×	`add-sqr-sqrt_binary64`
75×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	153	17
2	2086	17
0	7	17

Stop Event

1×	saturated
1×	node limit

Counts

2 → 63

simplify27.0ms (1%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-def_binary64`
612×	`associate-l_binary64`
536×	`unswap-sqr_binary64`
370×	`associate-r_binary64`
222×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	48
1	51	44
2	123	38
3	394	34
4	1126	29
5	3744	29

Stop Event

1×	node limit

Counts

68 → 70

prune62.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	8	71

Error

28.5b

Counts

71 → 8

Alt Table

Status	Error	Program
▶	29.4b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	30.0b	(+.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)))
	30.3b	(+.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)))
	31.4b	1
	30.0b	(log1p.f64 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
	30.1b	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
	29.9b	(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
	30.0b	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 1083 to 732 computations (32.4% saved)

localize9.0ms (0.4%)

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)))
✓	2.2b	(+.f64 x (-.f64 1 x))

series16.0ms (0.6%)

Counts

3 → 14

Calls

9 calls:

3.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))	x	-inf
3.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))	x	inf
2.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))	x	-inf
2.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))	x	inf
2.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))	x	0

rewrite81.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	236	29
2	3597	29
0	10	38

Stop Event

1×	saturated
1×	node limit

Counts

3 → 275

simplify11.0ms (0.4%)

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

prune232.0ms (8.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	305	3	308
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	311	5	316

Error

0.1b

Counts

316 → 5

Alt Table

Status	Error	Program
	29.4b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
	30.1b	(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (fma.f64 x x x))))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	30.1b	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
	30.0b	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 6697 to 4241 computations (36.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 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))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series10.0ms (0.4%)

Counts

1 → 1

Calls

3 calls:

4.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))	x	-inf
3.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))	x	inf
2.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))	x	0

rewrite44.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
86×	`*-un-lft-identity_binary64`
86×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	178	14
2	2442	14
0	8	14

Stop Event

1×	saturated
1×	node limit

Counts

1 → 25

simplify11.0ms (0.4%)

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

prune130.0ms (4.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	104	8	112

Error

0.0b

Counts

112 → 8

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	(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
	0.3b	(/.f64 1 (fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1))))
	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)))
	10.2b	(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))
	0.5b	(*.f64 (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -1) (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -1))
	0.2b	(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))

Compiler

Compiled 1789 to 1305 computations (27.1% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series37.0ms (1.4%)

Counts

4 → 7

Calls

12 calls:

6.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))	x	inf
5.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)	x	inf
5.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)	x	-inf
4.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)	x	0
4.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))	x	-inf

rewrite54.0ms (2%)

Algorithm

2×	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	45
1	216	45
2	2721	45
0	10	47

Stop Event

1×	saturated
1×	node limit

Counts

4 → 134

simplify28.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-def_binary64`
612×	`associate-l_binary64`
536×	`unswap-sqr_binary64`
370×	`associate-r_binary64`
222×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	50
1	51	46
2	123	40
3	394	36
4	1126	31
5	3744	31

Stop Event

1×	node limit

Counts

141 → 141

prune154.0ms (5.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	142	7	149

Error

0.0b

Counts

149 → 7

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	(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
	0.3b	(/.f64 1 (fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1))))
	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)))
	10.2b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
	0.5b	(*.f64 (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -1) (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -1))
	0.2b	(sqrt.f64 (pow.f64 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 1 x))) -2))

Compiler

Compiled 2357 to 1766 computations (25.1% saved)

regimes217.0ms (8.2%)

Accuracy

Total 0.1b remaining (73.3%)

Threshold costs 0.1b (73.3%)

Counts

140 → 1

Compiler

Compiled 4111 to 3289 computations (20% 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

end114.0ms (4.3%)

Stop Event

1×

fuel

Compiler

Compiled 134 to 109 computations (18.7% 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
0	1	1

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
0	1	1

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

analyze2.0ms (0.1%)

sample1.3s (49%)

preprocess17.0ms (0.7%)

simplify12.0ms (0.5%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series20.0ms (0.8%)

rewrite45.0ms (1.7%)

simplify27.0ms (1%)

prune62.0ms (2.3%)

localize9.0ms (0.4%)

series16.0ms (0.6%)

rewrite81.0ms (3%)

simplify11.0ms (0.4%)

prune232.0ms (8.7%)

localize6.0ms (0.2%)

series10.0ms (0.4%)

rewrite44.0ms (1.7%)

simplify11.0ms (0.4%)

prune130.0ms (4.9%)

localize6.0ms (0.2%)

series37.0ms (1.4%)

rewrite54.0ms (2%)

simplify28.0ms (1.1%)

prune154.0ms (5.8%)

regimes217.0ms (8.2%)

simplify2.0ms (0.1%)

end114.0ms (4.3%)

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
0	1	1

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