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 (52.2%)

Results

569.0ms	2065×	body	1024	valid
396.0ms	4419×	body	128	valid
229.0ms	986×	body	512	valid
90.0ms	547×	body	256	valid
88.0ms	239×	body	2048	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess19.0ms (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)

simplify9.0ms (0.3%)

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

29.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.4b	(-.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
✓	3.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series12.0ms (0.5%)

Counts

1 → 1

Calls

3 calls:

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

rewrite56.0ms (2.1%)

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

simplify7.0ms (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

prune112.0ms (4.2%)

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

27.9b

Counts

90 → 6

Alt Table

Status	Error	Program
▶	28.9b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	29.5b	(+.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)))
	31.3b	1
	29.5b	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
	29.3b	(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
	29.4b	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 2205 to 1383 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))
✓	0.1b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓	2.4b	(+.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

rewrite82.0ms (3.1%)

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

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

prune216.0ms (8.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	271	5	276
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	277	5	282

Error

0.1b

Counts

282 → 5

Alt Table

Status	Error	Program
	28.9b	(/.f64 (+.f64 x (-.f64 1 x)) (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	30.9b	(log.f64 (/.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (exp.f64 (sqrt.f64 x))))
	29.5b	(*.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))))
	29.4b	(+.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))

Compiler

Compiled 6150 to 3881 computations (36.9% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.3%)

Counts

1 → 1

Calls

3 calls:

3.0ms	(/.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

rewrite42.0ms (1.6%)

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

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

prune91.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	73	7	80

Error

0.0b

Counts

80 → 7

Alt Table

Status	Error	Program
	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1))))
	0.7b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))
	8.9b	(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))
	0.4b	(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
	29.4b	(*.f64 (/.f64 1 (+.f64 1 (-.f64 x x))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	14.3b	(.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))))

Compiler

Compiled 1366 to 992 computations (27.4% saved)

localize7.0ms (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)

series31.0ms (1.2%)

Counts

3 → 3

Calls

9 calls:

5.0ms	(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
3.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))	x	inf

rewrite52.0ms (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

simplify7.0ms (0.3%)

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

prune120.0ms (4.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Error

0.0b

Counts

113 → 8

Alt Table

Status	Error	Program
	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)))
	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1))))
	0.7b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))
	8.9b	(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))
	0.4b	(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
	29.4b	(*.f64 (/.f64 1 (+.f64 1 (-.f64 x x))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	14.3b	(.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))))

Compiler

Compiled 1879 to 1404 computations (25.3% saved)

regimes207.0ms (7.8%)

Accuracy

Total 0.2b remaining (86.9%)

Threshold costs 0.2b (86.9%)

Counts

125 → 1

Compiler

Compiled 4193 to 3263 computations (22.2% 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

Stop Event

1×

saturated

end132.0ms (5%)

Stop Event

1×

fuel

Compiler

Compiled 164 to 131 computations (20.1% 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

analyze3.0ms (0.1%)

sample1.4s (52.2%)

preprocess19.0ms (0.7%)

simplify9.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series12.0ms (0.5%)

rewrite56.0ms (2.1%)

simplify7.0ms (0.3%)

prune112.0ms (4.2%)

localize7.0ms (0.3%)

series16.0ms (0.6%)

rewrite82.0ms (3.1%)

simplify11.0ms (0.4%)

prune216.0ms (8.1%)

localize7.0ms (0.3%)

series9.0ms (0.3%)

rewrite42.0ms (1.6%)

simplify6.0ms (0.2%)

prune91.0ms (3.4%)

localize7.0ms (0.3%)

series31.0ms (1.2%)

rewrite52.0ms (1.9%)

simplify7.0ms (0.3%)

prune120.0ms (4.5%)

regimes207.0ms (7.8%)

simplify2.0ms (0.1%)

end132.0ms (5%)

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