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 (40.9%)

Results

624.0ms	2061×	body	1024	valid
410.0ms	4403×	body	128	valid
242.0ms	1014×	body	512	valid
98.0ms	560×	body	256	valid
80.0ms	218×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (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))

series40.0ms (1.1%)

Counts

2 → 5

Calls

2 calls:

33.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 x 1))

rewrite143.0ms (3.8%)

Algorithm

2×	egg-rewrite

Rules

91×	`egg`
43×	`egg`

Counts

2 → 134

Calls

2 calls:

80.0ms	(sqrt.f64 (+.f64 x 1))
61.0ms	(-.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	5	6
1	102	6
2	1131	6
3	4620	6
4	6219	6

simplify82.0ms (2.2%)

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

139 → 141

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

prune158.0ms (4.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	133	8	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	8	142

Error

28.5b

Counts

142 → 8

Alt Table

Status	Error	Program
	30.3b	1
	29.9b	(/.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))))))
	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))))))
	29.6b	(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)))
	29.6b	(+.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)))
	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)))
▶	29.4b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Compiler

Compiled 3038 to 1791 computations (41% saved)

localize8.0ms (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))

series25.0ms (0.6%)

Counts

3 → 14

Calls

3 calls:

14.0ms	(/.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))

rewrite176.0ms (4.6%)

Algorithm

3×	egg-rewrite

Rules

156×	`egg`
57×	`egg`
36×	`egg`

Counts

3 → 249

Calls

3 calls:

74.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
50.0ms	(+.f64 x (-.f64 1 x))
47.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	114	7
2	1521	7
3	5041	7
0	10	20
1	232	11
2	3194	11
3	4955	11
0	7	11
1	150	11
2	1826	11
3	4998	11

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

263 → 249

Iterations

Useful iterations: 0 (0.0ms)

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

prune367.0ms (9.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	296	2	298
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	304	2	306

Error

0.1b

Counts

306 → 2

Alt Table

Status	Error	Program
	29.3b	(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 x 1) (-.f64 x (hypot.f64 x (sqrt.f64 x)))))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Compiler

Compiled 6302 to 4022 computations (36.2% saved)

localize5.0ms (0.1%)

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)))

series14.0ms (0.4%)

Counts

1 → 1

Calls

1 calls:

14.0ms

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

rewrite52.0ms (1.4%)

Algorithm

1×	egg-rewrite

Rules

31× egg

Counts

1 → 31

Calls

1 calls:

52.0ms

(/.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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

32 → 31

Iterations

Useful iterations: 0 (0.0ms)

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

prune137.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	9	116
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	9	118

Error

0.0b

Counts

118 → 9

Alt Table

Status	Error	Program
	0.2b	(/.f64 1 (+.f64 (*.f64 (pow.f64 (pow.f64 (+.f64 x 1) 3/4) 1/2) (sqrt.f64 (pow.f64 (+.f64 x 1) 1/4))) (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)))
▶	0.2b	(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
	10.0b	(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
	9.6b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
	0.7b	(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.2b	(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (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)))))
	49.6b	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (fma.f64 x x -1)) (pow.f64 (/.f64 1 (-.f64 x 1)) 1/2)) (sqrt.f64 x)))

Compiler

Compiled 2002 to 1489 computations (25.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))
✓	0.2b	(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))

series80.0ms (2.1%)

Counts

2 → 8

Calls

2 calls:

67.0ms	(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
12.0ms	(fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))

rewrite95.0ms (2.5%)

Algorithm

2×	egg-rewrite

Rules

29×	`egg`
24×	`egg`

Counts

2 → 53

Calls

2 calls:

49.0ms	(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
45.0ms	(fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	195	14
2	2083	14
3	5201	14
0	8	16
1	169	11
2	1772	11
3	4884	11

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

456×	`fma-neg_binary64`
358×	`associate-/l/_binary64`
259×	`associate-/r/_binary64`
217×	`sub-neg_binary64`
209×	`distribute-rgt-out_binary64`

Counts

61 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	274
1	143	274
2	473	249
3	2150	245
4	4851	245
5	5008	245

prune128.0ms (3.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	115	8	123

Error

0.0b

Counts

123 → 8

Alt Table

Status	Error	Program
	0.2b	(/.f64 1 (+.f64 (*.f64 (pow.f64 (pow.f64 (+.f64 x 1) 3/4) 1/2) (sqrt.f64 (pow.f64 (+.f64 x 1) 1/4))) (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)))
	0.3b	(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))
	9.6b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
	0.2b	(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (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)))))
	49.6b	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (fma.f64 x x -1)) (pow.f64 (/.f64 1 (-.f64 x 1)) 1/2)) (sqrt.f64 x)))
	0.4b	(*.f64 (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 1 x) 1/4)) -1) (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 1 x) 1/4)) -1))

Compiler

Compiled 2109 to 1616 computations (23.4% saved)

regimes493.0ms (12.9%)

Accuracy

Total 0.1b remaining (81.4%)

Threshold costs 0.1b (81.4%)

Counts

210 → 1

Compiler

Compiled 6884 to 5325 computations (22.6% saved)

simplify2.0ms (0%)

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

end140.0ms (3.7%)

Compiler: Compiled 183 to 147 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%)

sample1.6s (40.9%)

simplify10.0ms (0.3%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series40.0ms (1.1%)

rewrite143.0ms (3.8%)

simplify82.0ms (2.2%)

prune158.0ms (4.1%)

localize8.0ms (0.2%)

series25.0ms (0.6%)

rewrite176.0ms (4.6%)

simplify11.0ms (0.3%)

prune367.0ms (9.6%)

localize5.0ms (0.1%)

series14.0ms (0.4%)

rewrite52.0ms (1.4%)

simplify6.0ms (0.2%)

prune137.0ms (3.6%)

localize9.0ms (0.2%)

series80.0ms (2.1%)

rewrite95.0ms (2.5%)

simplify64.0ms (1.7%)

prune128.0ms (3.4%)

regimes493.0ms (12.9%)

simplify2.0ms (0%)

end140.0ms (3.7%)

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