Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample741.0ms (13.6%)

Results

712.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9
3	11	9

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

27.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	26.2b	(sqrt.f64 (.f64 (.f64 2 x) x))

series10.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(sqrt.f64 (*.f64 (*.f64 2 x) x))

rewrite44.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

55× egg-rr

Counts

1 → 55

Calls

2 calls:

42.0ms	((sqrt.f64 (.f64 (.f64 2 x) x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	121	6
2	1317	6
3	4961	6
0	0	0
1	0	0

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Counts

67 → 57

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	24	80
3	25	80
4	29	80
5	47	80
6	58	80
7	63	80
8	75	80
9	72	80
10	58	80

prune35.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	51	6	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	7	58

Error

0.1b

Counts

58 → 7

Alt Table

Status	Error	Program
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	27.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
▶	11.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	11.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

Compiler

Compiled 768 to 509 computations (33.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
✓	0.5b	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
✓	0.6b	(cbrt.f64 (+.f64 x x))
✓	11.0b	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)

series1.1s (21.1%)

Counts

4 → 48

Calls

4 calls:

1.0s	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)
46.0ms	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
34.0ms	(cbrt.f64 (+.f64 x x))
22.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))

rewrite68.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

218× egg-rr

Counts

4 → 218

Calls

2 calls:

64.0ms

((pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2) (cbrt.f64 (+.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	215	26
2	1624	26
3	4958	26
0	0	0
1	0	0

simplify119.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-def_binary64`
790×	`unswap-sqr_binary64`
662×	`sqr-pow_binary64`
468×	`*-commutative_binary64`
344×	`distribute-rgt-in_binary64`

Counts

266 → 139

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	516
1	64	516
2	129	516
3	324	516
4	1021	516
5	1715	516
6	1918	516
7	2288	516
8	2999	516
9	3608	516
10	4272	516
11	4564	516
12	4655	516

prune99.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	231	2	233
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	232	8	240

Error

0.1b

Counts

240 → 8

Alt Table

Status	Error	Program
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	27.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	11.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	27.3b	(pow.f64 (pow.f64 (*.f64 x (+.f64 x x)) 1/4) 2)
	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	11.7b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2))

Compiler

Compiled 4949 to 2255 computations (54.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (+.f64 x x))
✓	0.6b	(cbrt.f64 x)
✓	1.0b	(cbrt.f64 2)
✓	11.0b	(pow.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2)

series1.2s (21.6%)

Counts

3 → 24

Calls

3 calls:

1.1s	(pow.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2)
30.0ms	(cbrt.f64 x)
0.0ms	(cbrt.f64 2)

rewrite49.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

61× egg-rr

Counts

3 → 61

Calls

2 calls:

48.0ms	((pow.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2) (cbrt.f64 2) (cbrt.f64 x))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	184	17
2	1903	17
3	4889	17
0	0	0
1	0	0

simplify102.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1302×	`fma-def_binary64`
866×	`unswap-sqr_binary64`
710×	`sqr-pow_binary64`
439×	`cube-prod_binary64`
351×	`associate-l_binary64`

Counts

85 → 68

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	248
1	45	248
2	84	248
3	149	248
4	309	248
5	781	248
6	1125	248
7	1950	248
8	2451	248
9	3078	248
10	3648	248
11	4266	248
12	4680	248
13	4782	248

prune95.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	0	5	5
Picked	0	1	1
Done	1	1	2
Total	160	10	170

Error

0.0b

Counts

170 → 10

Alt Table

Status	Error	Program
▶	11.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 2)) 3) (cbrt.f64 x)) x) 1/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	27.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
	12.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (.f64 (cbrt.f64 (.f64 x (cbrt.f64 (.f64 2 x)))) (cbrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 (.f64 2 x)))))))
	33.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (.f64 (sqrt.f64 (cbrt.f64 (*.f64 2 x))) (sqrt.f64 x)))
	27.3b	(pow.f64 (pow.f64 (*.f64 x (+.f64 x x)) 1/4) 2)
	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	11.7b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2))

Compiler

Compiled 3705 to 2338 computations (36.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(cbrt.f64 2)
✓	1.0b	(pow.f64 (cbrt.f64 (cbrt.f64 2)) 3)
✓	1.0b	(cbrt.f64 (cbrt.f64 2))
✓	11.0b	(pow.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 2)) 3) (cbrt.f64 x)) x) 1/2)

series1.1s (21.1%)

Counts

3 → 12

Calls

3 calls:

1.1s	(pow.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 2)) 3) (cbrt.f64 x)) x) 1/2)
0.0ms	(cbrt.f64 (cbrt.f64 2))
0.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 2)) 3)

rewrite49.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

67× egg-rr

Counts

3 → 67

Calls

2 calls:

48.0ms	((pow.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 2)) 3) (cbrt.f64 x)) x) 1/2) (cbrt.f64 (cbrt.f64 2)) (pow.f64 (cbrt.f64 (cbrt.f64 2)) 3))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	228	18
2	2280	18
3	5087	18
0	0	0
1	0	0

simplify138.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1024×	`sqr-pow_binary64`
744×	`fabs-mul_binary64`
722×	`cube-prod_binary64`
450×	`unswap-sqr_binary64`
390×	`pow-sqr_binary64`

Counts

79 → 71

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	184
1	32	184
2	62	184
3	99	184
4	192	184
5	464	184
6	641	184
7	1056	184
8	1095	184
9	1271	184
10	1472	184
11	1756	184
12	2046	184
13	2468	184
14	3023	184
15	3312	184
16	3602	184
17	3770	184
18	3845	184
19	3912	184
20	4688	184
21	4787	184

prune60.0ms (1.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	88	11	99

Error

0.0b

Counts

99 → 11

Alt Table

Status	Error	Program
✓	11.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 2)) 3) (cbrt.f64 x)) x) 1/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	27.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
	11.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (pow.f64 (pow.f64 2 1/9) 3) (cbrt.f64 x)) x) 1/2))
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
	12.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (.f64 (cbrt.f64 (.f64 x (cbrt.f64 (.f64 2 x)))) (cbrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 (.f64 2 x)))))))
	33.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (.f64 (sqrt.f64 (cbrt.f64 (*.f64 2 x))) (sqrt.f64 x)))
	27.3b	(pow.f64 (pow.f64 (*.f64 x (+.f64 x x)) 1/4) 2)
	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	11.7b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2))

Compiler

Compiled 2082 to 1446 computations (30.5% saved)

regimes135.0ms (2.5%)

Accuracy

Total 0.3b remaining (75.5%)

Threshold costs 0.3b (75.5%)

Counts

35 → 2

Compiler

Compiled 1731 to 1334 computations (22.9% saved)

bsearch16.0ms (0.3%)

Steps

Iters	Range		Point
10	-3.497324545450821e-304	3.1612837875203375e-298	3.57210598636777e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
2×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	19	25
2	27	25
3	32	25
4	37	25
5	39	25
6	39	25

end147.0ms (2.7%)

Compiler: Compiled 180 to 137 computations (23.9% saved)

Details

analyze4.0ms (0.1%)

sample741.0ms (13.6%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize3.0ms (0.1%)

series10.0ms (0.2%)

rewrite44.0ms (0.8%)

simplify12.0ms (0.2%)

prune35.0ms (0.6%)

localize10.0ms (0.2%)

series1.1s (21.1%)

rewrite68.0ms (1.2%)

simplify119.0ms (2.2%)

prune99.0ms (1.8%)

localize13.0ms (0.2%)

series1.2s (21.6%)

rewrite49.0ms (0.9%)

simplify102.0ms (1.9%)

prune95.0ms (1.7%)

localize17.0ms (0.3%)

series1.1s (21.1%)

rewrite49.0ms (0.9%)

simplify138.0ms (2.5%)

prune60.0ms (1.1%)

regimes135.0ms (2.5%)

bsearch16.0ms (0.3%)

simplify4.0ms (0.1%)

end147.0ms (2.7%)

Profiling