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)

sample1.0s (32.4%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune1.0ms (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

27.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	26.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
2.0ms	(.f64 2 (.f64 x x))

rewrite86.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

71× egg-rr

Counts

2 → 71

Calls

2 calls:

85.0ms	((sqrt.f64 (.f64 2 (.f64 x x))) (.f64 2 (.f64 x x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	121	13
2	1257	13
3	4991	13
4	6461	13
0	0	0
1	0	0

simplify106.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
644×	`fma-neg_binary64`
569×	`neg-mul-1_binary64`
441×	`fabs-mul_binary64`
416×	`distribute-rgt-neg-out_binary64`

Counts

95 → 75

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	164
1	20	164
2	41	164
3	76	164
4	160	164
5	416	164
6	614	164
7	992	164
8	1262	164
9	1713	164
10	2084	164
11	2649	164
12	2932	164
13	4196	164
14	4917	164
15	4747	164

prune39.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Error

0.1b

Counts

76 → 7

Alt Table

Status	Error	Program
	32.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
	43.4b	(sqrt.f64 (sqrt.f64 (*.f64 4 (pow.f64 x 4))))
▶	27.4b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	27.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 876 to 668 computations (23.7% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 2 (.f64 x x))
✓	0.4b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
✓	26.2b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
✓	26.9b	(cbrt.f64 (.f64 2 (.f64 x x)))

series113.0ms (3.5%)

Counts

3 → 36

Calls

3 calls:

64.0ms	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
35.0ms	(cbrt.f64 (.f64 2 (.f64 x x)))
14.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))

rewrite44.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

99× egg-rr

Counts

3 → 99

Calls

2 calls:

43.0ms	((cbrt.f64 (.f64 2 (.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	167	22
2	1651	22
3	4833	22
0	0	0
1	0	0

simplify125.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1025×	`fma-def_binary64`
513×	`fma-neg_binary64`
503×	`sqr-pow_binary64`
499×	`fabs-mul_binary64`
479×	`cube-prod_binary64`

Counts

135 → 104

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	296
1	30	296
2	60	296
3	112	296
4	238	296
5	615	296
6	880	296
7	1431	296
8	1811	296
9	2371	296
10	2825	296
11	3538	296
12	3828	296
13	4474	296
14	4974	296
15	4644	296

prune57.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	123	8	131

Error

0.1b

Counts

131 → 8

Alt Table

Status	Error	Program
▶	1.4b	(*.f64 (pow.f64 (cbrt.f64 2) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
	43.4b	(sqrt.f64 (sqrt.f64 (*.f64 4 (pow.f64 x 4))))
	32.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
✓	27.4b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	27.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 1505 to 1145 computations (23.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 (cbrt.f64 2) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
✓	0.5b	(pow.f64 (cbrt.f64 x) 2)
✓	0.6b	(cbrt.f64 x)
✓	1.0b	(cbrt.f64 2)

series95.0ms (2.9%)

Counts

4 → 36

Calls

4 calls:

41.0ms	(pow.f64 (cbrt.f64 x) 2)
29.0ms	(cbrt.f64 x)
24.0ms	(*.f64 (pow.f64 (cbrt.f64 2) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
0.0ms	(cbrt.f64 2)

rewrite48.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

90× egg-rr

Counts

4 → 90

Calls

2 calls:

46.0ms	((cbrt.f64 2) (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (*.f64 (pow.f64 (cbrt.f64 2) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	209	16
2	1801	16
3	5068	16
0	0	0
1	0	0

simplify100.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1185×	`fma-def_binary64`
735×	`sqr-pow_binary64`
412×	`unswap-sqr_binary64`
323×	`*-commutative_binary64`
233×	`pow-sqr_binary64`

Counts

126 → 98

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	240
1	40	240
2	73	240
3	181	240
4	545	240
5	911	240
6	952	240
7	1137	240
8	1388	240
9	1688	240
10	2036	240
11	2398	240
12	2858	240
13	3605	240
14	4489	240
15	4761	240

prune56.0ms (1.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	95	11	106

Error

0.1b

Counts

106 → 11

Alt Table

Status	Error	Program
	1.9b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 2)) 3) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
	32.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	1.6b	(.f64 (pow.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cbrt.f64 2))) (cbrt.f64 (exp.f64 (cbrt.f64 2))))) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 2))))) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	1.4b	(*.f64 (pow.f64 (pow.f64 2 1/3) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
	32.2b	(*.f64 (sqrt.f64 2) x)
✓	1.4b	(*.f64 (pow.f64 (cbrt.f64 2) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
✓	27.4b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	27.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
	12.0b	(.f64 (pow.f64 (cbrt.f64 2) 3/2) (pow.f64 (sqrt.f64 (.f64 x (cbrt.f64 x))) 3/2))

Compiler

Compiled 1518 to 1276 computations (15.9% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2)
✓	0.4b	(*.f64 (pow.f64 (pow.f64 2 1/3) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
	0.5b	(pow.f64 (cbrt.f64 x) 2)
	0.6b	(cbrt.f64 x)

series822.0ms (25.4%)

Counts

2 → 24

Calls

2 calls:

809.0ms	(pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2)
14.0ms	(*.f64 (pow.f64 (pow.f64 2 1/3) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))

rewrite43.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

39× egg-rr

Counts

2 → 38

Calls

2 calls:

42.0ms	((*.f64 (pow.f64 (pow.f64 2 1/3) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2)) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	238	7
2	2011	7
3	4800	7
0	0	0
1	0	0

simplify63.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
3×	`distribute-rgt-in_binary64`
3×	`sub-neg_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Counts

62 → 42

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	92
1	10	92
2	12	92
3	13	92
4	15	92
5	19	92
6	20	92
7	29	92
8	31	92
9	24	92

prune51.0ms (1.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	7	7
Picked	1	0	1
Done	0	3	3
Total	94	12	106

Error

0.1b

Counts

106 → 12

Alt Table

Status	Error	Program
	1.9b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 2)) 3) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
	32.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	1.6b	(.f64 (pow.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cbrt.f64 2))) (cbrt.f64 (exp.f64 (cbrt.f64 2))))) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 2))))) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	2.6b	(*.f64 (pow.f64 (pow.f64 2 1/3) 3/2) (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2) 3/2))
	11.6b	(.f64 (pow.f64 (pow.f64 2 1/3) 3/2) (pow.f64 (sqrt.f64 (.f64 x (cbrt.f64 x))) 3/2))
	32.2b	(*.f64 (sqrt.f64 2) x)
✓	1.4b	(*.f64 (pow.f64 (cbrt.f64 2) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
✓	27.4b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	27.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
	12.0b	(.f64 (pow.f64 (cbrt.f64 2) 3/2) (pow.f64 (sqrt.f64 (.f64 x (cbrt.f64 x))) 3/2))

Compiler

Compiled 1389 to 1154 computations (16.9% saved)

regimes114.0ms (3.5%)

Accuracy

Total 0.3b remaining (76.9%)

Threshold costs 0.3b (76.9%)

Counts

25 → 2

Compiler

Compiled 1327 to 1123 computations (15.4% saved)

bsearch17.0ms (0.5%)

Steps

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

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	25	25
2	33	25
3	38	25
4	40	25
5	40	25

end158.0ms (4.9%)

Compiler: Compiled 174 to 149 computations (14.4% saved)

Details

analyze4.0ms (0.1%)

sample1.0s (32.4%)

simplify8.0ms (0.2%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite86.0ms (2.7%)

simplify106.0ms (3.3%)

prune39.0ms (1.2%)

localize6.0ms (0.2%)

series113.0ms (3.5%)

rewrite44.0ms (1.4%)

simplify125.0ms (3.8%)

prune57.0ms (1.8%)

localize10.0ms (0.3%)

series95.0ms (2.9%)

rewrite48.0ms (1.5%)

simplify100.0ms (3.1%)

prune56.0ms (1.7%)

localize12.0ms (0.4%)

series822.0ms (25.4%)

rewrite43.0ms (1.3%)

simplify63.0ms (1.9%)

prune51.0ms (1.6%)

regimes114.0ms (3.5%)

bsearch17.0ms (0.5%)

simplify3.0ms (0.1%)

end158.0ms (4.9%)

Profiling