Details

analyze137.0ms (4.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
0%	50%	50%	5
6.2%	31.2%	62.5%	6
9.4%	28.1%	62.5%	7
14%	17.2%	68.8%	8
14.8%	16.4%	68.8%	9
17.6%	9.8%	72.7%	10
18.1%	8.8%	73.1%	11
19.6%	5.2%	75.2%	12
20%	4.5%	75.5%	13
20.7%	2.7%	76.6%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.5s (48.7%)

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))

Results

1.2s	8256×	body	128	valid
68.0ms	483×	body	128	invalid

Compiler

Compiled 112 to 97 computations (13.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
✓	0.2b	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
✓	0.4b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

series122.0ms (4%)

Counts

4 → 41

Calls

4 calls:

71.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
27.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
13.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
11.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

rewrite77.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

723×	`prod-diff_binary64`
142×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`
138×	`expm1-log1p-u_binary64`
136×	`add-log-exp_binary64`

Counts

4 → 126

Calls

4 calls:

74.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
74.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
74.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
74.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	306	49
2	3619	49
3	4971	49
0	0	0
1	0	0

prune153.0ms (5.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	4	168

Error

0.0b

Counts

168 → 4

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))
	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (neg.f64 rand) (.f64 -3 (sqrt.f64 (-.f64 a 1/3))))))
	0.4b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1))) 3)

Compiler

Compiled 3838 to 3130 computations (18.4% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))
✓	0.3b	(/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))

series61.0ms (2%)

Counts

2 → 33

Calls

2 calls:

32.0ms	(/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))
29.0ms	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))

rewrite81.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

657×	`prod-diff_binary64`
132×	`add-sqr-sqrt_binary64`
127×	`log1p-expm1-u_binary64`
127×	`expm1-log1p-u_binary64`
125×	`add-log-exp_binary64`

Counts

2 → 83

Calls

2 calls:

75.0ms	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))
75.0ms	(/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	273	32
2	3568	32
3	4878	32
0	0	0
1	0	0

prune91.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	116	4	120

Error

0.0b

Counts

120 → 4

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
✓	0.1b	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))
▶	0.1b	(pow.f64 (*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 rand 3) (pow.f64 (-.f64 a 1/3) -1/2) 1)) 1)
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1))) 3)

Compiler

Compiled 2719 to 2157 computations (20.7% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (-.f64 a 1/3) -1/2)
✓	0.1b	(*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 rand 3) (pow.f64 (-.f64 a 1/3) -1/2) 1))
✓	0.1b	(fma.f64 (/.f64 rand 3) (pow.f64 (-.f64 a 1/3) -1/2) 1)

series144.0ms (4.7%)

Counts

3 → 60

Calls

3 calls:

71.0ms	(*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 rand 3) (pow.f64 (-.f64 a 1/3) -1/2) 1))
67.0ms	(fma.f64 (/.f64 rand 3) (pow.f64 (-.f64 a 1/3) -1/2) 1)
4.0ms	(pow.f64 (-.f64 a 1/3) -1/2)

rewrite59.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

507×	`log-prod_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
180×	`log-pow_binary64`
125×	`add-sqr-sqrt_binary64`

Counts

3 → 76

Calls

3 calls:

57.0ms	(pow.f64 (-.f64 a 1/3) -1/2)
57.0ms	(*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 rand 3) (pow.f64 (-.f64 a 1/3) -1/2) 1))
57.0ms	(fma.f64 (/.f64 rand 3) (pow.f64 (-.f64 a 1/3) -1/2) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	41
1	260	41
2	2900	41
3	4824	41
0	0	0
1	0	0

prune126.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	136	4	140

Error

0.0b

Counts

140 → 4

Alt Table

Status	Error	Program
▶	0.4b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
✓	0.1b	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))
✓	0.1b	(pow.f64 (*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 rand 3) (pow.f64 (-.f64 a 1/3) -1/2) 1)) 1)
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1))) 3)

Compiler

Compiled 3399 to 2819 computations (17.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
✓	0.2b	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
✓	0.6b	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))

series54.0ms (1.8%)

Counts

3 → 17

Calls

3 calls:

21.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
18.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
15.0ms	(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))

rewrite57.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

970×	`prod-diff_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
102×	`add-sqr-sqrt_binary64`
98×	`log1p-expm1-u_binary64`

Counts

3 → 66

Calls

3 calls:

55.0ms	(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
55.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
55.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	202	34
2	2597	34
3	4964	34
0	0	0
1	0	0

prune67.0ms (2.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	82	5	87

Error

Counts

87 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 (fma.f64 (*.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3)) a) 1/3)
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1))) 3)
✓	0.4b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
✓	0.1b	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))
✓	0.1b	(pow.f64 (*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 rand 3) (pow.f64 (-.f64 a 1/3) -1/2) 1)) 1)

Compiler

Compiled 1638 to 1246 computations (23.9% saved)

regimes189.0ms (6.2%)

Accuracy

Total 0.1b remaining (85.3%)

Threshold costs 0.1b (85.3%)

Counts

45 → 1

Compiler

Compiled 2974 to 2446 computations (17.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	20	21
2	21	21
3	18	21

end95.0ms (3.2%)

Compiler: Compiled 113 to 92 computations (18.6% saved)

Details

analyze137.0ms (4.5%)

sample1.5s (48.7%)

localize10.0ms (0.3%)

series122.0ms (4%)

rewrite77.0ms (2.5%)

prune153.0ms (5.1%)

localize10.0ms (0.3%)

series61.0ms (2%)

rewrite81.0ms (2.7%)

prune91.0ms (3%)

localize10.0ms (0.3%)

series144.0ms (4.7%)

rewrite59.0ms (2%)

prune126.0ms (4.2%)

localize7.0ms (0.2%)

series54.0ms (1.8%)

rewrite57.0ms (1.9%)

prune67.0ms (2.2%)

regimes189.0ms (6.2%)

simplify2.0ms (0.1%)

end95.0ms (3.2%)

Profiling