Details

analyze183.0ms (4.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.3s (31.3%)

Results

1.2s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify61.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

▶

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 172 to 108 computations (37.2% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a -3 1)
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
✓	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.5b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series56.0ms (1.3%)

Counts

4 → 84

Calls

4 calls:

32.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
11.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
11.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
2.0ms	(fma.f64 a -3 1)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`fma-udef_binary64`

Counts

4 → 53

Calls

4 calls:

4.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.0ms	(fma.f64 a -3 1)

simplify102.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
528×	`fma-neg_binary64`
415×	`associate-+l+_binary64`
313×	`cancel-sign-sub-inv_binary64`
229×	`associate-+r+_binary64`

Counts

137 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2754
1	318	2352
2	969	2192
3	3184	2169
4	4818	2143
5	4983	2143

prune153.0ms (3.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	125	2	127

Error

0.0b

Counts

127 → 2

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

▶

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

✓

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 3526 to 1963 computations (44.3% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
✓	0.0b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.5b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series152.0ms (3.6%)

Counts

4 → 84

Calls

4 calls:

72.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
65.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
12.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
3.0ms	(.f64 (.f64 a a) (+.f64 1 a))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
15×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 102

Calls

4 calls:

8.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
7.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
6.0ms	(.f64 (.f64 a a) (+.f64 1 a))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify88.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

870×	`distribute-rgt-in_binary64`
807×	`distribute-lft-in_binary64`
278×	`cancel-sign-sub-inv_binary64`
257×	`associate-l_binary64`
213×	`associate-r_binary64`

Counts

186 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	3661
1	577	3211
2	1997	3007
3	5819	3007

prune218.0ms (5.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	188	4	192

Error

0.0b

Counts

192 → 4

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	18.1b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	18.0b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) 3)) 1)

Compiler

Compiled 7202 to 4087 computations (43.3% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4))
✓	0.2b	(pow.f64 (fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) 3)
✓	32.6b	(cbrt.f64 (pow.f64 (fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) 3))

series183.0ms (4.4%)

Counts

4 → 96

Calls

4 calls:

74.0ms	(pow.f64 (fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) 3)
41.0ms	(pow.f64 (hypot.f64 a b) 4)
35.0ms	(cbrt.f64 (pow.f64 (fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) 3))
33.0ms	(fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
12×	`add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`

Counts

4 → 78

Calls

4 calls:

2.0ms	(cbrt.f64 (pow.f64 (fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) 3))
1.0ms	(pow.f64 (fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) 3)
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4))

simplify157.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-def_binary64`
496×	`associate-+r+_binary64`
319×	`associate-+l+_binary64`
300×	`+-commutative_binary64`
225×	`associate-r_binary64`

Counts

174 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	6771
1	1048	6188
2	4171	6167
3	4892	6167
4	4951	6167

prune279.0ms (6.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	160	4	164

Error

0.0b

Counts

164 → 4

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	18.1b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	18.0b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) 3)) 1)

Compiler

Compiled 7060 to 4809 computations (31.9% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.2b	(pow.f64 (pow.f64 (hypot.f64 a b) 2) 6)
	0.5b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	27.9b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 6))

series65.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 6))
32.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) 6)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`unpow-prod-down_binary64`
12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 48

Calls

2 calls:

2.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) 6)
2.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 6))

simplify135.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

659×	`log-prod_binary64`
593×	`exp-prod_binary64`
531×	`associate-l_binary64`
487×	`associate-r_binary64`
303×	`fma-def_binary64`

Counts

96 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1810
1	251	1620
2	671	1491
3	2593	1444
4	4235	1444
5	5207	1444

prune228.0ms (5.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	181	4	185

Error

0.0b

Counts

185 → 4

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	18.1b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	18.0b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (fma.f64 (-.f64 1 (.f64 3 a)) (.f64 b b) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) 3)) 1)

Compiler

Compiled 6692 to 4356 computations (34.9% saved)

regimes556.0ms (13.4%)

Accuracy

Total 0.0b remaining (49.5%)

Threshold costs 0.0b (49.5%)

Counts

99 → 1

Compiler

Compiled 12867 to 9086 computations (29.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	34
1	23	34
2	22	34

end116.0ms (2.8%)

Compiler: Compiled 171 to 118 computations (31% saved)

Details

analyze183.0ms (4.4%)

sample1.3s (31.3%)

simplify61.0ms (1.5%)

prune5.0ms (0.1%)

localize16.0ms (0.4%)

series56.0ms (1.3%)

rewrite8.0ms (0.2%)

simplify102.0ms (2.5%)

prune153.0ms (3.7%)

localize16.0ms (0.4%)

series152.0ms (3.6%)

rewrite29.0ms (0.7%)

simplify88.0ms (2.1%)

prune218.0ms (5.2%)

localize18.0ms (0.4%)

series183.0ms (4.4%)

rewrite9.0ms (0.2%)

simplify157.0ms (3.8%)

prune279.0ms (6.7%)

localize19.0ms (0.4%)

series65.0ms (1.6%)

rewrite7.0ms (0.2%)

simplify135.0ms (3.2%)

prune228.0ms (5.5%)

regimes556.0ms (13.4%)

simplify3.0ms (0.1%)

end116.0ms (2.8%)

Profiling