Details

analyze186.0ms (4.2%)

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)

sample1.4s (31.6%)

Results

1.4s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify59.0ms (1.3%)

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)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a -3 1)
✓	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (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))
✓	0.3b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series50.0ms (1.1%)

Counts

4 → 84

Calls

4 calls:

27.0ms	(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)))
10.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
1.0ms	(fma.f64 a -3 1)

rewrite124.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

440×	`prod-diff_binary64`
320×	`fma-udef_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
209×	`log-pow_binary64`

Counts

4 → 94

Calls

4 calls:

120.0ms	(fma.f64 a -3 1)
120.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
120.0ms	(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))
120.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	64
1	283	64
2	2972	64
3	4897	64
4	4993	64
5	4944	64
0	0	0
1	0	0

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-def_binary64`
541×	`+-commutative_binary64`
524×	`sub-neg_binary64`
420×	`associate--l+_binary64`
415×	`fma-neg_binary64`

Counts

178 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	1651
1	195	1531
2	588	1259
3	2320	1236
4	4266	1236
5	5079	1236

prune183.0ms (4.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	137	4	141

Error

Counts

141 → 4

Alt Table

Status	Error	Program
	8.9b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))) (.f64 12 (.f64 a (pow.f64 b 2)))) -1)
	23.8b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 b a) 8)) (-.f64 (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (pow.f64 (hypot.f64 b a) 4))) -1)
	0.4b	(+.f64 (pow.f64 (cbrt.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 b a) 4))) 3) -1)
▶	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) 1)) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 4039 to 2286 computations (43.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series73.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

28.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) 1)) (pow.f64 (hypot.f64 a b) 4))
26.0ms	(pow.f64 (hypot.f64 a b) 4)
10.0ms	(hypot.f64 a b)
8.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) 1))

rewrite54.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

865×	`log1p-expm1-u_binary64`
865×	`expm1-log1p-u_binary64`
346×	`prod-diff_binary64`
103×	`add-sqr-sqrt_binary64`
98×	`add-cbrt-cube_binary64`

Counts

4 → 81

Calls

4 calls:

53.0ms	(hypot.f64 a b)
53.0ms	(pow.f64 (hypot.f64 a b) 4)
52.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) 1))
52.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) 1)) (pow.f64 (hypot.f64 a b) 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	224	45
2	2244	45
3	5871	45
0	0	0
1	0	0

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

550×	`fma-def_binary64`
526×	`cancel-sign-sub-inv_binary64`
494×	`fma-neg_binary64`
280×	`associate-+l+_binary64`
228×	`neg-mul-1_binary64`

Counts

177 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	1864
1	258	1742
2	799	1616
3	3182	1616
4	4779	1616
5	5080	1616

prune175.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	146	4	150

Error

Counts

150 → 4

Alt Table

Status	Error	Program
	8.9b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))) (.f64 12 (.f64 a (pow.f64 b 2)))) -1)
	23.8b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 b a) 8)) (-.f64 (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (pow.f64 (hypot.f64 b a) 4))) -1)
▶	0.6b	(+.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4))) 3) -1)
✓	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) 1)) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 3931 to 2056 computations (47.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (fma.f64 a a a) (*.f64 b b))
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4))
✓	0.6b	(pow.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4))) 3)
✓	11.9b	(cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4)))

series422.0ms (9.4%)

Counts

4 → 96

Calls

4 calls:

305.0ms	(pow.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4))) 3)
76.0ms	(cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4)))
28.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4))
12.0ms	(fma.f64 a (fma.f64 a a a) (*.f64 b b))

rewrite127.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

491×	`log-prod_binary64`
342×	`prod-diff_binary64`
224×	`fma-udef_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`

Counts

4 → 138

Calls

4 calls:

123.0ms	(fma.f64 a (fma.f64 a a a) (*.f64 b b))
123.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4))
123.0ms	(pow.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4))) 3)
123.0ms	(cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	80
1	253	80
2	2584	80
3	4926	80
4	4984	80
5	4908	80
0	0	0
1	0	0

simplify96.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
390×	`associate-+l+_binary64`
378×	`associate-r_binary64`
235×	`associate-l_binary64`
183×	`associate-/l*_binary64`

Counts

234 → 179

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	442	6220
1	1480	5731
2	5286	5731

prune375.0ms (8.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	179	4	183

Error

Counts

183 → 4

Alt Table

Status	Error	Program
▶	8.9b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))) (.f64 12 (.f64 a (pow.f64 b 2)))) -1)
	23.8b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 b a) 8)) (-.f64 (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (pow.f64 (hypot.f64 b a) 4))) -1)
✓	0.6b	(+.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4))) 3) -1)
✓	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) 1)) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 10196 to 6684 computations (34.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 4 (pow.f64 a 2))
✓	0.2b	(.f64 12 (.f64 a (pow.f64 b 2)))
✓	0.4b	(*.f64 a (pow.f64 b 2))
✓	2.4b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series31.0ms (0.7%)

Counts

4 → 0

Calls

4 calls:

11.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
10.0ms	(.f64 12 (.f64 a (pow.f64 b 2)))
7.0ms	(*.f64 a (pow.f64 b 2))
2.0ms	(*.f64 4 (pow.f64 a 2))

rewrite63.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

538×	`log-prod_binary64`
277×	`pow2_binary64`
233×	`pow-unpow_binary64`
195×	`pow1/3_binary64`
194×	`pow3_binary64`

Counts

4 → 77

Calls

4 calls:

61.0ms	(*.f64 4 (pow.f64 a 2))
61.0ms	(.f64 12 (.f64 a (pow.f64 b 2)))
61.0ms	(*.f64 a (pow.f64 b 2))
61.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	246	31
2	2469	31
3	5168	31
0	0	0
1	0	0

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune135.0ms (3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	77	4	81

Error

Counts

81 → 4

Alt Table

Status	Error	Program
✓	8.9b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))) (.f64 12 (.f64 a (pow.f64 b 2)))) -1)
	23.8b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 b a) 8)) (-.f64 (.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (pow.f64 (hypot.f64 b a) 4))) -1)
✓	0.6b	(+.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 b b)) (pow.f64 (hypot.f64 a b) 4))) 3) -1)
✓	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) 1)) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 3121 to 2319 computations (25.7% saved)

regimes564.0ms (12.6%)

Accuracy

Total 0.0b remaining (46.7%)

Threshold costs 0.0b (46.7%)

Counts

94 → 1

Compiler

Compiled 11259 to 7919 computations (29.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
2	19	32

end118.0ms (2.6%)

Compiler: Compiled 198 to 127 computations (35.9% saved)

Details

analyze186.0ms (4.2%)

sample1.4s (31.6%)

simplify59.0ms (1.3%)

prune5.0ms (0.1%)

localize13.0ms (0.3%)

series50.0ms (1.1%)

rewrite124.0ms (2.8%)

simplify80.0ms (1.8%)

prune183.0ms (4.1%)

localize11.0ms (0.2%)

series73.0ms (1.6%)

rewrite54.0ms (1.2%)

simplify85.0ms (1.9%)

prune175.0ms (3.9%)

localize14.0ms (0.3%)

series422.0ms (9.4%)

rewrite127.0ms (2.8%)

simplify96.0ms (2.1%)

prune375.0ms (8.4%)

localize15.0ms (0.3%)

series31.0ms (0.7%)

rewrite63.0ms (1.4%)

simplify7.0ms (0.2%)

prune135.0ms (3%)

regimes564.0ms (12.6%)

simplify2.0ms (0.1%)

end118.0ms (2.6%)

Profiling