Details

analyze192.0ms (5.4%)

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 (35.2%)

Results

1.2s	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify33.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
312×	`+-commutative_binary64`
277×	`fma-neg_binary64`
232×	`associate-+l+_binary64`
211×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	193	36
3	742	36
4	2867	32
5	4882	32

Stop Event

1×	node limit

Counts

1 → 2

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
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
	0.1b	(-.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)

Status

Error

Program

▶

0.0b

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

0.1b

(-.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)

Compiler

Compiled 172 to 109 computations (36.6% 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	(.f64 b (.f64 b (fma.f64 a -3 1)))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))
✓	0.1b	(*.f64 b (fma.f64 a -3 1))

series25.0ms (0.7%)

Counts

4 → 84

Calls

4 calls:

11.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))
8.0ms	(.f64 b (.f64 b (fma.f64 a -3 1)))
5.0ms	(*.f64 b (fma.f64 a -3 1))
1.0ms	(fma.f64 a -3 1)

rewrite51.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

830×	`log1p-expm1-u_binary64`
830×	`expm1-log1p-u_binary64`
328×	`prod-diff_binary64`
95×	`add-sqr-sqrt_binary64`
87×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	195	43
2	2243	43

Stop Event

1×	node limit

Counts

4 → 80

Calls

4 calls:

49.0ms	(fma.f64 a -3 1)
49.0ms	(.f64 b (.f64 b (fma.f64 a -3 1)))
49.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))
49.0ms	(*.f64 b (fma.f64 a -3 1))

simplify43.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

571×	`cancel-sign-sub-inv_binary64`
533×	`fma-neg_binary64`
442×	`fma-def_binary64`
372×	`associate-l_binary64`
269×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	1149
1	86	1002
2	240	838
3	691	834
4	2640	834

Stop Event

1×	node limit

Counts

164 → 107

prune106.0ms (3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	107	2	109

Error

0.0b

Counts

109 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
▶	0.1b	(-.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)

Status

Error

Program

✓

0.0b

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

▶

0.1b

(-.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)

Compiler

Compiled 2862 to 1623 computations (43.3% saved)

localize15.0ms (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))))))
✓	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series43.0ms (1.2%)

Counts

4 → 84

Calls

4 calls:

22.0ms	(+.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))))))
10.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
2.0ms	(.f64 (.f64 a a) (+.f64 1 a))

rewrite39.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

209×	`log1p-expm1-u_binary64`
209×	`expm1-log1p-u_binary64`
205×	`add-sqr-sqrt_binary64`
202×	`add-cbrt-cube_binary64`
195×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	73
1	442	65

Stop Event

1×	node limit

Counts

4 → 82

Calls

4 calls:

37.0ms	(+.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))))))
37.0ms	(.f64 (.f64 a a) (+.f64 1 a))
37.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
37.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

simplify45.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
528×	`cancel-sign-sub-inv_binary64`
408×	`associate--l+_binary64`
384×	`associate-+l+_binary64`
323×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	1606
1	180	1537
2	611	1321
3	2857	1298

Stop Event

1×	node limit

Counts

166 → 124

prune172.0ms (4.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	123	3	126

Error

Counts

126 → 3

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.1b	(-.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)
	0.1b	(-.f64 (+.f64 (fma.f64 4 (.f64 a (fma.f64 a a a)) (pow.f64 a 4)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (*.f64 a 2) 12))))) 1)

Compiler

Compiled 4469 to 2837 computations (36.5% saved)

localize29.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
	0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	2.4b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series32.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

23.0ms

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

10.0ms

(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite36.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

261×	`log1p-expm1-u_binary64`
261×	`expm1-log1p-u_binary64`
249×	`add-cbrt-cube_binary64`
240×	`add-log-exp_binary64`
239×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	55
1	558	51

Stop Event

1×	node limit

Counts

2 → 44

Calls

2 calls:

34.0ms

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

34.0ms

(*.f64 (pow.f64 a 2) (pow.f64 b 2))

simplify30.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

599×	`associate-l_binary64`
534×	`fma-def_binary64`
487×	`cancel-sign-sub-inv_binary64`
388×	`associate-+l+_binary64`
289×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	799
1	149	767
2	517	604
3	2602	581

Stop Event

1×	node limit

Counts

68 → 68

prune185.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	114	3	117

Error

Counts

117 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.1b	(-.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)
▶	0.1b	(-.f64 (+.f64 (fma.f64 4 (.f64 a (fma.f64 a a a)) (pow.f64 a 4)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (*.f64 a 2) 12))))) 1)

Compiler

Compiled 4428 to 3130 computations (29.3% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 a (-.f64 (.f64 a 2) 12))
✓	0.1b	(*.f64 a (fma.f64 a a a))
✓	0.1b	(fma.f64 4 (*.f64 a (fma.f64 a a a)) (pow.f64 a 4))
✓	1.1b	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (.f64 a 2) 12))))

series27.0ms (0.7%)

Counts

4 → 60

Calls

4 calls:

17.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (.f64 a 2) 12))))
4.0ms	(fma.f64 4 (*.f64 a (fma.f64 a a a)) (pow.f64 a 4))
3.0ms	(*.f64 a (fma.f64 a a a))
2.0ms	(.f64 a (-.f64 (.f64 a 2) 12))

rewrite68.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

319×	`log1p-udef_binary64`
181×	`add-sqr-sqrt_binary64`
176×	`log1p-expm1-u_binary64`
176×	`expm1-log1p-u_binary64`
174×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	375	50
2	4849	50

Stop Event

1×	node limit

Counts

4 → 84

Calls

4 calls:

65.0ms	(.f64 a (-.f64 (.f64 a 2) 12))
65.0ms	(*.f64 a (fma.f64 a a a))
65.0ms	(fma.f64 4 (*.f64 a (fma.f64 a a a)) (pow.f64 a 4))
65.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (.f64 a 2) 12))))

simplify34.0ms (1%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-def_binary64`
674×	`associate-l_binary64`
479×	`associate-r_binary64`
191×	`cancel-sign-sub-inv_binary64`
163×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	1073
1	110	905
2	318	785
3	1146	698

Stop Event

1×	node limit

Counts

144 → 117

prune167.0ms (4.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	117	3	120

Error

Counts

120 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.1b	(-.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)
✓	0.1b	(-.f64 (+.f64 (fma.f64 4 (.f64 a (fma.f64 a a a)) (pow.f64 a 4)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (*.f64 a 2) 12))))) 1)

Compiler

Compiled 4033 to 2327 computations (42.3% saved)

regimes790.0ms (22.2%)

Accuracy

Total 0.0b remaining (44%)

Threshold costs 0.0b (44%)

Counts

134 → 1

Compiler

Compiled 19392 to 13695 computations (29.4% 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	18	39
1	25	39
2	26	39

Stop Event

1×

saturated

end106.0ms (3%)

Compiler: Compiled 166 to 113 computations (31.9% saved)

Details

analyze192.0ms (5.4%)

sample1.3s (35.2%)

simplify33.0ms (0.9%)

prune5.0ms (0.1%)

localize16.0ms (0.4%)

series25.0ms (0.7%)

rewrite51.0ms (1.4%)

simplify43.0ms (1.2%)

prune106.0ms (3%)

localize15.0ms (0.4%)

series43.0ms (1.2%)

rewrite39.0ms (1.1%)

simplify45.0ms (1.3%)

prune172.0ms (4.8%)

localize29.0ms (0.8%)

series32.0ms (0.9%)

rewrite36.0ms (1%)

simplify30.0ms (0.9%)

prune185.0ms (5.2%)

localize17.0ms (0.5%)

series27.0ms (0.7%)

rewrite68.0ms (1.9%)

simplify34.0ms (1%)

prune167.0ms (4.7%)

regimes790.0ms (22.2%)

simplify2.0ms (0.1%)

end106.0ms (3%)

Profiling