Details

analyze175.0ms (4.7%)

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%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.4s (37.7%)

Results

1.3s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify58.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
556×	`cancel-sign-sub-inv_binary64`
552×	`unswap-sqr_binary64`
357×	`unsub-neg_binary64`
344×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	168	37
3	492	37
4	1604	33
5	2891	33
6	4309	33
7	5214	33

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	0.3b	(-.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 3 a))))) 1)

Status

Error

Program

▶

0.1b

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

0.3b

(-.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 3 a))))) 1)

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.5b	(.f64 (.f64 b b) (+.f64 a 3))

series69.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

31.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
19.0ms	(fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1)
11.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
7.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite83.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

307×	`expm1-udef_binary64`
306×	`log1p-udef_binary64`
176×	`add-sqr-sqrt_binary64`
173×	`log1p-expm1-u_binary64`
173×	`expm1-log1p-u_binary64`

Counts

4 → 108

Calls

4 calls:

79.0ms	(fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1)
79.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
79.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
79.0ms	(.f64 (.f64 b b) (+.f64 a 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	87
1	371	87
2	4305	87
3	5096	87

simplify94.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

909×	`fma-def_binary64`
688×	`fma-neg_binary64`
518×	`associate-+l+_binary64`
424×	`distribute-lft-out_binary64`
374×	`associate--l+_binary64`

Counts

204 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	2043
1	247	1828
2	809	1668
3	3272	1643
4	4900	1643
5	4975	1643

prune218.0ms (5.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	165	4	169
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	167	4	171

Error

0.0b

Counts

171 → 4

Alt Table

Status	Error	Program
	25.1b	(log.f64 (exp.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))))
	15.3b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)
	11.5b	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)
▶	0.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))

Compiler

Compiled 5090 to 2996 computations (41.1% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series71.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

32.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
16.0ms	(fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1)
15.0ms	(-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3))
7.0ms	(.f64 (+.f64 3 a) (.f64 b b))

rewrite87.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

300×	`expm1-udef_binary64`
300×	`log1p-udef_binary64`
169×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`

Counts

4 → 121

Calls

4 calls:

84.0ms	(fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1)
84.0ms	(-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3))
84.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
84.0ms	(.f64 (+.f64 3 a) (.f64 b b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	87
1	356	87
2	4240	87
3	5017	87

simplify105.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

909×	`fma-def_binary64`
688×	`fma-neg_binary64`
518×	`associate-+l+_binary64`
424×	`distribute-lft-out_binary64`
374×	`associate--l+_binary64`

Counts

217 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	2043
1	247	1828
2	809	1668
3	3272	1643
4	4900	1643
5	4975	1643

prune199.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	182	4	186

Error

0.0b

Counts

186 → 4

Alt Table

Status	Error	Program
	25.1b	(log.f64 (exp.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))))
	15.3b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)
▶	11.5b	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)
✓	0.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))

Compiler

Compiled 5567 to 3449 computations (38% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 a a 4) (*.f64 a -4))
✓	0.2b	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)
2.0ms	(+.f64 (fma.f64 a a 4) (*.f64 a -4))

rewrite101.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

759×	`prod-diff_binary64`
563×	`fma-udef_binary64`
299×	`fma-def_binary64`
197×	`fma-neg_binary64`
171×	`expm1-udef_binary64`

Counts

2 → 83

Calls

2 calls:

99.0ms	(+.f64 (fma.f64 a a 4) (*.f64 a -4))
99.0ms	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	207	25
2	2337	25
3	4764	25
4	4638	25
5	4895	25

simplify63.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

804×	`unswap-sqr_binary64`
646×	`cancel-sign-sub-inv_binary64`
389×	`fma-def_binary64`
318×	`difference-of-squares_binary64`
270×	`sub-neg_binary64`

Counts

107 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	277
1	76	250
2	164	217
3	464	198
4	1450	198
5	2774	198
6	4907	198

prune96.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	104	4	108

Error

0.0b

Counts

108 → 4

Alt Table

Status	Error	Program
	25.1b	(log.f64 (exp.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))))
	15.3b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)
▶	11.5b	(fma.f64 (*.f64 a a) (fma.f64 a (+.f64 a -4) 4) -1)
✓	0.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))

Compiler

Compiled 1942 to 1177 computations (39.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (+.f64 a -4) 4)
✓	0.2b	(fma.f64 (*.f64 a a) (fma.f64 a (+.f64 a -4) 4) -1)

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 (*.f64 a a) (fma.f64 a (+.f64 a -4) 4) -1)
2.0ms	(fma.f64 a (+.f64 a -4) 4)

rewrite48.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

820×	`log1p-expm1-u_binary64`
820×	`expm1-log1p-u_binary64`
98×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
85×	`add-cbrt-cube_binary64`

Counts

2 → 46

Calls

2 calls:

47.0ms	(fma.f64 a (+.f64 a -4) 4)
47.0ms	(fma.f64 (*.f64 a a) (fma.f64 a (+.f64 a -4) 4) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	188	23
2	2057	23
3	5051	23

simplify49.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

804×	`unswap-sqr_binary64`
646×	`cancel-sign-sub-inv_binary64`
389×	`fma-def_binary64`
318×	`difference-of-squares_binary64`
270×	`sub-neg_binary64`

Counts

70 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	277
1	76	250
2	164	217
3	464	198
4	1450	198
5	2774	198
6	4907	198

prune52.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	67	4	71

Error

0.0b

Counts

71 → 4

Alt Table

Status	Error	Program
	25.1b	(log.f64 (exp.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))))
	15.3b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)
✓	11.5b	(fma.f64 (*.f64 a a) (fma.f64 a (+.f64 a -4) 4) -1)
✓	0.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))

Compiler

Compiled 1056 to 677 computations (35.9% saved)

regimes589.0ms (15.7%)

Accuracy

Total 0.0b remaining (54.6%)

Threshold costs 0.0b (54.6%)

Counts

91 → 1

Compiler

Compiled 9938 to 6978 computations (29.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	35
1	27	35
2	30	35
3	32	35
4	33	35
5	32	35

end112.0ms (3%)

Compiler: Compiled 128 to 88 computations (31.3% saved)

Details

analyze175.0ms (4.7%)

sample1.4s (37.7%)

simplify58.0ms (1.5%)

prune5.0ms (0.1%)

localize17.0ms (0.5%)

series69.0ms (1.8%)

rewrite83.0ms (2.2%)

simplify94.0ms (2.5%)

prune218.0ms (5.8%)

localize16.0ms (0.4%)

series71.0ms (1.9%)

rewrite87.0ms (2.3%)

simplify105.0ms (2.8%)

prune199.0ms (5.3%)

localize8.0ms (0.2%)

series7.0ms (0.2%)

rewrite101.0ms (2.7%)

simplify63.0ms (1.7%)

prune96.0ms (2.6%)

localize6.0ms (0.2%)

series5.0ms (0.1%)

rewrite48.0ms (1.3%)

simplify49.0ms (1.3%)

prune52.0ms (1.4%)

regimes589.0ms (15.7%)

simplify3.0ms (0.1%)

end112.0ms (3%)

Profiling