Details

analyze213.0ms (5.1%)

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)

sample1.3s (30.9%)

Results

1.2s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify57.0ms (1.4%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	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))
	0.2b	(-.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 3 a))))) 1)

Status

Error

Program

▶

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))

0.2b

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

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	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)))
✓	1.0b	(.f64 (.f64 b b) (+.f64 a 3))

series70.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

27.0ms	(+.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))
26.0ms	(pow.f64 (hypot.f64 a b) 4)
10.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
7.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite111.0ms (2.6%)

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 → 105

Calls

4 calls:

72.0ms	(pow.f64 (hypot.f64 a b) 4)
72.0ms	(+.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))
72.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
72.0ms	(.f64 (.f64 b b) (+.f64 a 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	70
1	371	70
2	4305	70
3	5096	70

simplify72.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

730×	`associate-l_binary64`
719×	`fma-def_binary64`
624×	`fma-neg_binary64`
505×	`associate-+l+_binary64`
341×	`distribute-lft-out_binary64`

Counts

201 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	1855
1	207	1761
2	710	1597
3	2967	1573
4	5116	1573

prune203.0ms (4.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	152	3	155

Error

Counts

155 → 3

Alt Table

Status	Error	Program
	14.5b	(+.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
▶	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
	0.0b	(+.f64 (fma.f64 4 (.f64 a (fma.f64 b b a)) (fma.f64 (.f64 b b) (fma.f64 2 (*.f64 a a) 12) (pow.f64 b 4))) (fma.f64 (pow.f64 a 3) (+.f64 a -4) -1))

Compiler

Compiled 4767 to 2788 computations (41.5% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 4 (.f64 a (pow.f64 b 2)))
✓	0.2b	(*.f64 12 (pow.f64 b 2))
✓	0.9b	(*.f64 a (pow.f64 b 2))
✓	3.2b	(*.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))
9.0ms	(.f64 4 (.f64 a (pow.f64 b 2)))
8.0ms	(*.f64 a (pow.f64 b 2))
2.0ms	(*.f64 12 (pow.f64 b 2))

rewrite55.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Counts

4 → 80

Calls

4 calls:

54.0ms	(.f64 4 (.f64 a (pow.f64 b 2)))
54.0ms	(*.f64 12 (pow.f64 b 2))
54.0ms	(*.f64 a (pow.f64 b 2))
54.0ms	(*.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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune136.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	80	3	83

Error

Counts

83 → 3

Alt Table

Status	Error	Program
	14.5b	(+.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
▶	0.0b	(+.f64 (fma.f64 4 (.f64 a (fma.f64 b b a)) (fma.f64 (.f64 b b) (fma.f64 2 (*.f64 a a) 12) (pow.f64 b 4))) (fma.f64 (pow.f64 a 3) (+.f64 a -4) -1))

Compiler

Compiled 4042 to 3056 computations (24.4% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (.f64 a (fma.f64 b b a)) (fma.f64 (.f64 b b) (fma.f64 2 (*.f64 a a) 12) (pow.f64 b 4)))
✓	0.0b	(fma.f64 (pow.f64 a 3) (+.f64 a -4) -1)
✓	0.1b	(*.f64 a (fma.f64 b b a))
✓	1.4b	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 12) (pow.f64 b 4))

series47.0ms (1.1%)

Counts

4 → 84

Calls

4 calls:

19.0ms	(fma.f64 4 (.f64 a (fma.f64 b b a)) (fma.f64 (.f64 b b) (fma.f64 2 (*.f64 a a) 12) (pow.f64 b 4)))
17.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 12) (pow.f64 b 4))
8.0ms	(*.f64 a (fma.f64 b b a))
3.0ms	(fma.f64 (pow.f64 a 3) (+.f64 a -4) -1)

rewrite70.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

458×	`prod-diff_binary64`
186×	`add-sqr-sqrt_binary64`
182×	`log1p-expm1-u_binary64`
182×	`expm1-log1p-u_binary64`
179×	`add-cbrt-cube_binary64`

Counts

4 → 92

Calls

4 calls:

68.0ms	(fma.f64 4 (.f64 a (fma.f64 b b a)) (fma.f64 (.f64 b b) (fma.f64 2 (*.f64 a a) 12) (pow.f64 b 4)))
68.0ms	(fma.f64 (pow.f64 a 3) (+.f64 a -4) -1)
68.0ms	(*.f64 a (fma.f64 b b a))
68.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 12) (pow.f64 b 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	66
1	411	66
2	4200	66
3	4806	66

simplify121.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

740×	`associate-l_binary64`
724×	`fma-neg_binary64`
552×	`unswap-sqr_binary64`
485×	`distribute-rgt-out_binary64`
419×	`associate-r_binary64`

Counts

176 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	1623
1	125	1395
2	329	1209
3	1108	1195
4	2611	1195
5	4672	1195
6	4967	1195
7	4990	1195
8	4949	1195

prune161.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	127	3	130

Error

Counts

130 → 3

Alt Table

Status	Error	Program
▶	14.5b	(+.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
✓	0.0b	(+.f64 (fma.f64 4 (.f64 a (fma.f64 b b a)) (fma.f64 (.f64 b b) (fma.f64 2 (*.f64 a a) 12) (pow.f64 b 4))) (fma.f64 (pow.f64 a 3) (+.f64 a -4) -1))

Compiler

Compiled 4431 to 2481 computations (44% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 8)) (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)))
	1.0b	(.f64 (.f64 b b) (+.f64 a 3))
✓	19.7b	(sqrt.f64 (pow.f64 (hypot.f64 a b) 8))

series54.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(+.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
26.0ms	(sqrt.f64 (pow.f64 (hypot.f64 a b) 8))

rewrite77.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

333×	`log1p-udef_binary64`
191×	`add-sqr-sqrt_binary64`
188×	`log1p-expm1-u_binary64`
188×	`expm1-log1p-u_binary64`
184×	`add-cbrt-cube_binary64`

Counts

2 → 61

Calls

2 calls:

74.0ms	(+.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
74.0ms	(sqrt.f64 (pow.f64 (hypot.f64 a b) 8))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	409	40
2	4704	40
3	5094	40

simplify97.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

624×	`associate-l_binary64`
609×	`fma-def_binary64`
558×	`fma-neg_binary64`
528×	`cancel-sign-sub-inv_binary64`
496×	`associate-+l+_binary64`

Counts

109 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	1227
1	180	1183
2	607	1008
3	2680	990
4	4858	990
5	4993	990
6	4963	990

prune168.0ms (4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	161	3	164

Error

Counts

164 → 3

Alt Table

Status	Error	Program
✓	14.5b	(+.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
✓	0.0b	(+.f64 (fma.f64 4 (.f64 a (fma.f64 b b a)) (fma.f64 (.f64 b b) (fma.f64 2 (*.f64 a a) 12) (pow.f64 b 4))) (fma.f64 (pow.f64 a 3) (+.f64 a -4) -1))

Compiler

Compiled 4990 to 2936 computations (41.2% saved)

regimes940.0ms (22.5%)

Accuracy

Total 0.0b remaining (56.7%)

Threshold costs 0.0b (56.7%)

Counts

173 → 1

Compiler

Compiled 24851 to 17306 computations (30.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	47
1	30	47
2	38	47
3	50	47
4	55	47
5	58	47
6	59	47
7	56	47

end124.0ms (3%)

Compiler: Compiled 175 to 125 computations (28.6% saved)

Details

analyze213.0ms (5.1%)

sample1.3s (30.9%)

simplify57.0ms (1.4%)

prune5.0ms (0.1%)

localize14.0ms (0.3%)

series70.0ms (1.7%)

rewrite111.0ms (2.6%)

simplify72.0ms (1.7%)

prune203.0ms (4.9%)

localize22.0ms (0.5%)

series31.0ms (0.7%)

rewrite55.0ms (1.3%)

simplify7.0ms (0.2%)

prune136.0ms (3.3%)

localize17.0ms (0.4%)

series47.0ms (1.1%)

rewrite70.0ms (1.7%)

simplify121.0ms (2.9%)

prune161.0ms (3.9%)

localize15.0ms (0.3%)

series54.0ms (1.3%)

rewrite77.0ms (1.8%)

simplify97.0ms (2.3%)

prune168.0ms (4%)

regimes940.0ms (22.5%)

simplify3.0ms (0.1%)

end124.0ms (3%)

Profiling