Details

analyze688.0ms (16.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
12.5%	87.3%	0.2%	7
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
43.7%	56.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.1s (26.4%)

Symmetry

(sort z t)

Results

977.0ms	8256×	body	128	valid
53.0ms	408×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify116.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1226×	`div-sub_binary64`
778×	`fma-def_binary64`
701×	`unsub-neg_binary64`
456×	`sub-neg_binary64`
437×	`fma-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	16
2	50	16
3	121	16
4	299	16
5	674	16
6	1361	16
7	2742	16
8	3706	16
9	3871	16
10	4083	16
11	4304	16
12	4387	16
13	5424	16

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	6.1b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series102.0ms (2.4%)

Counts

2 → 84

Calls

2 calls:

91.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
11.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

rewrite64.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

745×	`prod-diff_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
110×	`add-sqr-sqrt_binary64`
105×	`log1p-expm1-u_binary64`

Counts

2 → 79

Calls

2 calls:

62.0ms	(*.f64 (-.f64 y z) (-.f64 y t))
62.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	206	23
2	3030	23
3	5203	23
0	0	0
1	0	0

simplify65.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

646×	`times-frac_binary64`
502×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
247×	`associate-r_binary64`
220×	`associate-l_binary64`

Counts

163 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	278	4329
1	1070	4092
2	5240	4092

prune123.0ms (3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	4	143

Error

Counts

143 → 4

Alt Table

Status	Error	Program
	0.3b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
▶	0.3b	(-.f64 1 (pow.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x) -1))
	1.3b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	0.8b	(-.f64 1 (*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 y t))))

Compiler

Compiled 5000 to 2287 computations (54.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.9b	(pow.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x) -1)
✓	5.5b	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

series134.0ms (3.2%)

Counts

2 → 96

Calls

2 calls:

102.0ms	(pow.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x) -1)
31.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

rewrite68.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

745×	`prod-diff_binary64`
229×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`
123×	`log1p-expm1-u_binary64`
123×	`expm1-log1p-u_binary64`

Counts

2 → 96

Calls

2 calls:

66.0ms	(pow.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x) -1)
66.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	248	26
2	3422	26
3	5321	26
0	0	0
1	0	0

simplify78.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

646×	`times-frac_binary64`
524×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
248×	`associate-r_binary64`
216×	`associate-l_binary64`

Counts

192 → 166

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	296	4996
1	1121	4823
2	5048	4823

prune182.0ms (4.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	218	3	221

Error

Counts

221 → 3

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y t)) (-.f64 y z)))
✓	0.3b	(-.f64 1 (pow.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x) -1))

Compiler

Compiled 6421 to 2859 computations (55.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.8b	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))
✓	5.4b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))

series270.0ms (6.5%)

Counts

2 → 84

Calls

2 calls:

168.0ms	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))
102.0ms	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))

rewrite139.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

727×	`prod-diff_binary64`
220×	`log1p-udef_binary64`
124×	`add-sqr-sqrt_binary64`
117×	`log1p-expm1-u_binary64`
117×	`expm1-log1p-u_binary64`

Counts

2 → 59

Calls

2 calls:

137.0ms	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))
137.0ms	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	242	26
2	3218	26
3	5061	26
0	0	0
1	0	0

simplify98.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

747×	`associate-/l*_binary64`
702×	`associate-/r*_binary64`
228×	`fma-def_binary64`
158×	`+-commutative_binary64`
145×	`associate-*r/_binary64`

Counts

143 → 150

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	449	6894
1	1681	6689
2	5004	6689

prune190.0ms (4.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	201	3	204

Error

Counts

204 → 3

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
▶	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y t)) (-.f64 y z)))
✓	0.3b	(-.f64 1 (pow.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x) -1))

Compiler

Compiled 8178 to 4092 computations (50% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y t))
✓	2.4b	(/.f64 (/.f64 x (-.f64 y t)) (-.f64 y z))

series110.0ms (2.6%)

Counts

2 → 72

Calls

2 calls:

94.0ms	(/.f64 (/.f64 x (-.f64 y t)) (-.f64 y z))
16.0ms	(/.f64 x (-.f64 y t))

rewrite63.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

754×	`prod-diff_binary64`
210×	`log1p-udef_binary64`
114×	`add-sqr-sqrt_binary64`
109×	`log1p-expm1-u_binary64`
109×	`expm1-log1p-u_binary64`

Counts

2 → 79

Calls

2 calls:

62.0ms	(/.f64 x (-.f64 y t))
62.0ms	(/.f64 (/.f64 x (-.f64 y t)) (-.f64 y z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	212	20
2	3226	20
3	5163	20
0	0	0
1	0	0

simplify72.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

656×	`times-frac_binary64`
523×	`associate-/l*_binary64`
407×	`associate-/r*_binary64`
244×	`associate-r_binary64`
216×	`associate-l_binary64`

Counts

151 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	297	4378
1	1116	4229
2	5010	4229

prune116.0ms (2.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	142	3	145

Error

Counts

145 → 3

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
✓	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y t)) (-.f64 y z)))
✓	0.3b	(-.f64 1 (pow.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x) -1))

Compiler

Compiled 4997 to 2303 computations (53.9% saved)

regimes286.0ms (6.9%)

Accuracy

Total 0.6b remaining (97.3%)

Threshold costs 0.6b (97.3%)

Counts

46 → 1

Compiler

Compiled 5256 to 3718 computations (29.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	32	16
3	40	16
4	45	16
5	46	16
6	45	16

end64.0ms (1.5%)

Remove: (sort z t)
Compiler: Compiled 109 to 74 computations (32.1% saved)

Details

analyze688.0ms (16.5%)

sample1.1s (26.4%)

simplify116.0ms (2.8%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series102.0ms (2.4%)

rewrite64.0ms (1.5%)

simplify65.0ms (1.6%)

prune123.0ms (3%)

localize8.0ms (0.2%)

series134.0ms (3.2%)

rewrite68.0ms (1.6%)

simplify78.0ms (1.9%)

prune182.0ms (4.4%)

localize8.0ms (0.2%)

series270.0ms (6.5%)

rewrite139.0ms (3.3%)

simplify98.0ms (2.3%)

prune190.0ms (4.6%)

localize7.0ms (0.2%)

series110.0ms (2.6%)

rewrite63.0ms (1.5%)

simplify72.0ms (1.7%)

prune116.0ms (2.8%)

regimes286.0ms (6.9%)

simplify2.0ms (0.1%)

end64.0ms (1.5%)

Profiling