Details

analyze630.0ms (7.1%)

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)

sample1.0s (11.7%)

Symmetry

(sort z t)

Results

920.0ms	8256×	body	128	valid
42.0ms	377×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify121.0ms (1.4%)

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

prune2.0ms (0%)

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	7.5b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series136.0ms (1.5%)

Counts

2 → 84

Calls

2 calls:

127.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
8.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

rewrite64.0ms (0.7%)

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 → 77

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

simplify121.0ms (1.4%)

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

161 → 140

Iterations

Useful iterations: 1 (0.0ms)

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

prune169.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	135	6	141

Error

Counts

141 → 6

Alt Table

Status	Error	Program
	0.3b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	2.6b	(-.f64 1 (*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 y t))))
	29.8b	(-.f64 1 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))))))
✓	0.1b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
	15.3b	(-.f64 1 (pow.f64 (sqrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) 2))
▶	0.3b	(-.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) 3))

Compiler

Compiled 5039 to 2325 computations (53.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.4b	(pow.f64 (cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) 3)
	7.5b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
✓	24.7b	(cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

series3.6s (41.1%)

Counts

2 → 96

Calls

2 calls:

2.3s	(pow.f64 (cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) 3)
1.3s	(cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

rewrite71.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

745×	`prod-diff_binary64`
128×	`add-sqr-sqrt_binary64`
125×	`log1p-expm1-u_binary64`
125×	`expm1-log1p-u_binary64`
120×	`add-cbrt-cube_binary64`

Counts

2 → 93

Calls

2 calls:

69.0ms	(pow.f64 (cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) 3)
69.0ms	(cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	254	28
2	3469	28
3	4929	28
0	0	0
1	0	0

simplify231.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

384×	`associate-+r+_binary64`
311×	`fma-def_binary64`
272×	`associate-r_binary64`
259×	`associate-/l*_binary64`
246×	`associate-/r*_binary64`

Counts

189 → 242

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1704	21995
1	5394	21995

prune673.0ms (7.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	380	2	382
Fresh	3	1	4
Picked	0	1	1
Done	1	0	1
Total	384	4	388

Error

Counts

388 → 4

Alt Table

Status	Error	Program
	0.3b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	2.5b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
▶	0.1b	(-.f64 1 (.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))) x))
✓	0.3b	(-.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) 3))

Compiler

Compiled 36013 to 20047 computations (44.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.4b	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))
✓	7.4b	(.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))) x)

series207.0ms (2.3%)

Counts

2 → 84

Calls

2 calls:

132.0ms	(.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))) x)
74.0ms	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))

rewrite64.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

727×	`prod-diff_binary64`
220×	`log1p-udef_binary64`
123×	`add-sqr-sqrt_binary64`
116×	`log1p-expm1-u_binary64`
116×	`expm1-log1p-u_binary64`

Counts

2 → 58

Calls

2 calls:

63.0ms	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))
63.0ms	(.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	240	26
2	3208	26
3	5052	26
0	0	0
1	0	0

simplify116.0ms (1.3%)

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

142 → 150

Iterations

Useful iterations: 1 (0.0ms)

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

prune193.0ms (2.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	200	4	204

Error

Counts

204 → 4

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	2.5b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	0.1b	(-.f64 1 (.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))) x))
✓	0.3b	(-.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) 3))

Compiler

Compiled 8198 to 4116 computations (49.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y t))
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	1.2b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t)))

series156.0ms (1.8%)

Counts

3 → 96

Calls

3 calls:

132.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t)))
16.0ms	(/.f64 x (-.f64 y t))
8.0ms	(/.f64 1 (-.f64 y z))

rewrite72.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

745×	`prod-diff_binary64`
128×	`add-sqr-sqrt_binary64`
121×	`log1p-expm1-u_binary64`
121×	`expm1-log1p-u_binary64`
118×	`add-cbrt-cube_binary64`

Counts

3 → 111

Calls

3 calls:

70.0ms	(/.f64 x (-.f64 y t))
70.0ms	(/.f64 1 (-.f64 y z))
70.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	248	27
2	3503	27
3	5004	27
0	0	0
1	0	0

simplify87.0ms (1%)

Algorithm

1×	egg-herbie

Rules

668×	`times-frac_binary64`
531×	`associate-/l*_binary64`
417×	`associate-/r*_binary64`
244×	`associate-r_binary64`
216×	`associate-l_binary64`

Counts

207 → 188

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	319	4870
1	1167	4715
2	5026	4715

prune230.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	188	4	192

Error

Counts

192 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	2.5b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	0.1b	(-.f64 1 (.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))) x))
✓	0.3b	(-.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) 3))

Compiler

Compiled 5856 to 2801 computations (52.2% saved)

regimes657.0ms (7.4%)

Accuracy

Total 0.6b remaining (97.9%)

Threshold costs 0.6b (97.9%)

Counts

60 → 1

Compiler

Compiled 6943 to 4905 computations (29.4% saved)

simplify5.0ms (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	12	16
1	21	16
2	33	16
3	41	16
4	46	16
5	47	16
6	46	16

end134.0ms (1.5%)

Remove: (sort z t)
Compiler: Compiled 127 to 87 computations (31.5% saved)

Details

analyze630.0ms (7.1%)

sample1.0s (11.7%)

simplify121.0ms (1.4%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series136.0ms (1.5%)

rewrite64.0ms (0.7%)

simplify121.0ms (1.4%)

prune169.0ms (1.9%)

localize9.0ms (0.1%)

series3.6s (41.1%)

rewrite71.0ms (0.8%)

simplify231.0ms (2.6%)

prune673.0ms (7.6%)

localize8.0ms (0.1%)

series207.0ms (2.3%)

rewrite64.0ms (0.7%)

simplify116.0ms (1.3%)

prune193.0ms (2.2%)

localize11.0ms (0.1%)

series156.0ms (1.8%)

rewrite72.0ms (0.8%)

simplify87.0ms (1%)

prune230.0ms (2.6%)

regimes657.0ms (7.4%)

simplify5.0ms (0.1%)

end134.0ms (1.5%)

Profiling