Details

analyze715.0ms (5.4%)

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 (8.1%)

Symmetry

(sort z t)

Results

942.0ms	8256×	body	128	valid
48.0ms	421×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify120.0ms (0.9%)

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

1.3b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	6.4b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series241.0ms (1.8%)

Counts

3 → 132

Calls

3 calls:

130.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
102.0ms	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
9.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`prod-diff_binary64`
54×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
40×	`associate-/r/_binary64`

Counts

3 → 168

Calls

3 calls:

8.0ms	(*.f64 (-.f64 y z) (-.f64 y t))
8.0ms	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
7.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

simplify186.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

787×	`times-frac_binary64`
279×	`fma-def_binary64`
192×	`distribute-rgt-in_binary64`
175×	`distribute-lft-in_binary64`
165×	`sub-neg_binary64`

Counts

300 → 344

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	627	13333
1	1955	11667
2	5135	11667

prune349.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	338	6	344
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	338	7	345

Error

Counts

345 → 7

Alt Table

Status	Error	Program
✓	1.3b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
	0.9b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t))))
	0.6b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
▶	0.3b	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	1.3b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
	1.6b	(-.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 y t)))) (cbrt.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 y t))))) (cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))))
	10.3b	(-.f64 1 (cbrt.f64 (pow.f64 (/.f64 x (*.f64 (-.f64 y t) (-.f64 y z))) 3)))

Compiler

Compiled 14051 to 5046 computations (64.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
✓	0.0b	(/.f64 x (-.f64 y t))
✓	1.0b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t))))
✓	1.1b	(/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))

series282.0ms (2.2%)

Counts

4 → 168

Calls

4 calls:

134.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t))))
101.0ms	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
28.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))
18.0ms	(/.f64 x (-.f64 y t))

rewrite703.0ms (5.4%)

Algorithm

1×	rewrite-expression-head

Rules

4764×	`times-frac_binary64`
3332×	`add-sqr-sqrt_binary64`
3309×	`*-un-lft-identity_binary64`
2053×	`add-cube-cbrt_binary64`
1005×	`prod-diff_binary64`

Counts

4 → 2032

Calls

4 calls:

102.0ms	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
20.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t))))
11.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))
3.0ms	(/.f64 x (-.f64 y t))

simplify2.8s (21.6%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-def_binary64`
279×	`neg-sub0_binary64`
276×	`neg-mul-1_binary64`
256×	`associate-/r/_binary64`
234×	`*-commutative_binary64`

Counts

2200 → 1909

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1338	162704
1	4239	161510
2	5022	161510

prune2.4s (17.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1907	2	1909
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	1911	5	1916

Error

Counts

1916 → 5

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 1 (/.f64 -1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	0.6b	(-.f64 1 (*.f64 (/.f64 1 (/.f64 (-.f64 y z) x)) (/.f64 1 (-.f64 y t))))
	0.6b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	1.3b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
	10.3b	(-.f64 1 (cbrt.f64 (pow.f64 (/.f64 x (*.f64 (-.f64 y t) (-.f64 y z))) 3)))

Compiler

Compiled 115596 to 39320 computations (66% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 -1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	0.0b	(/.f64 x (-.f64 y t))
✓	1.0b	(/.f64 -1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t))))
	1.1b	(/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))

series294.0ms (2.2%)

Counts

2 → 96

Calls

2 calls:

194.0ms	(/.f64 -1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t))))
100.0ms	(+.f64 1 (/.f64 -1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))

rewrite185.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

1050×	`times-frac_binary64`
672×	`*-un-lft-identity_binary64`
670×	`add-sqr-sqrt_binary64`
382×	`add-cube-cbrt_binary64`
144×	`distribute-lft-out--_binary64`

Counts

2 → 479

Calls

2 calls:

59.0ms	(+.f64 1 (/.f64 -1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
22.0ms	(/.f64 -1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t))))

simplify394.0ms (3%)

Algorithm

1×	egg-herbie

Rules

843×	`times-frac_binary64`
583×	`associate-/r/_binary64`
190×	`fma-def_binary64`
157×	`sub-neg_binary64`
150×	`associate-/l*_binary64`

Counts

575 → 667

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1094	23437
1	3031	23011
2	5018	23011

prune695.0ms (5.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	913	0	913
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	913	5	918

Error

Counts

918 → 5

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 1 (/.f64 -1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	0.6b	(-.f64 1 (*.f64 (/.f64 1 (/.f64 (-.f64 y z) x)) (/.f64 1 (-.f64 y t))))
▶	0.6b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	1.3b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
	10.3b	(-.f64 1 (cbrt.f64 (pow.f64 (/.f64 x (*.f64 (-.f64 y t) (-.f64 y z))) 3)))

Compiler

Compiled 29304 to 10155 computations (65.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y z))
✓	0.0b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	1.6b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))

series284.0ms (2.2%)

Counts

3 → 120

Calls

3 calls:

150.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
114.0ms	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
19.0ms	(/.f64 x (-.f64 y z))

rewrite232.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

936×	`times-frac_binary64`
860×	`add-sqr-sqrt_binary64`
850×	`*-un-lft-identity_binary64`
469×	`add-cube-cbrt_binary64`
333×	`prod-diff_binary64`

Counts

3 → 656

Calls

3 calls:

40.0ms	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
9.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
4.0ms	(/.f64 x (-.f64 y z))

simplify712.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
423×	`fma-def_binary64`
233×	`*-commutative_binary64`
221×	`neg-mul-1_binary64`
219×	`neg-sub0_binary64`

Counts

776 → 776

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1142	53032
1	3796	51855
2	5232	51855

prune620.0ms (4.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	776	0	776
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	776	5	781

Error

Counts

781 → 5

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 1 (/.f64 -1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	0.6b	(-.f64 1 (*.f64 (/.f64 1 (/.f64 (-.f64 y z) x)) (/.f64 1 (-.f64 y t))))
✓	0.6b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	1.3b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
	10.3b	(-.f64 1 (cbrt.f64 (pow.f64 (/.f64 x (*.f64 (-.f64 y t) (-.f64 y z))) 3)))

Compiler

Compiled 40506 to 9244 computations (77.2% saved)

regimes583.0ms (4.4%)

Accuracy

Total 1.0b remaining (99.2%)

Threshold costs 1.0b (99.2%)

Counts

94 → 1

Compiler

Compiled 11279 to 7739 computations (31.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	23	22
2	35	22
3	41	22
4	44	22
5	42	22

end203.0ms (1.5%)

Compiler: Compiled 160 to 115 computations (28.1% saved)

Details

analyze715.0ms (5.4%)

sample1.1s (8.1%)

simplify120.0ms (0.9%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series241.0ms (1.8%)

rewrite41.0ms (0.3%)

simplify186.0ms (1.4%)

prune349.0ms (2.7%)

localize9.0ms (0.1%)

series282.0ms (2.2%)

rewrite703.0ms (5.4%)

simplify2.8s (21.6%)

prune2.4s (17.9%)

localize9.0ms (0.1%)

series294.0ms (2.2%)

rewrite185.0ms (1.4%)

simplify394.0ms (3%)

prune695.0ms (5.3%)

localize7.0ms (0.1%)

series284.0ms (2.2%)

rewrite232.0ms (1.8%)

simplify712.0ms (5.4%)

prune620.0ms (4.7%)

regimes583.0ms (4.4%)

simplify3.0ms (0%)

end203.0ms (1.5%)

Profiling