Details

analyze633.0ms (10.1%)

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)

sample1.1s (17.7%)

Symmetry

(sort z t)

Results

993.0ms	8256×	body	128	valid
49.0ms	411×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify118.0ms (1.9%)

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

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(-.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 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))
✓	4.9b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series307.0ms (4.9%)

Counts

3 → 132

Calls

3 calls:

212.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
87.0ms	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
8.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

rewrite42.0ms (0.7%)

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:

9.0ms	(*.f64 (-.f64 y z) (-.f64 y t))
8.0ms	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
6.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

simplify184.0ms (2.9%)

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

prune315.0ms (5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	340	4	344
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	341	4	345

Error

Counts

345 → 4

Alt Table

Status	Error	Program
	0.5b	(+.f64 1 (neg.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))))
	0.6b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	0.6b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
▶	0.3b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t))))

Compiler

Compiled 13922 to 4982 computations (64.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cbrt.f64 x) (-.f64 y t))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	0.6b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t)))

series272.0ms (4.3%)

Counts

4 → 108

Calls

4 calls:

137.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t)))
62.0ms	(/.f64 (cbrt.f64 x) (-.f64 y t))
36.0ms	(cbrt.f64 x)
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`add-sqr-sqrt_binary64`
79×	`*-un-lft-identity_binary64`
72×	`times-frac_binary64`
54×	`cbrt-prod_binary64`
51×	`add-cube-cbrt_binary64`

Counts

4 → 191

Calls

4 calls:

16.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t)))
6.0ms	(/.f64 (cbrt.f64 x) (-.f64 y t))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify142.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

869×	`times-frac_binary64`
753×	`associate-/l*_binary64`
510×	`associate-/r*_binary64`
209×	`fma-def_binary64`
160×	`*-commutative_binary64`

Counts

299 → 323

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	523	8537
1	1675	7717
2	5621	7717

prune296.0ms (4.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	356	1	357
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	357	4	361

Error

Counts

361 → 4

Alt Table

Status	Error	Program
▶	0.5b	(+.f64 1 (neg.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))))
	0.6b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	0.6b	(-.f64 1 (*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 y t))))
✓	0.3b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t))))

Compiler

Compiled 11375 to 3752 computations (67% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (neg.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))))
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
	4.9b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series98.0ms (1.5%)

Counts

1 → 48

Calls

1 calls:

97.0ms

(+.f64 1 (neg.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`distribute-lft-out_binary64`
2×	`sum-log_binary64`

Counts

1 → 21

Calls

1 calls:

12.0ms

(+.f64 1 (neg.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))))

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

515×	`times-frac_binary64`
391×	`associate-/l*_binary64`
331×	`associate-/r*_binary64`
200×	`associate-r_binary64`
191×	`associate-+r+_binary64`

Counts

69 → 72

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	272	2975
1	981	2813
2	4877	2813
3	5002	2813

prune266.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	257	4	261

Error

Counts

261 → 4

Alt Table

Status	Error	Program
✓	0.5b	(+.f64 1 (neg.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))))
▶	0.6b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	0.6b	(-.f64 1 (*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 y t))))
✓	0.3b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t))))

Compiler

Compiled 9472 to 3989 computations (57.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	0.0b	(/.f64 x (-.f64 y z))
✓	1.4b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))

series241.0ms (3.8%)

Counts

3 → 120

Calls

3 calls:

128.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
94.0ms	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
18.0ms	(/.f64 x (-.f64 y z))

rewrite188.0ms (3%)

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:

36.0ms	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
9.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
5.0ms	(/.f64 x (-.f64 y z))

simplify754.0ms (12%)

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

prune573.0ms (9.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	776	0	776
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	776	4	780

Error

Counts

780 → 4

Alt Table

Status	Error	Program
✓	0.5b	(+.f64 1 (neg.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))))
✓	0.6b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	0.6b	(-.f64 1 (*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 y t))))
✓	0.3b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t))))

Compiler

Compiled 40492 to 9228 computations (77.2% saved)

regimes510.0ms (8.1%)

Accuracy

Total 0.7b remaining (97.5%)

Threshold costs 0.7b (97.5%)

Counts

79 → 1

Compiler

Compiled 10319 to 6779 computations (34.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	27	26
2	44	26
3	58	26
4	68	26
5	72	26
6	73	26
7	72	26

end73.0ms (1.2%)

Remove: (sort z t)
Compiler: Compiled 154 to 102 computations (33.8% saved)

Details

analyze633.0ms (10.1%)

sample1.1s (17.7%)

simplify118.0ms (1.9%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series307.0ms (4.9%)

rewrite42.0ms (0.7%)

simplify184.0ms (2.9%)

prune315.0ms (5%)

localize14.0ms (0.2%)

series272.0ms (4.3%)

rewrite41.0ms (0.7%)

simplify142.0ms (2.2%)

prune296.0ms (4.7%)

localize8.0ms (0.1%)

series98.0ms (1.5%)

rewrite13.0ms (0.2%)

simplify81.0ms (1.3%)

prune266.0ms (4.2%)

localize7.0ms (0.1%)

series241.0ms (3.8%)

rewrite188.0ms (3%)

simplify754.0ms (12%)

prune573.0ms (9.1%)

regimes510.0ms (8.1%)

simplify3.0ms (0%)

end73.0ms (1.2%)

Profiling