Details

analyze294.0ms (4.7%)

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
25%	74.9%	0.2%	5
25%	74.9%	0.2%	6
25%	74.9%	0.2%	7
37.4%	62.4%	0.2%	8
56.1%	43.7%	0.2%	9
56.1%	43.7%	0.2%	10
56.1%	43.7%	0.2%	11
65.5%	34.3%	0.2%	12
76.4%	23.4%	0.2%	13
76.4%	23.4%	0.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample821.0ms (13.2%)

Symmetry

(sort y t)

Results

742.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-neg_binary64`
750×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
204×	`unsub-neg_binary64`
135×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	35	13
3	88	13
4	231	13
5	568	13
6	1029	13
7	1474	13
8	1787	13
9	1744	13
10	1744	13
11	1905	13
12	1905	13
13	1862	13

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

6.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	6.9b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 t z))
✓	6.9b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

series129.0ms (2.1%)

Counts

2 → 84

Calls

2 calls:

119.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
10.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

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

simplify129.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
452×	`associate-/l*_binary64`
442×	`associate-/r*_binary64`
280×	`associate-l_binary64`
188×	`fma-def_binary64`

Counts

173 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	5441
1	1244	5124
2	4955	5124
3	5000	5124

prune153.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	5	194

Error

0.0b

Counts

194 → 5

Alt Table

Status	Error	Program
	7.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	2.5b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
▶	1.5b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	1.9b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	2.9b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 5638 to 2069 computations (63.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	0.0b	(/.f64 x (-.f64 t z))
✓	1.5b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))

series136.0ms (2.2%)

Counts

3 → 96

Calls

3 calls:

110.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
17.0ms	(/.f64 x (-.f64 t z))
9.0ms	(/.f64 1 (-.f64 y z))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
67×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 156

Calls

3 calls:

16.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
4.0ms	(/.f64 1 (-.f64 y z))
4.0ms	(/.f64 x (-.f64 t z))

simplify112.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

719×	`times-frac_binary64`
570×	`associate-/l*_binary64`
453×	`associate-/r*_binary64`
186×	`associate-*l/_binary64`
181×	`associate-*r/_binary64`

Counts

252 → 278

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	457	6865
1	1402	6443
2	5057	6443

prune206.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	276	2	278
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	276	7	283

Error

Counts

283 → 7

Alt Table

Status	Error	Program
	7.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	2.5b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	1.5b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
▶	1.9b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	23.6b	(.f64 (/.f64 1 (-.f64 y z)) (.f64 (sqrt.f64 (/.f64 x (-.f64 t z))) (sqrt.f64 (/.f64 x (-.f64 t z)))))
	2.9b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	2.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z)))) (-.f64 y z)) (cbrt.f64 (/.f64 x (-.f64 t z))))

Compiler

Compiled 7463 to 2926 computations (60.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cbrt.f64 x) (-.f64 t z))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))

series321.0ms (5.2%)

Counts

4 → 108

Calls

4 calls:

129.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
92.0ms	(cbrt.f64 x)
62.0ms	(/.f64 (cbrt.f64 x) (-.f64 t z))
37.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

rewrite45.0ms (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:

18.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
5.0ms	(/.f64 (cbrt.f64 x) (-.f64 t z))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify134.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

732×	`times-frac_binary64`
661×	`associate-/l*_binary64`
463×	`associate-/r*_binary64`
192×	`fma-def_binary64`
138×	`*-commutative_binary64`

Counts

299 → 333

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	501	7999
1	1545	7170
2	5077	7170

prune265.0ms (4.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	367	0	367
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	367	7	374

Error

Counts

374 → 7

Alt Table

Status	Error	Program
	7.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	2.5b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	1.5b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
✓	1.9b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	23.6b	(.f64 (/.f64 1 (-.f64 y z)) (.f64 (sqrt.f64 (/.f64 x (-.f64 t z))) (sqrt.f64 (/.f64 x (-.f64 t z)))))
	2.9b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
▶	2.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z)))) (-.f64 y z)) (cbrt.f64 (/.f64 x (-.f64 t z))))

Compiler

Compiled 10530 to 2936 computations (72.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z)))) (-.f64 y z)) (cbrt.f64 (/.f64 x (-.f64 t z))))
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z))))
✓	0.6b	(/.f64 (*.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z)))) (-.f64 y z))
✓	15.0b	(cbrt.f64 (/.f64 x (-.f64 t z)))

series1.5s (24.5%)

Counts

4 → 168

Calls

4 calls:

576.0ms	(/.f64 (*.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z)))) (-.f64 y z))
512.0ms	(*.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z))))
303.0ms	(cbrt.f64 (/.f64 x (-.f64 t z)))
130.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z)))) (-.f64 y z)) (cbrt.f64 (/.f64 x (-.f64 t z))))

rewrite95.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

154×	`cbrt-prod_binary64`
151×	`add-sqr-sqrt_binary64`
131×	`*-un-lft-identity_binary64`
123×	`times-frac_binary64`
71×	`add-cube-cbrt_binary64`

Counts

4 → 235

Calls

4 calls:

24.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z)))) (-.f64 y z)) (cbrt.f64 (/.f64 x (-.f64 t z))))
21.0ms	(*.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z))))
15.0ms	(/.f64 (*.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z)))) (-.f64 y z))
3.0ms	(cbrt.f64 (/.f64 x (-.f64 t z)))

simplify268.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

839×	`associate-/l*_binary64`
613×	`fma-def_binary64`
314×	`*-commutative_binary64`
226×	`+-commutative_binary64`
140×	`associate-+r+_binary64`

Counts

403 → 520

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1009	17084
1	2976	16331
2	5988	16331

prune580.0ms (9.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	692	0	692
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	692	7	699

Error

Counts

699 → 7

Alt Table

Status	Error	Program
	7.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	2.5b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	1.5b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
✓	1.9b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	23.6b	(.f64 (/.f64 1 (-.f64 y z)) (.f64 (sqrt.f64 (/.f64 x (-.f64 t z))) (sqrt.f64 (/.f64 x (-.f64 t z)))))
	2.9b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
✓	2.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) (cbrt.f64 (/.f64 x (-.f64 t z)))) (-.f64 y z)) (cbrt.f64 (/.f64 x (-.f64 t z))))

Compiler

Compiled 30535 to 11189 computations (63.4% saved)

regimes584.0ms (9.4%)

Accuracy

Total 1.0b remaining (97.9%)

Threshold costs 0b (0%)

Counts

93 → 3

Compiler

Compiled 10730 to 6305 computations (41.2% saved)

bsearch3.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	31	58
2	36	58
3	38	58
4	39	58
5	37	58

end233.0ms (3.8%)

Compiler: Compiled 301 to 140 computations (53.5% saved)

Details

analyze294.0ms (4.7%)

sample821.0ms (13.2%)

simplify81.0ms (1.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series129.0ms (2.1%)

rewrite26.0ms (0.4%)

simplify129.0ms (2.1%)

prune153.0ms (2.5%)

localize7.0ms (0.1%)

series136.0ms (2.2%)

rewrite37.0ms (0.6%)

simplify112.0ms (1.8%)

prune206.0ms (3.3%)

localize10.0ms (0.2%)

series321.0ms (5.2%)

rewrite45.0ms (0.7%)

simplify134.0ms (2.2%)

prune265.0ms (4.3%)

localize10.0ms (0.2%)

series1.5s (24.5%)

rewrite95.0ms (1.5%)

simplify268.0ms (4.3%)

prune580.0ms (9.3%)

regimes584.0ms (9.4%)

bsearch3.0ms (0%)

simplify4.0ms (0.1%)

end233.0ms (3.8%)

Profiling