Details

analyze601.0ms (8.7%)

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
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
12.5%	87.3%	0.2%	7
18.7%	81.1%	0.2%	8
46.8%	53%	0.2%	9
47.6%	52.2%	0.2%	10
48.3%	51.5%	0.2%	11
54.2%	45.6%	0.2%	12
67.6%	32.2%	0.2%	13
68.2%	31.6%	0.2%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample170.0ms (2.4%)

Algorithm

1×

intervals

Symmetry

(sort y z)

Results

12.0ms	256×	body	128	valid
2.0ms	35×	body	128	invalid

Compiler

Compiled 39 to 31 computations (20.5% saved)

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

382×	`fma-def_binary64`
322×	`fma-neg_binary64`
113×	`cancel-sign-sub-inv_binary64`
53×	`unsub-neg_binary64`
52×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	16
1	27	16
2	51	15
3	95	14
4	192	12
5	326	12
6	479	12
7	626	12
8	798	12
9	857	12
10	783	12

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))

series11.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

11.0ms

(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Rules

422×	`distribute-lft-in_binary64`
422×	`distribute-rgt-in_binary64`
368×	`distribute-lft-neg-out_binary64`
366×	`distribute-rgt-neg-out_binary64`
319×	`associate-l_binary64`

Counts

58 → 29

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	750
1	50	651
2	95	649
3	396	649
4	2320	649
5	4993	649
6	4952	649

prune24.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	2	30

Error

0.0b

Counts

30 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

Status

Error

Program

✓

0.0b

(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))

▶

1.3b

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

Compiler

Compiled 430 to 236 computations (45.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))
✓	0.5b	(cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))
✓	0.6b	(.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

series378.0ms (5.4%)

Counts

3 → 144

Calls

3 calls:

241.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

124.0ms

(cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))

13.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

1.0ms

(cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))

simplify243.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

498×	`*-commutative_binary64`
259×	`+-commutative_binary64`
236×	`fma-def_binary64`
214×	`cancel-sign-sub-inv_binary64`
213×	`sub-neg_binary64`

Counts

237 → 286

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1229	16513
1	4201	15974
2	5298	15974

prune889.0ms (12.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	580	1	581
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	580	3	583

Error

Counts

583 → 3

Alt Table

Status	Error	Program
▶	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))
✓	0.0b	(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

Compiler

Compiled 46797 to 30961 computations (33.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))
✓	0.5b	(.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))))
	0.5b	(cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

series458.0ms (6.6%)

Counts

3 → 144

Calls

3 calls:

317.0ms

(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))))

122.0ms

(cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

18.0ms

(*.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`cbrt-prod_binary64`
37×	`add-sqr-sqrt_binary64`
34×	`pow1_binary64`
24×	`pow1/3_binary64`
23×	`add-exp-log_binary64`

Counts

3 → 109

Calls

3 calls:

12.0ms

(*.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

10.0ms

(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t)))))

1.0ms

(cbrt.f64 (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

simplify396.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

517×	`*-commutative_binary64`
272×	`+-commutative_binary64`
246×	`fma-def_binary64`
218×	`sub-neg_binary64`
202×	`associate-r_binary64`

Counts

253 → 307

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1297	18759
1	4355	17484
2	4994	17484
3	4986	17484

prune2.4s (34%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	1037	0	1037
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	1037	3	1040

Error

Counts

1040 → 3

Alt Table

Status	Error	Program
✓	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))
✓	0.0b	(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t))) (cbrt.f64 (fma.f64 (.f64 y z) -1/2 (fma.f64 1/8 x t)))) (cbrt.f64 (fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))))

Compiler

Compiled 119657 to 78506 computations (34.4% saved)

regimes392.0ms (5.6%)

Accuracy

Total 0.0b remaining (8.5%)

Threshold costs 0.0b (8.5%)

Counts

34 → 1

Compiler

Compiled 10000 to 6377 computations (36.2% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	16
1	22	16
2	28	16
3	38	16
4	45	16
5	50	16
6	52	16
7	50	16

end6.0ms (0.1%)

Remove: (sort y z)
Compiler: Compiled 45 to 33 computations (26.7% saved)

sample815.0ms (11.7%)

Algorithm

1×

intervals

Results

376.0ms	7999×	body	128	valid
54.0ms	1166×	body	128	invalid
2.0ms	1×	body	2048	valid

Compiler

Compiled 147 to 97 computations (34% saved)

Iter	Nodes	Cost
0	15	16
1	27	16
2	51	15
3	95	14
4	192	12
5	326	12
6	479	12
7	626	12
8	798	12
9	857	12
10	783	12

Iter	Nodes	Cost
0	15	16
1	27	16
2	51	15
3	95	14
4	192	12
5	326	12
6	479	12
7	626	12
8	798	12
9	857	12
10	783	12

Details

analyze601.0ms (8.7%)

sample170.0ms (2.4%)

simplify29.0ms (0.4%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

series11.0ms (0.2%)

rewrite1.0ms (0%)

simplify69.0ms (1%)

prune24.0ms (0.3%)

localize10.0ms (0.1%)

series378.0ms (5.4%)

rewrite20.0ms (0.3%)

simplify243.0ms (3.5%)

prune889.0ms (12.8%)

localize12.0ms (0.2%)

series458.0ms (6.6%)

rewrite41.0ms (0.6%)

simplify396.0ms (5.7%)

prune2.4s (34%)

regimes392.0ms (5.6%)

simplify9.0ms (0.1%)

end6.0ms (0.1%)

sample815.0ms (11.7%)

Profiling

Iter	Nodes	Cost
0	15	16
1	27	16
2	51	15
3	95	14
4	192	12
5	326	12
6	479	12
7	626	12
8	798	12
9	857	12
10	783	12