Details

analyze694.0ms (10.4%)

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
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)

sample1.2s (18%)

Symmetry

(sort y t)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify97.0ms (1.5%)

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

prune3.0ms (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)

localize12.0ms (0.2%)

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)))

series262.0ms (3.9%)

Counts

2 → 84

Calls

2 calls:

236.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
26.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite51.0ms (0.8%)

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:

20.0ms	(*.f64 (-.f64 y z) (-.f64 t z))
18.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

simplify206.0ms (3.1%)

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

prune285.0ms (4.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	6	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	187	7	194

Error

0.0b

Counts

194 → 7

Alt Table

Status	Error	Program
✓	6.9b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
	21.3b	(.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 z z)))) (+.f64 t z))
▶	2.2b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	2.6b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	37.1b	(/.f64 (sqrt.f64 x) (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) (sqrt.f64 x)))
	23.9b	(.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t z))) (+.f64 y z))
	3.2b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))

Compiler

Compiled 5709 to 2105 computations (63.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cbrt.f64 x) (-.f64 t z))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(cbrt.f64 x)
✓	1.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))

series459.0ms (6.9%)

Counts

4 → 108

Calls

4 calls:

228.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
104.0ms	(/.f64 (cbrt.f64 x) (-.f64 t z))
64.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
62.0ms	(cbrt.f64 x)

rewrite50.0ms (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:

21.0ms	(.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))
5.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify163.0ms (2.4%)

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

prune376.0ms (5.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	364	3	367
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	368	6	374

Error

0.0b

Counts

374 → 6

Alt Table

Status	Error	Program
	2.3b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 1 (/.f64 (-.f64 t z) (cbrt.f64 x))))
✓	6.9b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
	37.1b	(/.f64 (sqrt.f64 x) (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) (sqrt.f64 x)))
	23.9b	(.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t z))) (+.f64 y z))
	2.7b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
▶	2.0b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

Compiler

Compiled 10496 to 2927 computations (72.1% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 t z))
✓	2.0b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

series170.0ms (2.6%)

Counts

2 → 72

Calls

2 calls:

147.0ms	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
22.0ms	(/.f64 x (-.f64 t z))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
176×	`*-un-lft-identity_binary64`
176×	`add-sqr-sqrt_binary64`
88×	`add-cube-cbrt_binary64`
44×	`distribute-lft-out--_binary64`

Counts

2 → 189

Calls

2 calls:

10.0ms	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
5.0ms	(/.f64 x (-.f64 t z))

simplify163.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

540×	`times-frac_binary64`
486×	`associate-/r*_binary64`
474×	`associate-/l*_binary64`
314×	`associate-/l/_binary64`
154×	`fma-def_binary64`

Counts

261 → 270

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	528	8754
1	1585	8488
2	4991	8488

prune294.0ms (4.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	269	7	276

Error

Counts

276 → 7

Alt Table

Status	Error	Program
	2.3b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 1 (/.f64 (-.f64 t z) (cbrt.f64 x))))
✓	6.9b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
	17.6b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 x (-.f64 t z)) 3)) (-.f64 y z))
▶	2.0b	(/.f64 (*.f64 x (/.f64 1 (-.f64 t z))) (-.f64 y z))
	37.1b	(/.f64 (sqrt.f64 x) (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) (sqrt.f64 x)))
	2.7b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
✓	2.0b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

Compiler

Compiled 7653 to 2344 computations (69.4% saved)

localize72.0ms (1.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 t z))
✓	0.2b	(*.f64 x (/.f64 1 (-.f64 t z)))
✓	2.0b	(/.f64 (*.f64 x (/.f64 1 (-.f64 t z))) (-.f64 y z))

series271.0ms (4.1%)

Counts

3 → 108

Calls

3 calls:

221.0ms	(/.f64 (*.f64 x (/.f64 1 (-.f64 t z))) (-.f64 y z))
32.0ms	(*.f64 x (/.f64 1 (-.f64 t z)))
17.0ms	(/.f64 1 (-.f64 t z))

rewrite58.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
31×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`

Counts

3 → 124

Calls

3 calls:

18.0ms	(/.f64 (*.f64 x (/.f64 1 (-.f64 t z))) (-.f64 y z))
16.0ms	(*.f64 x (/.f64 1 (-.f64 t z)))
7.0ms	(/.f64 1 (-.f64 t z))

simplify305.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

754×	`times-frac_binary64`
571×	`associate-/l*_binary64`
458×	`associate-/r*_binary64`
146×	`fma-def_binary64`
124×	`associate-*l/_binary64`

Counts

232 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	425	6073
1	1317	5717
2	4878	5711
3	4977	5711

prune367.0ms (5.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	242	7	249

Error

Counts

249 → 7

Alt Table

Status	Error	Program
	2.3b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 1 (/.f64 (-.f64 t z) (cbrt.f64 x))))
✓	6.9b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
	17.6b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 x (-.f64 t z)) 3)) (-.f64 y z))
✓	2.0b	(/.f64 (*.f64 x (/.f64 1 (-.f64 t z))) (-.f64 y z))
	37.1b	(/.f64 (sqrt.f64 x) (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) (sqrt.f64 x)))
	2.7b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
✓	2.0b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

Compiler

Compiled 6372 to 2750 computations (56.8% saved)

regimes664.0ms (10%)

Accuracy

Total 0.6b remaining (96.4%)

Threshold costs 0.6b (96.4%)

Counts

64 → 3

Compiler

Compiled 7327 to 4177 computations (43% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	69
1	24	69
2	30	69
3	32	69
4	33	69
5	33	69

end377.0ms (5.7%)

Compiler: Compiled 315 to 142 computations (54.9% saved)

Details

analyze694.0ms (10.4%)

sample1.2s (18%)

simplify97.0ms (1.5%)

prune3.0ms (0%)

localize12.0ms (0.2%)

series262.0ms (3.9%)

rewrite51.0ms (0.8%)

simplify206.0ms (3.1%)

prune285.0ms (4.3%)

localize15.0ms (0.2%)

series459.0ms (6.9%)

rewrite50.0ms (0.7%)

simplify163.0ms (2.4%)

prune376.0ms (5.6%)

localize13.0ms (0.2%)

series170.0ms (2.6%)

rewrite39.0ms (0.6%)

simplify163.0ms (2.4%)

prune294.0ms (4.4%)

localize72.0ms (1.1%)

series271.0ms (4.1%)

rewrite58.0ms (0.9%)

simplify305.0ms (4.6%)

prune367.0ms (5.5%)

regimes664.0ms (10%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end377.0ms (5.7%)

Profiling