Details

analyze630.0ms (11.7%)

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
0%	99.8%	0.2%	7
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
41.7%	58.1%	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 14 to 9 computations (35.7% saved)

sample1.0s (19.5%)

Symmetry

(sort y t)

Results

922.0ms	8256×	body	128	valid
49.0ms	414×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify75.0ms (1.4%)

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

8.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.3b	(/.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))
✓	8.3b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

series133.0ms (2.5%)

Counts

2 → 84

Calls

2 calls:

123.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
10.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite21.0ms (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)))

simplify124.0ms (2.3%)

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

prune160.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	186	7	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	7	194

Error

0.0b

Counts

194 → 7

Alt Table

Status	Error	Program
	8.3b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))
	3.9b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
	3.8b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
▶	1.9b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	8.5b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	8.4b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) x))
	28.1b	(.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 z z)))) (+.f64 t z))

Compiler

Compiled 5696 to 2107 computations (63% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y z))
✓	1.8b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

series184.0ms (3.4%)

Counts

2 → 72

Calls

2 calls:

168.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
16.0ms	(/.f64 x (-.f64 y z))

rewrite111.0ms (2.1%)

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:

84.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
4.0ms	(/.f64 x (-.f64 y z))

simplify135.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

261 → 270

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	526	8754
1	1583	8488
2	5002	8488

prune185.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	266	4	270
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	268	9	277

Error

Counts

277 → 9

Alt Table

Status	Error	Program
	8.3b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))
▶	1.9b	(/.f64 (*.f64 x (/.f64 1 (-.f64 y z))) (-.f64 t z))
	4.2b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 t z))))
	3.8b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
✓	1.9b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	8.5b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	8.4b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) x))
	2.1b	(/.f64 1 (/.f64 (-.f64 t z) (/.f64 x (-.f64 y z))))
	8.2b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 t z)))

Compiler

Compiled 7740 to 2397 computations (69% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	0.2b	(*.f64 x (/.f64 1 (-.f64 y z)))
✓	1.8b	(/.f64 (*.f64 x (/.f64 1 (-.f64 y z))) (-.f64 t z))

series135.0ms (2.5%)

Counts

3 → 108

Calls

3 calls:

109.0ms	(/.f64 (*.f64 x (/.f64 1 (-.f64 y z))) (-.f64 t z))
17.0ms	(*.f64 x (/.f64 1 (-.f64 y z)))
8.0ms	(/.f64 1 (-.f64 y z))

rewrite32.0ms (0.6%)

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:

11.0ms	(*.f64 x (/.f64 1 (-.f64 y z)))
8.0ms	(/.f64 (*.f64 x (/.f64 1 (-.f64 y z))) (-.f64 t z))
4.0ms	(/.f64 1 (-.f64 y z))

simplify163.0ms (3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

232 → 240

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	421	6073
1	1307	5711
2	4884	5705
3	4992	5705
4	4976	5705

prune247.0ms (4.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	240	9	249

Error

Counts

249 → 9

Alt Table

Status	Error	Program
	8.3b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))
✓	1.9b	(/.f64 (*.f64 x (/.f64 1 (-.f64 y z))) (-.f64 t z))
	4.2b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 t z))))
	3.8b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
✓	1.9b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	8.5b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	8.4b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) x))
▶	2.1b	(/.f64 1 (/.f64 (-.f64 t z) (/.f64 x (-.f64 y z))))
	8.2b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 t z)))

Compiler

Compiled 6500 to 2837 computations (56.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 y z))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 t z) (/.f64 x (-.f64 y z))))
✓	1.8b	(/.f64 (-.f64 t z) (/.f64 x (-.f64 y z)))

series145.0ms (2.7%)

Counts

2 → 96

Calls

2 calls:

115.0ms	(/.f64 1 (/.f64 (-.f64 t z) (/.f64 x (-.f64 y z))))
30.0ms	(/.f64 (-.f64 t z) (/.f64 x (-.f64 y z)))

rewrite155.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

1245×	`times-frac_binary64`
825×	`*-un-lft-identity_binary64`
825×	`add-sqr-sqrt_binary64`
457×	`add-cube-cbrt_binary64`
184×	`distribute-lft-out--_binary64`

Counts

2 → 621

Calls

2 calls:

23.0ms	(/.f64 1 (/.f64 (-.f64 t z) (/.f64 x (-.f64 y z))))
10.0ms	(/.f64 (-.f64 t z) (/.f64 x (-.f64 y z)))

simplify391.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

681×	`associate-/r/_binary64`
654×	`times-frac_binary64`
230×	`associate-/l/_binary64`
167×	`fma-def_binary64`
144×	`distribute-rgt-in_binary64`

Counts

717 → 732

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	681	23791
1	1958	23320
2	5008	23320

prune508.0ms (9.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	788	1	789
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	790	8	798

Error

Counts

798 → 8

Alt Table

Status	Error	Program
	8.3b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))
✓	1.9b	(/.f64 (*.f64 x (/.f64 1 (-.f64 y z))) (-.f64 t z))
	4.2b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 t z))))
	3.8b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
✓	1.9b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	8.5b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	8.2b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 t z)))
	3.5b	(/.f64 1 (*.f64 (/.f64 (-.f64 t z) x) (-.f64 y z)))

Compiler

Compiled 22243 to 6180 computations (72.2% saved)

regimes518.0ms (9.6%)

Accuracy

Total 1.3b remaining (99.2%)

Threshold costs 0b (0%)

Counts

83 → 3

Compiler

Compiled 9714 to 5592 computations (42.4% saved)

bsearch3.0ms (0%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
10×	`*-commutative_binary64`
9×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	81
1	39	81
2	52	81
3	72	81
4	82	81
5	88	81
6	90	81
7	90	81

end235.0ms (4.4%)

Compiler: Compiled 365 to 185 computations (49.3% saved)

Details

analyze630.0ms (11.7%)

sample1.0s (19.5%)

simplify75.0ms (1.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series133.0ms (2.5%)

rewrite21.0ms (0.4%)

simplify124.0ms (2.3%)

prune160.0ms (3%)

localize6.0ms (0.1%)

series184.0ms (3.4%)

rewrite111.0ms (2.1%)

simplify135.0ms (2.5%)

prune185.0ms (3.4%)

localize7.0ms (0.1%)

series135.0ms (2.5%)

rewrite32.0ms (0.6%)

simplify163.0ms (3%)

prune247.0ms (4.6%)

localize7.0ms (0.1%)

series145.0ms (2.7%)

rewrite155.0ms (2.9%)

simplify391.0ms (7.3%)

prune508.0ms (9.5%)

regimes518.0ms (9.6%)

bsearch3.0ms (0%)

simplify6.0ms (0.1%)

end235.0ms (4.4%)

Profiling