Details

analyze462.0ms (19.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.4%	10.1%	12
55%	30.3%	14.7%	13
59.5%	25.4%	15.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample995.0ms (41.2%)

Symmetry

(sort x y)

Results

778.0ms	8256×	body	128	valid
51.0ms	582×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify45.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-neg_binary64`
461×	`fma-def_binary64`
143×	`distribute-rgt-in_binary64`
135×	`cancel-sign-sub-inv_binary64`
117×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	32	10
3	73	10
4	190	10
5	423	10
6	676	10
7	1136	10
8	1124	10
9	1359	10
10	1394	10
11	1394	10
12	1351	10

prune2.0ms (0.1%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (+.f64 x y) (-.f64 1 z))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

7.0ms

(*.f64 (+.f64 x y) (-.f64 1 z))

rewrite17.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
17×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

1 → 58

Calls

1 calls:

13.0ms

(*.f64 (+.f64 x y) (-.f64 1 z))

simplify85.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

725×	`distribute-rgt-in_binary64`
670×	`distribute-lft-in_binary64`
623×	`fma-def_binary64`
470×	`fma-neg_binary64`
304×	`*-commutative_binary64`

Counts

94 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1510
1	295	1288
2	1142	1234
3	3920	1126
4	4552	1126
5	4752	1126

prune50.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	3	91

Error

Counts

91 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (-.f64 1 z))
	30.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 z)))
▶	0.0b	(+.f64 (+.f64 y x) (neg.f64 (*.f64 z (+.f64 y x))))

Compiler

Compiled 1722 to 748 computations (56.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (+.f64 y x))
✓	0.0b	(+.f64 (+.f64 y x) (neg.f64 (*.f64 z (+.f64 y x))))

series15.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

9.0ms	(+.f64 (+.f64 y x) (neg.f64 (*.f64 z (+.f64 y x))))
6.0ms	(*.f64 z (+.f64 y x))

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
12×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`flip-+_binary64`
6×	`associate-*r/_binary64`

Counts

2 → 59

Calls

2 calls:

6.0ms	(+.f64 (+.f64 y x) (neg.f64 (*.f64 z (+.f64 y x))))
5.0ms	(*.f64 z (+.f64 y x))

simplify86.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

560×	`unsub-neg_binary64`
416×	`times-frac_binary64`
382×	`associate-+l+_binary64`
349×	`*-commutative_binary64`
320×	`associate-+r+_binary64`

Counts

119 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	1487
1	373	1274
2	1548	1229
3	3917	1229
4	4812	1229
5	5204	1229

prune52.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	108	3	111

Error

Counts

111 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (-.f64 1 z))
▶	30.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 z)))
✓	0.0b	(+.f64 (+.f64 y x) (neg.f64 (*.f64 z (+.f64 y x))))

Compiler

Compiled 1756 to 501 computations (71.5% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 z))
✓	0.2b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 z)))

series56.0ms (2.3%)

Counts

2 → 56

Calls

2 calls:

48.0ms	(*.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 z))
7.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 z)))

rewrite46.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
56×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
54×	`prod-diff_binary64`

Counts

2 → 164

Calls

2 calls:

15.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 z)))
10.0ms	(*.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 z))

simplify177.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

606×	`cancel-sign-sub-inv_binary64`
401×	`associate-l_binary64`
393×	`associate-r_binary64`
327×	`exp-prod_binary64`
316×	`associate--r+_binary64`

Counts

220 → 249

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	5036
1	704	4346
2	2586	4158
3	4483	4158
4	4898	4158
5	4976	4158

prune110.0ms (4.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	249	3	252

Error

Counts

252 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (-.f64 1 z))
✓	30.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 z)))
✓	0.0b	(+.f64 (+.f64 y x) (neg.f64 (*.f64 z (+.f64 y x))))

Compiler

Compiled 7419 to 2690 computations (63.7% saved)

regimes126.0ms (5.2%)

Accuracy

Total 0.0b remaining (70.7%)

Threshold costs 0.0b (70.7%)

Counts

23 → 1

Compiler

Compiled 1634 to 1034 computations (36.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	18	10
3	20	10
4	21	10
5	20	10

end51.0ms (2.1%)

Remove: (sort x y)
Compiler: Compiled 79 to 51 computations (35.4% saved)

Details

analyze462.0ms (19.1%)

sample995.0ms (41.2%)

simplify45.0ms (1.9%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite17.0ms (0.7%)

simplify85.0ms (3.5%)

prune50.0ms (2.1%)

localize5.0ms (0.2%)

series15.0ms (0.6%)

rewrite14.0ms (0.6%)

simplify86.0ms (3.6%)

prune52.0ms (2.2%)

localize6.0ms (0.3%)

series56.0ms (2.3%)

rewrite46.0ms (1.9%)

simplify177.0ms (7.3%)

prune110.0ms (4.6%)

regimes126.0ms (5.2%)

simplify2.0ms (0.1%)

end51.0ms (2.1%)

Profiling