Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample572.0ms (32.4%)

Infinites

20.6% of outputs are infinite.

Symmetry

(sort x y)

Results

515.0ms	8255×	body	128	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify10.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def_binary64`
33×	`distribute-rgt-in_binary64`
26×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
21×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	19	10
2	45	10
3	88	10
4	170	10
5	254	10
6	256	10
7	258	10
8	252	10

prune4.0ms (0.2%)

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 z 1))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

6.0ms

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

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`flip-+_binary64`
6×	`flip3-+_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`

Counts

1 → 32

Calls

1 calls:

6.0ms

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

simplify68.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

759×	`distribute-rgt-in_binary64`
724×	`distribute-lft-in_binary64`
449×	`fma-def_binary64`
414×	`fma-neg_binary64`
258×	`unsub-neg_binary64`

Counts

68 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	908
1	269	804
2	911	798
3	3385	798
4	4092	798
5	5126	798

prune38.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	4	62

Error

Counts

62 → 4

Alt Table

Status	Error	Program
	22.4b	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 z 1)) (-.f64 x y))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
▶	1.5b	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
	16.9b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))

Compiler

Compiled 1004 to 516 computations (48.6% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
✓	1.4b	(+.f64 (.f64 y z) (+.f64 (.f64 z x) x))

series14.0ms (0.8%)

Counts

2 → 18

Calls

2 calls:

7.0ms	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
7.0ms	(+.f64 (.f64 y z) (+.f64 (.f64 z x) x))

rewrite14.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-log-exp_binary64`
9×	`sum-log_binary64`
5×	`*-un-lft-identity_binary64`
4×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

2 → 36

Calls

2 calls:

7.0ms	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
5.0ms	(+.f64 (.f64 y z) (+.f64 (.f64 z x) x))

simplify54.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

657×	`distribute-rgt-in_binary64`
601×	`fma-neg_binary64`
599×	`distribute-lft-in_binary64`
485×	`fma-def_binary64`
316×	`associate-l_binary64`

Counts

54 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	628
1	211	560
2	824	544
3	4610	544
4	5125	544

prune39.0ms (2.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	69	4	73

Error

Counts

73 → 4

Alt Table

Status	Error	Program
	22.4b	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 z 1)) (-.f64 x y))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
✓	1.5b	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
▶	16.9b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))

Compiler

Compiled 1163 to 316 computations (72.8% saved)

localize8.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 z 1))
✓	0.1b	(*.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1)))
✓	0.1b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))

series40.0ms (2.2%)

Counts

3 → 68

Calls

3 calls:

26.0ms	(*.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1)))
7.0ms	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
7.0ms	(sqrt.f64 (+.f64 z 1))

rewrite29.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`sqrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
32×	`frac-times_binary64`
18×	`*-un-lft-identity_binary64`

Counts

3 → 104

Calls

3 calls:

10.0ms	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
8.0ms	(*.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1)))
2.0ms	(sqrt.f64 (+.f64 z 1))

simplify120.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

769×	`fma-def_binary64`
725×	`associate--l+_binary64`
625×	`fma-neg_binary64`
373×	`*-commutative_binary64`
341×	`cancel-sign-sub-inv_binary64`

Counts

172 → 191

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	192	2970
1	515	2690
2	1569	2658
3	3339	2639
4	4913	2639
5	5177	2639

prune139.0ms (7.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	227	4	231

Error

Counts

231 → 4

Alt Table

Status	Error	Program
▶	22.4b	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 z 1)) (-.f64 x y))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
✓	1.5b	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
✓	16.9b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))

Compiler

Compiled 5128 to 3171 computations (38.2% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.9b	(.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 z 1))
✓	4.4b	(-.f64 (.f64 x x) (.f64 y y))
✓	18.4b	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 z 1)) (-.f64 x y))

series63.0ms (3.6%)

Counts

3 → 96

Calls

3 calls:

34.0ms	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 z 1)) (-.f64 x y))
23.0ms	(.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 z 1))
6.0ms	(-.f64 (.f64 x x) (.f64 y y))

rewrite24.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`flip--_binary64`

Counts

3 → 86

Calls

3 calls:

8.0ms	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 z 1)) (-.f64 x y))
6.0ms	(.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 z 1))
4.0ms	(-.f64 (.f64 x x) (.f64 y y))

simplify110.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

1024×	`div-sub_binary64`
795×	`fma-def_binary64`
321×	`associate-/l/_binary64`
170×	`distribute-rgt-in_binary64`
166×	`distribute-lft-in_binary64`

Counts

182 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	3820
1	521	3292
2	2169	2992
3	4322	2992
4	6837	2992

prune114.0ms (6.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	166	4	170

Error

Counts

170 → 4

Alt Table

Status	Error	Program
✓	22.4b	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 z 1)) (-.f64 x y))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
✓	1.5b	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
✓	16.9b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))

Compiler

Compiled 3941 to 1371 computations (65.2% saved)

regimes168.0ms (9.5%)

Accuracy

Total 0.0b remaining (83.5%)

Threshold costs 0.0b (83.5%)

Counts

30 → 1

Compiler

Compiled 2258 to 1437 computations (36.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	12	13
2	12	13

end99.0ms (5.6%)

Remove: (sort x y)
Compiler: Compiled 106 to 66 computations (37.7% saved)

Details

analyze2.0ms (0.1%)

sample572.0ms (32.4%)

simplify10.0ms (0.6%)

prune4.0ms (0.2%)

localize5.0ms (0.3%)

series7.0ms (0.4%)

rewrite8.0ms (0.4%)

simplify68.0ms (3.8%)

prune38.0ms (2.1%)

localize7.0ms (0.4%)

series14.0ms (0.8%)

rewrite14.0ms (0.8%)

simplify54.0ms (3.1%)

prune39.0ms (2.2%)

localize8.0ms (0.5%)

series40.0ms (2.2%)

rewrite29.0ms (1.6%)

simplify120.0ms (6.8%)

prune139.0ms (7.9%)

localize10.0ms (0.5%)

series63.0ms (3.6%)

rewrite24.0ms (1.3%)

simplify110.0ms (6.2%)

prune114.0ms (6.4%)

regimes168.0ms (9.5%)

simplify2.0ms (0.1%)

end99.0ms (5.6%)

Profiling