Details

analyze605.0ms (17.1%)

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
0%	99.8%	0.2%	8
49.1%	50.7%	0.2%	9
49.5%	50.3%	0.2%	10
49.7%	50.1%	0.2%	11
50.2%	49.6%	0.2%	12
60.5%	39.3%	0.2%	13
60.6%	37.9%	1.4%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.4s (39.1%)

Symmetry

(sort x y)

Results

887.0ms	8256×	body	128	valid
377.0ms	2908×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify160.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1491×	`fma-neg_binary64`
579×	`fma-def_binary64`
465×	`distribute-rgt-in_binary64`
419×	`div-sub_binary64`
329×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	45	13
3	70	13
4	138	13
5	257	13
6	498	13
7	922	13
8	1615	13
9	2472	13
10	2435	13
11	2431	13
12	2427	13
13	2428	13
14	2428	13
15	3596	13
16	3260	13
17	3260	13
18	3260	13
19	3140	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

0.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series21.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

21.0ms

(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-/l*_binary64`
6×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

1 → 32

Calls

1 calls:

7.0ms

(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

simplify72.0ms (2%)

Algorithm

1×	egg-herbie

Rules

429×	`div-sub_binary64`
352×	`distribute-rgt-in_binary64`
333×	`distribute-lft-in_binary64`
268×	`neg-mul-1_binary64`
200×	`associate-/l*_binary64`

Counts

80 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1540
1	274	1260
2	889	1216
3	3171	1099
4	4711	1099
5	5041	1099

prune38.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	5	62

Error

Counts

62 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
	34.5b	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (.f64 (.f64 t 2) (+.f64 (+.f64 x y) z)))
	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))
▶	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
	32.0b	(.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (.f64 t 2))) (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))))

Compiler

Compiled 1107 to 478 computations (56.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series40.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

29.0ms	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
11.0ms	(/.f64 (+.f64 x y) (*.f64 t 2))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`times-frac_binary64`
65×	`*-un-lft-identity_binary64`
56×	`prod-diff_binary64`
40×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`

Counts

2 → 118

Calls

2 calls:

9.0ms	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
4.0ms	(/.f64 (+.f64 x y) (*.f64 t 2))

simplify135.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-def_binary64`
458×	`times-frac_binary64`
418×	`associate-/l*_binary64`
345×	`fma-neg_binary64`
184×	`distribute-rgt-in_binary64`

Counts

202 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	4746
1	550	3965
2	1542	2814
3	4196	2814
4	4970	2814
5	4864	2814

prune121.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	167	5	172

Error

Counts

172 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
	34.5b	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (.f64 (.f64 t 2) (+.f64 (+.f64 x y) z)))
▶	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
	32.0b	(.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (.f64 t 2))) (sqrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))))

Compiler

Compiled 4767 to 2606 computations (45.3% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))

series23.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

22.0ms

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

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 41

Calls

1 calls:

9.0ms

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

simplify84.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-l_binary64`
427×	`associate-r_binary64`
356×	`div-sub_binary64`
350×	`associate-*r/_binary64`
340×	`associate-*l/_binary64`

Counts

89 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1760
1	327	1464
2	1329	1288
3	3680	1288
4	4980	1288
5	5099	1288

prune47.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	82	4	86

Error

Counts

86 → 4

Alt Table

Status	Error	Program
▶	0.8b	(.f64 (.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) t))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
	34.5b	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (.f64 (.f64 t 2) (+.f64 (+.f64 x y) z)))
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))

Compiler

Compiled 1458 to 637 computations (56.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) t))
✓	0.4b	(/.f64 (sqrt.f64 1/2) t)
✓	0.5b	(*.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2))

series85.0ms (2.4%)

Counts

3 → 84

Calls

3 calls:

73.0ms	(.f64 (.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) t))
10.0ms	(*.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2))
3.0ms	(/.f64 (sqrt.f64 1/2) t)

rewrite36.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
28×	`associate-r_binary64`

Counts

3 → 117

Calls

3 calls:

10.0ms	(.f64 (.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) t))
8.0ms	(*.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2))
3.0ms	(/.f64 (sqrt.f64 1/2) t)

simplify126.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-/l*_binary64`
466×	`associate-*l/_binary64`
450×	`associate-*r/_binary64`
406×	`div-sub_binary64`
283×	`fma-def_binary64`

Counts

201 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	3676
1	471	3073
2	1669	2821
3	4426	2797
4	5827	2797

prune98.0ms (2.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	183	4	187

Error

Counts

187 → 4

Alt Table

Status	Error	Program
✓	0.8b	(.f64 (.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) t))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
	34.5b	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (.f64 (.f64 t 2) (+.f64 (+.f64 x y) z)))
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))

Compiler

Compiled 3631 to 2079 computations (42.7% saved)

regimes322.0ms (9.1%)

Accuracy

Total 0.0b remaining (86.9%)

Threshold costs 0.0b (86.9%)

Counts

43 → 1

Compiler

Compiled 5136 to 3708 computations (27.8% 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	10	13
1	14	13
2	19	13
3	21	13
4	22	13
5	22	13

end65.0ms (1.8%)

Remove: (sort x y)
Compiler: Compiled 124 to 83 computations (33.1% saved)

Details

analyze605.0ms (17.1%)

sample1.4s (39.1%)

simplify160.0ms (4.5%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series21.0ms (0.6%)

rewrite9.0ms (0.2%)

simplify72.0ms (2%)

prune38.0ms (1.1%)

localize7.0ms (0.2%)

series40.0ms (1.1%)

rewrite25.0ms (0.7%)

simplify135.0ms (3.8%)

prune121.0ms (3.4%)

localize6.0ms (0.2%)

series23.0ms (0.6%)

rewrite11.0ms (0.3%)

simplify84.0ms (2.4%)

prune47.0ms (1.3%)

localize8.0ms (0.2%)

series85.0ms (2.4%)

rewrite36.0ms (1%)

simplify126.0ms (3.6%)

prune98.0ms (2.8%)

regimes322.0ms (9.1%)

simplify2.0ms (0.1%)

end65.0ms (1.8%)

Profiling