Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	25%	13
75%	0%	25%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample788.0ms (32.9%)

Results

755.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3×	`fma-neg_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	15	8
2	21	8
3	24	8
4	26	8
5	27	8
6	24	8

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (fma.f64 x x -3) 6)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 (fma.f64 x x -3) 6)

rewrite41.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

540×	`log1p-expm1-u_binary64`
540×	`expm1-log1p-u_binary64`
265×	`unpow-prod-down_binary64`
237×	`log-prod_binary64`
152×	`pow2_binary64`

Counts

1 → 44

Calls

1 calls:

40.0ms

(/.f64 (fma.f64 x x -3) 6)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	129	8
2	1414	8
3	4957	8
0	0	0
1	0	0

simplify149.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

56 → 49

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	87
1	18	87
2	29	87
3	50	87
4	99	87
5	236	87
6	716	87
7	1141	87
8	1143	87
9	1291	87
10	1461	87
11	1643	87
12	1866	87
13	2151	87
14	2570	87
15	3135	87
16	3821	87
17	4039	87
18	4283	87
19	4365	87
20	4398	87
21	4419	87
22	4987	87

prune36.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	44	5	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	6	50

Error

0.3b

Counts

50 → 6

Alt Table

Status	Error	Program
	18.7b	-1/2
	45.9b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)) 2)
	0.4b	(*.f64 1/6 (pow.f64 (/.f64 1 (fma.f64 x x -3)) -1))
	45.9b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 (sqrt.f64 (fma.f64 x x -3)) 1/6))
▶	0.4b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	0.3b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 664 to 511 computations (23% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 1/6 (*.f64 x x) -1/2)

series2.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(fma.f64 1/6 (*.f64 x x) -1/2)

rewrite85.0ms (3.6%)

Algorithm

2×	batch-egg-rewrite

Rules

873×	`log1p-udef_binary64`
472×	`log1p-expm1-u_binary64`
472×	`expm1-log1p-u_binary64`
242×	`unpow-prod-down_binary64`
213×	`log-prod_binary64`

Counts

1 → 37

Calls

1 calls:

84.0ms

(fma.f64 1/6 (*.f64 x x) -1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	122	8
2	1230	8
3	4835	8
4	6186	8
0	0	0
1	0	0

simplify146.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

49 → 41

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	87
1	18	87
2	29	87
3	50	87
4	99	87
5	236	87
6	716	87
7	1141	87
8	1143	87
9	1291	87
10	1461	87
11	1643	87
12	1866	87
13	2151	87
14	2570	87
15	3135	87
16	3821	87
17	4039	87
18	4283	87
19	4365	87
20	4398	87
21	4419	87
22	4987	87

prune31.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	41	6	47

Error

0.3b

Counts

47 → 6

Alt Table

Status	Error	Program
	18.7b	-1/2
	45.9b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)) 2)
▶	13.1b	(/.f64 (+.f64 (.f64 1/216 (pow.f64 x 6)) -1/8) (+.f64 (pow.f64 (.f64 1/6 (.f64 x x)) 2) (-.f64 1/4 (.f64 (.f64 1/6 (.f64 x x)) -1/2))))
	45.9b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 (sqrt.f64 (fma.f64 x x -3)) 1/6))
✓	0.4b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	0.3b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 600 to 417 computations (30.5% saved)

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 1/6 (.f64 x x)) 2)
✓	0.3b	(*.f64 1/216 (pow.f64 x 6))
✓	0.5b	(.f64 1/6 (.f64 x x))
✓	11.9b	(/.f64 (+.f64 (.f64 1/216 (pow.f64 x 6)) -1/8) (+.f64 (pow.f64 (.f64 1/6 (.f64 x x)) 2) (-.f64 1/4 (.f64 (.f64 1/6 (.f64 x x)) -1/2))))

series14.0ms (0.6%)

Counts

4 → 36

Calls

4 calls:

5.0ms	(/.f64 (+.f64 (.f64 1/216 (pow.f64 x 6)) -1/8) (+.f64 (pow.f64 (.f64 1/6 (.f64 x x)) 2) (-.f64 1/4 (.f64 (.f64 1/6 (.f64 x x)) -1/2))))
4.0ms	(*.f64 1/216 (pow.f64 x 6))
3.0ms	(pow.f64 (.f64 1/6 (.f64 x x)) 2)
2.0ms	(.f64 1/6 (.f64 x x))

rewrite95.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

771×	`prod-diff_binary64`
199×	`log1p-expm1-u_binary64`
199×	`expm1-log1p-u_binary64`
195×	`add-sqr-sqrt_binary64`
192×	`add-cbrt-cube_binary64`

Counts

4 → 87

Calls

4 calls:

93.0ms	(pow.f64 (.f64 1/6 (.f64 x x)) 2)
93.0ms	(*.f64 1/216 (pow.f64 x 6))
93.0ms	(.f64 1/6 (.f64 x x))
93.0ms	(/.f64 (+.f64 (.f64 1/216 (pow.f64 x 6)) -1/8) (+.f64 (pow.f64 (.f64 1/6 (.f64 x x)) 2) (-.f64 1/4 (.f64 (.f64 1/6 (.f64 x x)) -1/2))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	59
1	433	48
2	4606	48
3	5946	48
0	0	0
1	0	0

simplify157.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

1078×	`sqr-pow_binary64`
520×	`pow-sqr_binary64`
443×	`cube-prod_binary64`
411×	`associate-l_binary64`
377×	`fabs-mul_binary64`

Counts

123 → 91

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	255
1	25	255
2	45	255
3	93	255
4	224	255
5	660	255
6	982	255
7	1004	255
8	1158	255
9	1343	255
10	1583	255
11	1847	255
12	2175	255
13	2561	255
14	3093	255
15	3738	255
16	3922	255
17	4110	255
18	4172	255
19	4192	255
20	4201	255
21	4674	255

prune123.0ms (5.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	105	7	112

Error

0.3b

Counts

112 → 7

Alt Table

Status	Error	Program
▶	17.2b	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 1/216 (pow.f64 x 6) -1/8) 3) (pow.f64 (-.f64 (fma.f64 1/36 (pow.f64 x 4) 1/4) (.f64 (.f64 x x) -1/12)) 3)))
	45.9b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 (sqrt.f64 (fma.f64 x x -3)) 1/6))
	18.7b	-1/2
	45.9b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)) 2)
✓	13.1b	(/.f64 (+.f64 (.f64 1/216 (pow.f64 x 6)) -1/8) (+.f64 (pow.f64 (.f64 1/6 (.f64 x x)) 2) (-.f64 1/4 (.f64 (.f64 1/6 (.f64 x x)) -1/2))))
✓	0.4b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	0.3b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 2985 to 2271 computations (23.9% saved)

localize17.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 1/216 (pow.f64 x 6) -1/8)
✓	0.5b	(.f64 (.f64 x x) -1/12)
✓	12.6b	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 1/216 (pow.f64 x 6) -1/8) 3) (pow.f64 (-.f64 (fma.f64 1/36 (pow.f64 x 4) 1/4) (.f64 (.f64 x x) -1/12)) 3)))
✓	13.7b	(/.f64 (pow.f64 (fma.f64 1/216 (pow.f64 x 6) -1/8) 3) (pow.f64 (-.f64 (fma.f64 1/36 (pow.f64 x 4) 1/4) (.f64 (.f64 x x) -1/12)) 3))

series16.0ms (0.7%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 1/216 (pow.f64 x 6) -1/8) 3) (pow.f64 (-.f64 (fma.f64 1/36 (pow.f64 x 4) 1/4) (.f64 (.f64 x x) -1/12)) 3)))
4.0ms	(/.f64 (pow.f64 (fma.f64 1/216 (pow.f64 x 6) -1/8) 3) (pow.f64 (-.f64 (fma.f64 1/36 (pow.f64 x 4) 1/4) (.f64 (.f64 x x) -1/12)) 3))
3.0ms	(fma.f64 1/216 (pow.f64 x 6) -1/8)
2.0ms	(.f64 (.f64 x x) -1/12)

rewrite97.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

780×	`prod-diff_binary64`
204×	`log1p-expm1-u_binary64`
204×	`expm1-log1p-u_binary64`
198×	`add-cbrt-cube_binary64`
196×	`add-sqr-sqrt_binary64`

Counts

4 → 119

Calls

4 calls:

92.0ms	(fma.f64 1/216 (pow.f64 x 6) -1/8)
92.0ms	(.f64 (.f64 x x) -1/12)
92.0ms	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 1/216 (pow.f64 x 6) -1/8) 3) (pow.f64 (-.f64 (fma.f64 1/36 (pow.f64 x 4) 1/4) (.f64 (.f64 x x) -1/12)) 3)))
92.0ms	(/.f64 (pow.f64 (fma.f64 1/216 (pow.f64 x 6) -1/8) 3) (pow.f64 (-.f64 (fma.f64 1/36 (pow.f64 x 4) 1/4) (.f64 (.f64 x x) -1/12)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	75
1	459	72
2	4725	72
3	5969	72
0	0	0
1	0	0

simplify81.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

840×	`fma-neg_binary64`
829×	`distribute-rgt-neg-in_binary64`
670×	`distribute-lft-neg-in_binary64`
618×	`cancel-sign-sub-inv_binary64`
351×	`*-commutative_binary64`

Counts

167 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	448
1	76	440
2	159	432
3	415	432
4	1321	432
5	3238	432
6	4598	432
7	5094	432

prune159.0ms (6.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	138	7	145

Error

0.3b

Counts

145 → 7

Alt Table

Status	Error	Program
✓	17.2b	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 1/216 (pow.f64 x 6) -1/8) 3) (pow.f64 (-.f64 (fma.f64 1/36 (pow.f64 x 4) 1/4) (.f64 (.f64 x x) -1/12)) 3)))
	45.9b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 (sqrt.f64 (fma.f64 x x -3)) 1/6))
	45.9b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)) 2)
✓	13.1b	(/.f64 (+.f64 (.f64 1/216 (pow.f64 x 6)) -1/8) (+.f64 (pow.f64 (.f64 1/6 (.f64 x x)) 2) (-.f64 1/4 (.f64 (.f64 1/6 (.f64 x x)) -1/2))))
	19.4b	(cbrt.f64 -1/8)
✓	0.4b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	0.3b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 3947 to 3134 computations (20.6% saved)

regimes207.0ms (8.6%)

Accuracy

Total 0.1b remaining (63.4%)

Threshold costs 0.1b (63.4%)

Counts

48 → 1

Compiler

Compiled 3202 to 2580 computations (19.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end106.0ms (4.4%)

Compiler: Compiled 106 to 82 computations (22.6% saved)

Details

analyze5.0ms (0.2%)

sample788.0ms (32.9%)

simplify8.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite41.0ms (1.7%)

simplify149.0ms (6.2%)

prune36.0ms (1.5%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite85.0ms (3.6%)

simplify146.0ms (6.1%)

prune31.0ms (1.3%)

localize14.0ms (0.6%)

series14.0ms (0.6%)

rewrite95.0ms (4%)

simplify157.0ms (6.6%)

prune123.0ms (5.1%)

localize17.0ms (0.7%)

series16.0ms (0.7%)

rewrite97.0ms (4%)

simplify81.0ms (3.4%)

prune159.0ms (6.6%)

regimes207.0ms (8.6%)

simplify2.0ms (0.1%)

end106.0ms (4.4%)

Profiling