Details

analyze407.0ms (9.7%)

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
28.1%	71.8%	0.1%	9
37.4%	49.9%	12.6%	10
43.7%	43.7%	12.6%	11
49.1%	38.2%	12.6%	12
54.6%	26.5%	18.9%	13
58.5%	22.6%	18.9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample852.0ms (20.3%)

Results

759.0ms	8256×	body	128	valid
63.0ms	667×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	8
2	16	8
3	17	8
4	17	8

prune2.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 34 to 17 computations (50% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (*.f64 y z) x)

series8.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(fma.f64 z (*.f64 y z) x)

rewrite41.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

522×	`log1p-expm1-u_binary64`
522×	`expm1-log1p-u_binary64`
351×	`unpow-prod-down_binary64`
296×	`log-prod_binary64`
160×	`pow2_binary64`

Counts

1 → 37

Calls

1 calls:

40.0ms

(fma.f64 z (*.f64 y z) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	118	8
2	1371	8
3	5179	8
0	0	0
1	0	0

simplify158.0ms (3.8%)

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

73 → 42

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	255
1	16	255
2	27	255
3	48	255
4	97	255
5	234	255
6	714	255
7	1139	255
8	1141	255
9	1289	255
10	1459	255
11	1641	255
12	1864	255
13	2149	255
14	2568	255
15	3133	255
16	3819	255
17	4037	255
18	4281	255
19	4363	255
20	4396	255
21	4417	255
22	4986	255

prune27.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	5	43

Error

0.0b

Counts

43 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (*.f64 y z) x)
	4.5b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
	31.3b	(pow.f64 (sqrt.f64 (fma.f64 z (*.f64 z y) x)) 2)
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 3)
	41.8b	(/.f64 (+.f64 (pow.f64 (.f64 z (.f64 z y)) 3) (pow.f64 x 3)) (+.f64 (pow.f64 (.f64 z (.f64 z y)) 2) (-.f64 (.f64 x x) (.f64 (.f64 z (.f64 z y)) x))))

Compiler

Compiled 654 to 239 computations (63.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (*.f64 z y) x)
✓	0.5b	(cbrt.f64 (fma.f64 z (*.f64 z y) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 3)

series1.4s (34.2%)

Counts

3 → 108

Calls

3 calls:

1.4s	(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 3)
39.0ms	(cbrt.f64 (fma.f64 z (*.f64 z y) x))
11.0ms	(fma.f64 z (*.f64 z y) x)

rewrite81.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

690×	`log1p-expm1-u_binary64`
690×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
130×	`log-pow_binary64`

Counts

3 → 104

Calls

3 calls:

79.0ms	(fma.f64 z (*.f64 z y) x)
79.0ms	(cbrt.f64 (fma.f64 z (*.f64 z y) x))
79.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	166	26
2	1817	26
3	4955	26
4	4918	26
0	0	0
1	0	0

simplify83.0ms (2%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-def_binary64`
407×	`associate-*l/_binary64`
286×	`associate-/r/_binary64`
221×	`cancel-sign-sub-inv_binary64`
209×	`unswap-sqr_binary64`

Counts

212 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	3450
1	667	3268
2	2254	2974
3	5012	2974

prune94.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	149	5	154

Error

0.0b

Counts

154 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (*.f64 y z) x)
▶	4.5b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
	31.3b	(pow.f64 (sqrt.f64 (fma.f64 z (*.f64 z y) x)) 2)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 3)
	41.8b	(/.f64 (+.f64 (pow.f64 (.f64 z (.f64 z y)) 3) (pow.f64 x 3)) (+.f64 (pow.f64 (.f64 z (.f64 z y)) 2) (-.f64 (.f64 x x) (.f64 (.f64 z (.f64 z y)) x))))

Compiler

Compiled 3752 to 2220 computations (40.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
✓	8.9b	(*.f64 y (pow.f64 z 2))

series18.0ms (0.4%)

Counts

2 → 9

Calls

2 calls:

11.0ms	(+.f64 (*.f64 y (pow.f64 z 2)) x)
7.0ms	(*.f64 y (pow.f64 z 2))

rewrite50.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

811×	`prod-diff_binary64`
778×	`log1p-expm1-u_binary64`
778×	`expm1-log1p-u_binary64`
84×	`add-sqr-sqrt_binary64`
79×	`add-log-exp_binary64`

Counts

2 → 51

Calls

2 calls:

48.0ms	(+.f64 (*.f64 y (pow.f64 z 2)) x)
48.0ms	(*.f64 y (pow.f64 z 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	172	15
2	1984	15
3	6248	15
0	0	0
1	0	0

simplify144.0ms (3.4%)

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

60 → 53

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	39
1	13	39
2	23	39
3	42	39
4	89	39
5	222	39
6	694	39
7	1099	39
8	1101	39
9	1249	39
10	1419	39
11	1601	39
12	1826	39
13	2111	39
14	2530	39
15	3095	39
16	3781	39
17	3999	39
18	4243	39
19	4325	39
20	4358	39
21	4379	39
22	4948	39

prune29.0ms (0.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	2	0	2
Picked	0	1	1
Done	0	2	2
Total	53	5	58

Error

0.0b

Counts

58 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (*.f64 y z) x)
▶	14.1b	(+.f64 (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)) x)
	34.8b	(+.f64 (pow.f64 (*.f64 z (sqrt.f64 y)) 2) x)
✓	4.5b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 3)

Compiler

Compiled 758 to 275 computations (63.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)) x)
✓	0.2b	(pow.f64 (.f64 y (.f64 z z)) 3)
✓	8.9b	(.f64 y (.f64 z z))
✓	25.5b	(cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3))

series59.0ms (1.4%)

Counts

4 → 108

Calls

4 calls:

18.0ms	(cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3))
18.0ms	(pow.f64 (.f64 y (.f64 z z)) 3)
16.0ms	(+.f64 (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)) x)
7.0ms	(.f64 y (.f64 z z))

rewrite56.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

903×	`log1p-expm1-u_binary64`
903×	`expm1-log1p-u_binary64`
119×	`egg-rr`
94×	`add-sqr-sqrt_binary64`
90×	`add-cbrt-cube_binary64`

Counts

4 → 119

Calls

4 calls:

54.0ms	(+.f64 (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)) x)
54.0ms	(pow.f64 (.f64 y (.f64 z z)) 3)
54.0ms	(.f64 y (.f64 z z))
54.0ms	(cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	197	32
2	2323	32
3	5418	32
0	0	0
1	0	0

simplify93.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

712×	`unswap-sqr_binary64`
507×	`fma-def_binary64`
473×	`associate-l_binary64`
414×	`distribute-rgt-in_binary64`
364×	`associate-r_binary64`

Counts

227 → 112

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	887
1	50	887
2	123	887
3	352	887
4	1313	887
5	2899	887
6	3447	887
7	4223	887
8	4811	887

prune71.0ms (1.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	110	7	117

Error

0.0b

Counts

117 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (*.f64 y z) x)
✓	14.1b	(+.f64 (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)) x)
	41.0b	(+.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 z (sqrt.f64 y)) 3) (pow.f64 (*.f64 z (sqrt.f64 y)) 3))) x)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 z (*.f64 z y) x)) 3)
	34.8b	(+.f64 (pow.f64 (*.f64 z (sqrt.f64 y)) 2) x)
✓	4.5b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
	4.7b	(+.f64 (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (*.f64 z z))) x)

Compiler

Compiled 1570 to 614 computations (60.9% saved)

regimes371.0ms (8.8%)

Accuracy

Total 0.1b remaining (72.7%)

Threshold costs 0.1b (72.7%)

Counts

21 → 1

Compiler

Compiled 1417 to 865 computations (39% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end84.0ms (2%)

Compiler: Compiled 108 to 69 computations (36.1% saved)

Details

analyze407.0ms (9.7%)

sample852.0ms (20.3%)

simplify6.0ms (0.1%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite41.0ms (1%)

simplify158.0ms (3.8%)

prune27.0ms (0.7%)

localize7.0ms (0.2%)

series1.4s (34.2%)

rewrite81.0ms (1.9%)

simplify83.0ms (2%)

prune94.0ms (2.2%)

localize5.0ms (0.1%)

series18.0ms (0.4%)

rewrite50.0ms (1.2%)

simplify144.0ms (3.4%)

prune29.0ms (0.7%)

localize7.0ms (0.2%)

series59.0ms (1.4%)

rewrite56.0ms (1.3%)

simplify93.0ms (2.2%)

prune71.0ms (1.7%)

regimes371.0ms (8.8%)

simplify2.0ms (0%)

end84.0ms (2%)

Profiling