Details

analyze4.0ms (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%	24.9%	13
75%	0%	25%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample731.0ms (34.8%)

Results

687.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify23.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

271×	`fma-def_binary64`
257×	`fma-neg_binary64`
76×	`cancel-sign-sub-inv_binary64`
55×	`sub-neg_binary64`
32×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	54	11
3	122	11
4	222	9
5	361	9
6	423	9
7	587	9
8	645	9
9	664	9
10	593	9

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))

Compiler

Compiled 37 to 29 computations (21.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))
✓	0.3b	(*.f64 x 3/25)

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))
2.0ms	(*.f64 x 3/25)

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))
2.0ms	(*.f64 x 3/25)

simplify70.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

965×	`fma-def_binary64`
478×	`associate-l_binary64`
351×	`associate-r_binary64`
338×	`+-commutative_binary64`
285×	`unswap-sqr_binary64`

Counts

68 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	79	632
1	179	528
2	566	526
3	1620	526
4	3361	526
5	4345	526
6	4910	526

prune73.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	5	76
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Error

Counts

77 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))
	0.3b	(-.f64 1 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 3/25 x 253/1000))))
	5.3b	(-.f64 1 (.f64 x (+.f64 253/1000 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 3/25 3/25) 3/25))))))
	5.3b	(-.f64 1 (/.f64 (.f64 x (-.f64 (.f64 253/1000 253/1000) (.f64 (.f64 x 3/25) (.f64 x 3/25)))) (-.f64 253/1000 (.f64 x 3/25))))
	0.3b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
▶	0.3b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (.f64 x (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))) (cbrt.f64 3/25)))))

Compiler

Compiled 1244 to 958 computations (23% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (+.f64 253/1000 (.f64 (.f64 x (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))) (cbrt.f64 3/25))))
✓	0.2b	(.f64 x (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25)))
✓	0.4b	(.f64 (.f64 x (*.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))) (cbrt.f64 3/25))
✓	1.0b	(*.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))

series36.0ms (1.7%)

Counts

4 → 36

Calls

4 calls:

13.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))) (cbrt.f64 3/25))
12.0ms	(.f64 x (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25)))
11.0ms	(.f64 x (+.f64 253/1000 (.f64 (.f64 x (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))) (cbrt.f64 3/25))))
0.0ms	(*.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))

rewrite26.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
27×	`pow1_binary64`
22×	`add-exp-log_binary64`
19×	`cbrt-prod_binary64`
17×	`*-un-lft-identity_binary64`

Counts

4 → 113

Calls

4 calls:

8.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))) (cbrt.f64 3/25))
5.0ms	(.f64 x (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25)))
4.0ms	(*.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))
4.0ms	(.f64 x (+.f64 253/1000 (.f64 (.f64 x (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))) (cbrt.f64 3/25))))

simplify89.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

865×	`fma-def_binary64`
348×	`*-commutative_binary64`
267×	`unswap-sqr_binary64`
234×	`associate-+l+_binary64`
232×	`distribute-lft-in_binary64`

Counts

149 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	1526
1	301	1294
2	1043	1282
3	2285	1252
4	4956	1252
5	4989	1252

prune185.0ms (8.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	174	5	179

Error

Counts

179 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))
	0.3b	(-.f64 1 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 3/25 x 253/1000))))
▶	0.2b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 9/625 1/3)) (cbrt.f64 3/25)))))
	5.3b	(-.f64 1 (/.f64 (.f64 x (-.f64 (.f64 253/1000 253/1000) (.f64 (.f64 x 3/25) (.f64 x 3/25)))) (-.f64 253/1000 (.f64 x 3/25))))
	0.3b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))

Compiler

Compiled 3683 to 3181 computations (13.6% saved)

localize28.0ms (1.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 9/625 1/3)) (cbrt.f64 3/25))))
✓	0.2b	(*.f64 x (pow.f64 9/625 1/3))
✓	0.4b	(.f64 (.f64 x (pow.f64 9/625 1/3)) (cbrt.f64 3/25))

series115.0ms (5.5%)

Counts

3 → 36

Calls

3 calls:

54.0ms	(*.f64 x (pow.f64 9/625 1/3))
41.0ms	(.f64 (.f64 x (pow.f64 9/625 1/3)) (cbrt.f64 3/25))
19.0ms	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 9/625 1/3)) (cbrt.f64 3/25))))

rewrite17.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
12×	`add-cbrt-cube_binary64`
11×	`prod-exp_binary64`

Counts

3 → 77

Calls

3 calls:

5.0ms	(.f64 (.f64 x (pow.f64 9/625 1/3)) (cbrt.f64 3/25))
4.0ms	(*.f64 x (pow.f64 9/625 1/3))
4.0ms	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 9/625 1/3)) (cbrt.f64 3/25))))

simplify70.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

634×	`unswap-sqr_binary64`
449×	`*-commutative_binary64`
286×	`fma-def_binary64`
270×	`distribute-rgt-neg-in_binary64`
246×	`associate-l_binary64`

Counts

113 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1555
1	309	1338
2	1174	1329
3	2628	1329
4	5065	1329

prune197.0ms (9.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	132	5	137

Error

Counts

137 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))
	0.3b	(-.f64 1 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 3/25 x 253/1000))))
✓	0.2b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 9/625 1/3)) (cbrt.f64 3/25)))))
	5.3b	(-.f64 1 (/.f64 (.f64 x (-.f64 (.f64 253/1000 253/1000) (.f64 (.f64 x 3/25) (.f64 x 3/25)))) (-.f64 253/1000 (.f64 x 3/25))))
▶	0.3b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))

Compiler

Compiled 2743 to 2322 computations (15.3% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
✓	0.1b	(*.f64 253/1000 x)
✓	0.4b	(*.f64 3/25 (pow.f64 x 2))

series7.0ms (0.4%)

Counts

3 → 3

Calls

3 calls:

3.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
3.0ms	(*.f64 3/25 (pow.f64 x 2))
2.0ms	(*.f64 253/1000 x)

rewrite14.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`associate-r_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 63

Calls

3 calls:

4.0ms	(*.f64 253/1000 x)
4.0ms	(*.f64 3/25 (pow.f64 x 2))
4.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))

simplify85.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
484×	`associate-l_binary64`
452×	`distribute-rgt-out_binary64`
388×	`associate-r_binary64`
351×	`cancel-sign-sub-inv_binary64`

Counts

66 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	705
1	226	611
2	573	582
3	2216	580
4	4154	580
5	4978	580
6	4929	580

prune93.0ms (4.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	93	4	97

Error

Counts

97 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))
	0.3b	(-.f64 1 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 3/25 x 253/1000))))
✓	0.2b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 9/625 1/3)) (cbrt.f64 3/25)))))
	0.3b	(-.f64 1 (fma.f64 3/25 (pow.f64 x 2) (*.f64 253/1000 x)))

Compiler

Compiled 1565 to 1242 computations (20.6% saved)

regimes130.0ms (6.2%)

Accuracy

Total 0.1b remaining (84%)

Threshold costs 0.1b (84%)

Counts

46 → 1

Compiler

Compiled 2110 to 1704 computations (19.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	19	13
2	28	13
3	39	13
4	52	13
5	55	13
6	56	13
7	53	13

end65.0ms (3.1%)

Compiler: Compiled 72 to 56 computations (22.2% saved)

Details

analyze4.0ms (0.2%)

sample731.0ms (34.8%)

simplify23.0ms (1.1%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite9.0ms (0.4%)

simplify70.0ms (3.3%)

prune73.0ms (3.5%)

localize9.0ms (0.4%)

series36.0ms (1.7%)

rewrite26.0ms (1.2%)

simplify89.0ms (4.2%)

prune185.0ms (8.8%)

localize28.0ms (1.3%)

series115.0ms (5.5%)

rewrite17.0ms (0.8%)

simplify70.0ms (3.3%)

prune197.0ms (9.4%)

localize8.0ms (0.4%)

series7.0ms (0.4%)

rewrite14.0ms (0.7%)

simplify85.0ms (4.1%)

prune93.0ms (4.4%)

regimes130.0ms (6.2%)

simplify3.0ms (0.1%)

end65.0ms (3.1%)

Profiling