Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample743.0ms (26.9%)

Results

694.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify28.0ms (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 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 253/1000 (*.f64 x 3/25))
✓	0.1b	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))
✓	0.2b	(*.f64 x 3/25)

series6.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

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

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`

Counts

3 → 60

Calls

3 calls:

4.0ms	(*.f64 x 3/25)
4.0ms	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))
2.0ms	(+.f64 253/1000 (*.f64 x 3/25))

simplify77.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

747×	`associate-+l+_binary64`
687×	`fma-def_binary64`
673×	`associate-+r+_binary64`
364×	`unswap-sqr_binary64`
295×	`*-commutative_binary64`

Counts

96 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	864
1	207	699
2	630	692
3	1515	690
4	2469	690
5	4451	690
6	5059	690

prune104.0ms (3.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	5	105

Error

0.0b

Counts

105 → 5

Alt Table

Status	Error	Program
	9.0b	(-.f64 1 (cbrt.f64 (pow.f64 (*.f64 x (fma.f64 3/25 x 253/1000)) 3)))
	3.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 3/25 3/25) 3/25))))))
	33.8b	(-.f64 1 (.f64 (sqrt.f64 x) (.f64 (fma.f64 3/25 x 253/1000) (sqrt.f64 x))))
▶	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	18.4b	(-.f64 1 (.f64 (sqrt.f64 (.f64 x (fma.f64 3/25 x 253/1000))) (sqrt.f64 (*.f64 x (fma.f64 3/25 x 253/1000)))))

Compiler

Compiled 1591 to 1238 computations (22.2% saved)

localize6.0ms (0.2%)

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)
✓	0.2b	(*.f64 3/25 (pow.f64 x 2))

series7.0ms (0.3%)

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 (0.5%)

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:

5.0ms	(*.f64 3/25 (pow.f64 x 2))
4.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
3.0ms	(*.f64 253/1000 x)

simplify119.0ms (4.3%)

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

prune166.0ms (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Error

Counts

97 → 4

Alt Table

Status	Error	Program
	3.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 3/25 3/25) 3/25))))))
▶	0.1b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	18.4b	(-.f64 1 (.f64 (sqrt.f64 (.f64 x (fma.f64 3/25 x 253/1000))) (sqrt.f64 (*.f64 x (fma.f64 3/25 x 253/1000)))))

Compiler

Compiled 1631 to 1296 computations (20.5% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x))
✓	0.1b	(*.f64 x (sqrt.f64 3/25))
	0.1b	(*.f64 253/1000 x)
✓	0.2b	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))

series38.0ms (1.4%)

Counts

3 → 36

Calls

3 calls:

16.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))
14.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x))
8.0ms	(*.f64 x (sqrt.f64 3/25))

rewrite26.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`pow1_binary64`
18×	`pow-prod-down_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

3 → 74

Calls

3 calls:

12.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))
7.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x))
4.0ms	(*.f64 x (sqrt.f64 3/25))

simplify123.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-neg_binary64`
341×	`distribute-lft-out_binary64`
340×	`fma-def_binary64`
326×	`cancel-sign-sub-inv_binary64`
315×	`unswap-sqr_binary64`

Counts

110 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	981
1	223	899
2	797	829
3	2066	829
4	4718	829
5	5053	829

prune285.0ms (10.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	152	4	156

Error

Counts

156 → 4

Alt Table

Status	Error	Program
▶	3.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 3/25 3/25) 3/25))))))
✓	0.1b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	18.4b	(-.f64 1 (.f64 (sqrt.f64 (.f64 x (fma.f64 3/25 x 253/1000))) (sqrt.f64 (*.f64 x (fma.f64 3/25 x 253/1000)))))

Compiler

Compiled 3086 to 2442 computations (20.9% saved)

localize23.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x x) x)
✓	0.1b	(.f64 x (+.f64 253/1000 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 3/25 3/25) 3/25)))))
✓	0.1b	(.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 3/25 3/25) 3/25))
✓	37.8b	(cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 3/25 3/25) 3/25)))

series51.0ms (1.8%)

Counts

4 → 48

Calls

4 calls:

23.0ms	(.f64 x (+.f64 253/1000 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 3/25 3/25) 3/25)))))
16.0ms	(cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 3/25 3/25) 3/25)))
6.0ms	(.f64 (.f64 x x) x)
6.0ms	(.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 3/25 3/25) 3/25))

rewrite108.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`pow1_binary64`
57×	`pow-prod-down_binary64`
50×	`add-cbrt-cube_binary64`
47×	`add-exp-log_binary64`
46×	`pow-plus_binary64`

Counts

4 → 132

Calls

4 calls:

47.0ms	(.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 3/25 3/25) 3/25))
30.0ms	(cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 3/25 3/25) 3/25)))
10.0ms	(.f64 (.f64 x x) x)
10.0ms	(.f64 x (+.f64 253/1000 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 3/25 3/25) 3/25)))))

simplify150.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
388×	`associate-+l+_binary64`
339×	`associate-+r+_binary64`
303×	`unswap-sqr_binary64`
295×	`*-commutative_binary64`

Counts

180 → 146

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1785
1	287	1509
2	965	1471
3	2119	1415
4	4030	1399
5	4708	1399
6	4947	1399
7	4899	1399

prune171.0ms (6.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	146	4	150

Error

Counts

150 → 4

Alt Table

Status	Error	Program
✓	3.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 3/25 3/25) 3/25))))))
✓	0.1b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	18.4b	(-.f64 1 (.f64 (sqrt.f64 (.f64 x (fma.f64 3/25 x 253/1000))) (sqrt.f64 (*.f64 x (fma.f64 3/25 x 253/1000)))))

Compiler

Compiled 3299 to 2363 computations (28.4% saved)

regimes365.0ms (13.2%)

Accuracy

Total 0.1b remaining (71.8%)

Threshold costs 0.1b (71.8%)

Counts

117 → 1

Compiler

Compiled 4953 to 4031 computations (18.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
9×	`+-commutative_binary64`
8×	`distribute-lft-neg-in_binary64`
8×	`distribute-rgt-neg-in_binary64`
8×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	21	23
2	29	23
3	49	23
4	64	23
5	78	23
6	84	23
7	86	23
8	84	23

end117.0ms (4.2%)

Compiler: Compiled 97 to 78 computations (19.6% saved)

Details

analyze1.0ms (0%)

sample743.0ms (26.9%)

simplify28.0ms (1%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite13.0ms (0.5%)

simplify77.0ms (2.8%)

prune104.0ms (3.7%)

localize6.0ms (0.2%)

series7.0ms (0.3%)

rewrite14.0ms (0.5%)

simplify119.0ms (4.3%)

prune166.0ms (6%)

localize15.0ms (0.5%)

series38.0ms (1.4%)

rewrite26.0ms (1%)

simplify123.0ms (4.4%)

prune285.0ms (10.3%)

localize23.0ms (0.8%)

series51.0ms (1.8%)

rewrite108.0ms (3.9%)

simplify150.0ms (5.4%)

prune171.0ms (6.2%)

regimes365.0ms (13.2%)

simplify4.0ms (0.1%)

end117.0ms (4.2%)

Profiling