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%	24.9%	13
75%	0%	25%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample732.0ms (33.5%)

Results

687.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify26.0ms (1.2%)

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

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 53 to 41 computations (22.6% 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 (0.3%)

Counts

3 → 36

Calls

3 calls:

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

rewrite41.0ms (1.9%)

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:

33.0ms	(*.f64 x 3/25)
4.0ms	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))
2.0ms	(+.f64 253/1000 (*.f64 x 3/25))

simplify70.0ms (3.2%)

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

prune146.0ms (6.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	101	5	106

Error

Counts

106 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))
	8.1b	(-.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))))
	12.6b	(-.f64 1 (/.f64 (.f64 x (fma.f64 (pow.f64 x 3) 27/15625 16194277/1000000000)) (+.f64 (.f64 253/1000 253/1000) (-.f64 (.f64 (.f64 x 3/25) (.f64 x 3/25)) (.f64 253/1000 (*.f64 x 3/25))))))
	0.1b	(-.f64 1 (.f64 (+.f64 253/1000 (.f64 x 3/25)) x))
▶	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))

Compiler

Compiled 1617 to 1266 computations (21.7% saved)

localize6.0ms (0.3%)

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))

series9.0ms (0.4%)

Counts

3 → 3

Calls

3 calls:

4.0ms	(*.f64 3/25 (pow.f64 x 2))
3.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
1.0ms	(*.f64 253/1000 x)

rewrite14.0ms (0.6%)

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

simplify88.0ms (4%)

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

prune113.0ms (5.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	92	5	97

Error

Counts

97 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))
	8.1b	(-.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))))
	12.6b	(-.f64 1 (/.f64 (.f64 x (fma.f64 (pow.f64 x 3) 27/15625 16194277/1000000000)) (+.f64 (.f64 253/1000 253/1000) (-.f64 (.f64 (.f64 x 3/25) (.f64 x 3/25)) (.f64 253/1000 (*.f64 x 3/25))))))
	0.1b	(-.f64 1 (.f64 (+.f64 253/1000 (.f64 x 3/25)) x))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))

Compiler

Compiled 1675 to 1336 computations (20.2% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series29.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

11.0ms	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))))
9.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))
6.0ms	(+.f64 253/1000 (.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))
3.0ms	(*.f64 x (sqrt.f64 3/25))

rewrite20.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`

Counts

4 → 87

Calls

4 calls:

6.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))
4.0ms	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))))
3.0ms	(*.f64 x (sqrt.f64 3/25))
2.0ms	(+.f64 253/1000 (.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))

simplify129.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-neg_binary64`
441×	`+-commutative_binary64`
279×	`fma-def_binary64`
276×	`*-commutative_binary64`
230×	`distribute-rgt-in_binary64`

Counts

135 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1194
1	276	1015
2	924	1009
3	2111	994
4	3439	994
5	4548	994
6	4940	994
7	4898	994

prune141.0ms (6.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	142	5	147

Error

Counts

147 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))
	8.1b	(-.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))))
	12.6b	(-.f64 1 (/.f64 (.f64 x (fma.f64 (pow.f64 x 3) 27/15625 16194277/1000000000)) (+.f64 (.f64 253/1000 253/1000) (-.f64 (.f64 (.f64 x 3/25) (.f64 x 3/25)) (.f64 253/1000 (*.f64 x 3/25))))))
▶	0.1b	(-.f64 1 (.f64 (+.f64 253/1000 (.f64 x 3/25)) x))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))

Compiler

Compiled 2660 to 2222 computations (16.5% 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 (+.f64 253/1000 (.f64 x 3/25)) x)
	0.2b	(*.f64 x 3/25)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

4.0ms

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

simplify54.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

800×	`unswap-sqr_binary64`
692×	`fma-def_binary64`
384×	`associate-+l+_binary64`
346×	`associate-+r+_binary64`
331×	`*-commutative_binary64`

Counts

34 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	443
1	127	328
2	408	326
3	1203	326
4	2198	326
5	3482	326
6	4959	326

prune101.0ms (4.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	100	5	105

Error

Counts

105 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))
	8.1b	(-.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))))
	12.6b	(-.f64 1 (/.f64 (.f64 x (fma.f64 (pow.f64 x 3) 27/15625 16194277/1000000000)) (+.f64 (.f64 253/1000 253/1000) (-.f64 (.f64 (.f64 x 3/25) (.f64 x 3/25)) (.f64 253/1000 (*.f64 x 3/25))))))
✓	0.1b	(-.f64 1 (.f64 (+.f64 253/1000 (.f64 x 3/25)) x))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))

Compiler

Compiled 1492 to 1167 computations (21.8% saved)

regimes336.0ms (15.4%)

Accuracy

Total 0.2b remaining (88.8%)

Threshold costs 0.2b (88.8%)

Counts

113 → 1

Compiler

Compiled 5862 to 4744 computations (19.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-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	14
1	15	14
2	19	14
3	21	14
4	22	14
5	21	14

end86.0ms (3.9%)

Compiler: Compiled 109 to 90 computations (17.4% saved)

Details

analyze5.0ms (0.2%)

sample732.0ms (33.5%)

simplify26.0ms (1.2%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite41.0ms (1.9%)

simplify70.0ms (3.2%)

prune146.0ms (6.7%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite14.0ms (0.6%)

simplify88.0ms (4%)

prune113.0ms (5.2%)

localize7.0ms (0.3%)

series29.0ms (1.3%)

rewrite20.0ms (0.9%)

simplify129.0ms (5.9%)

prune141.0ms (6.5%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite6.0ms (0.3%)

simplify54.0ms (2.5%)

prune101.0ms (4.6%)

regimes336.0ms (15.4%)

simplify2.0ms (0.1%)

end86.0ms (3.9%)

Profiling