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)

sample703.0ms (33.9%)

Results

659.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify24.0ms (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 (0.2%)

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)))
1.0ms	(*.f64 x 3/25)
1.0ms	(+.f64 253/1000 (*.f64 x 3/25))

rewrite10.0ms (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 (+.f64 253/1000 (.f64 x 3/25)))
2.0ms	(*.f64 x 3/25)
2.0ms	(+.f64 253/1000 (*.f64 x 3/25))

simplify72.0ms (3.4%)

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

prune101.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	99	7	106

Error

0.0b

Counts

106 → 7

Alt Table

Status	Error	Program
	0.5b	(-.f64 1 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (fma.f64 3/25 x 253/1000) (cbrt.f64 x))))
	0.2b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	12.1b	(-.f64 1 (.f64 (.f64 x (sqrt.f64 (fma.f64 3/25 x 253/1000))) (sqrt.f64 (+.f64 253/1000 (*.f64 x 3/25)))))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))
▶	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))
	5.4b	(-.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))))
	0.2b	(-.f64 1 (.f64 x (/.f64 (fma.f64 (.f64 x x) -9/625 64009/1000000) (fma.f64 x -3/25 253/1000))))

Compiler

Compiled 1647 to 1282 computations (22.2% saved)

localize8.0ms (0.4%)

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)))
✓	0.0b	(*.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))

series24.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

9.0ms	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))))
7.0ms	(.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))

rewrite19.0ms (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:

5.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))
4.0ms	(*.f64 x (sqrt.f64 3/25))
4.0ms	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))))
2.0ms	(+.f64 253/1000 (.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))

simplify106.0ms (5.1%)

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

prune166.0ms (8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	141	8	149

Error

Counts

149 → 8

Alt Table

Status	Error	Program
	0.5b	(-.f64 1 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (fma.f64 3/25 x 253/1000) (cbrt.f64 x))))
▶	0.2b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	12.1b	(-.f64 1 (.f64 (.f64 x (sqrt.f64 (fma.f64 3/25 x 253/1000))) (sqrt.f64 (+.f64 253/1000 (*.f64 x 3/25)))))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))
	0.3b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 (sqrt.f64 3/25))) (sqrt.f64 (sqrt.f64 3/25))))))
	5.4b	(-.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))))
	0.2b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25))))))

Compiler

Compiled 2742 to 2288 computations (16.6% 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))

series6.0ms (0.3%)

Counts

3 → 3

Calls

3 calls:

3.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
2.0ms	(*.f64 3/25 (pow.f64 x 2))
1.0ms	(*.f64 253/1000 x)

rewrite16.0ms (0.8%)

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:

7.0ms	(*.f64 253/1000 x)
4.0ms	(*.f64 3/25 (pow.f64 x 2))
3.0ms	(+.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

prune110.0ms (5.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	2	3	5
Picked	0	1	1
Done	1	1	2
Total	93	7	100

Error

Counts

100 → 7

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
	12.1b	(-.f64 1 (.f64 (.f64 x (sqrt.f64 (fma.f64 3/25 x 253/1000))) (sqrt.f64 (+.f64 253/1000 (*.f64 x 3/25)))))
▶	0.2b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25))))))
	0.2b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))
	0.3b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 (sqrt.f64 3/25))) (sqrt.f64 (sqrt.f64 3/25))))))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))

Compiler

Compiled 1705 to 1366 computations (19.9% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 253/1000 (.f64 (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25))))
✓	0.1b	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25)))))
✓	0.3b	(*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2))
✓	0.6b	(.f64 (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25)))

series38.0ms (1.8%)

Counts

4 → 48

Calls

4 calls:

14.0ms	(*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2))
8.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25)))
8.0ms	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25)))))
8.0ms	(+.f64 253/1000 (.f64 (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25))))

rewrite22.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
21×	`add-exp-log_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 98

Calls

4 calls:

6.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25)))
5.0ms	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25)))))
4.0ms	(*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2))
2.0ms	(+.f64 253/1000 (.f64 (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)) (sqrt.f64 (sqrt.f64 3/25))))

simplify104.0ms (5%)

Algorithm

1×	egg-herbie

Rules

515×	`*-commutative_binary64`
480×	`unswap-sqr_binary64`
300×	`fma-def_binary64`
253×	`fma-neg_binary64`
237×	`associate-l_binary64`

Counts

146 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	2458
1	346	2030
2	1201	1924
3	2665	1303
4	4710	1303
5	4862	1303

prune187.0ms (9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	153	6	159

Error

Counts

159 → 6

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
	12.1b	(-.f64 1 (.f64 (.f64 x (sqrt.f64 (fma.f64 3/25 x 253/1000))) (sqrt.f64 (+.f64 253/1000 (*.f64 x 3/25)))))
	0.2b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x (*.f64 (pow.f64 (sqrt.f64 3/25) 3/2) (sqrt.f64 (sqrt.f64 3/25)))))))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))
	0.2b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))

Compiler

Compiled 3293 to 2840 computations (13.8% saved)

regimes147.0ms (7.1%)

Accuracy

Total 0.1b remaining (96.7%)

Threshold costs 0.1b (96.7%)

Counts

50 → 1

Compiler

Compiled 2311 to 1845 computations (20.2% 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

end89.0ms (4.3%)

Compiler: Compiled 108 to 90 computations (16.7% saved)

Details

analyze4.0ms (0.2%)

sample703.0ms (33.9%)

simplify24.0ms (1.2%)

prune3.0ms (0.2%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite10.0ms (0.5%)

simplify72.0ms (3.4%)

prune101.0ms (4.9%)

localize8.0ms (0.4%)

series24.0ms (1.2%)

rewrite19.0ms (0.9%)

simplify106.0ms (5.1%)

prune166.0ms (8%)

localize6.0ms (0.3%)

series6.0ms (0.3%)

rewrite16.0ms (0.8%)

simplify85.0ms (4.1%)

prune110.0ms (5.3%)

localize11.0ms (0.5%)

series38.0ms (1.8%)

rewrite22.0ms (1.1%)

simplify104.0ms (5%)

prune187.0ms (9%)

regimes147.0ms (7.1%)

simplify3.0ms (0.1%)

end89.0ms (4.3%)

Profiling