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 (34.6%)

Results

659.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify23.0ms (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

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)

localize6.0ms (0.3%)

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)))
✓	0.3b	(*.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)
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)))
3.0ms	(*.f64 x 3/25)
2.0ms	(+.f64 253/1000 (*.f64 x 3/25))

simplify94.0ms (4.6%)

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 (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	100	5	105

Error

0.0b

Counts

105 → 5

Alt Table

Status	Error	Program
	31.8b	(-.f64 1 (.f64 (sqrt.f64 x) (.f64 (fma.f64 3/25 x 253/1000) (sqrt.f64 x))))
	8.8b	(-.f64 1 (/.f64 (.f64 x (fma.f64 (.f64 x x) -9/625 64009/1000000)) (-.f64 253/1000 (*.f64 x 3/25))))
	0.4b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
▶	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))

Compiler

Compiled 1565 to 1218 computations (22.2% saved)

localize9.0ms (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))))
✓	0.3b	(.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))

series29.0ms (1.4%)

Counts

4 → 48

Calls

4 calls:

9.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))
9.0ms	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))))
7.0ms	(+.f64 253/1000 (.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))
3.0ms	(*.f64 x (sqrt.f64 3/25))

rewrite22.0ms (1.1%)

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

simplify105.0ms (5.2%)

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

prune123.0ms (6%)

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

0.0b

Counts

147 → 5

Alt Table

Status	Error	Program
	31.8b	(-.f64 1 (.f64 (sqrt.f64 x) (.f64 (fma.f64 3/25 x 253/1000) (sqrt.f64 x))))
	8.8b	(-.f64 1 (/.f64 (.f64 x (fma.f64 (.f64 x x) -9/625 64009/1000000)) (-.f64 253/1000 (*.f64 x 3/25))))
▶	0.4b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))

Compiler

Compiled 2620 to 2184 computations (16.6% saved)

localize7.0ms (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)
✓	0.4b	(*.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))
1.0ms	(*.f64 253/1000 x)

rewrite13.0ms (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)

simplify84.0ms (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

prune92.0ms (4.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	92	5	97

Error

0.0b

Counts

97 → 5

Alt Table

Status	Error	Program
▶	0.4b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))
	8.8b	(-.f64 1 (/.f64 (.f64 x (fma.f64 (.f64 x x) -9/625 64009/1000000)) (-.f64 253/1000 (*.f64 x 3/25))))
✓	0.4b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))

Compiler

Compiled 1615 to 1286 computations (20.4% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x))
	0.1b	(*.f64 253/1000 x)
✓	0.2b	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))
✓	0.4b	(*.f64 (sqrt.f64 3/25) (pow.f64 x 2))

series19.0ms (0.9%)

Counts

3 → 24

Calls

3 calls:

8.0ms	(+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x))
7.0ms	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))
4.0ms	(*.f64 (sqrt.f64 3/25) (pow.f64 x 2))

rewrite21.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
12×	`associate-l_binary64`
10×	`sqrt-prod_binary64`
10×	`add-cbrt-cube_binary64`

Counts

3 → 74

Calls

3 calls:

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

simplify92.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-neg_binary64`
382×	`unswap-sqr_binary64`
373×	`*-commutative_binary64`
290×	`fma-def_binary64`
219×	`distribute-rgt-in_binary64`

Counts

98 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	102	1180
1	255	1111
2	819	1068
3	1879	1040
4	3901	1000
5	4918	1000
6	4947	1000

prune148.0ms (7.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	133	5	138

Error

Counts

138 → 5

Alt Table

Status	Error	Program
✓	0.4b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))
	8.8b	(-.f64 1 (/.f64 (.f64 x (fma.f64 (.f64 x x) -9/625 64009/1000000)) (-.f64 253/1000 (*.f64 x 3/25))))
	0.5b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (sqrt.f64 (.f64 (sqrt.f64 3/25) (pow.f64 x 2))))) (*.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))

Compiler

Compiled 2762 to 2317 computations (16.1% saved)

regimes127.0ms (6.2%)

Accuracy

Total 0.1b remaining (84.8%)

Threshold costs 0.1b (84.8%)

Counts

46 → 1

Compiler

Compiled 2020 to 1617 computations (20% 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

end174.0ms (8.6%)

Compiler: Compiled 102 to 85 computations (16.7% saved)

Details

analyze4.0ms (0.2%)

sample703.0ms (34.6%)

simplify23.0ms (1.2%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

series6.0ms (0.3%)

rewrite10.0ms (0.5%)

simplify94.0ms (4.6%)

prune101.0ms (5%)

localize9.0ms (0.4%)

series29.0ms (1.4%)

rewrite22.0ms (1.1%)

simplify105.0ms (5.2%)

prune123.0ms (6%)

localize7.0ms (0.3%)

series7.0ms (0.3%)

rewrite13.0ms (0.6%)

simplify84.0ms (4.1%)

prune92.0ms (4.5%)

localize9.0ms (0.4%)

series19.0ms (0.9%)

rewrite21.0ms (1%)

simplify92.0ms (4.5%)

prune148.0ms (7.3%)

regimes127.0ms (6.2%)

simplify3.0ms (0.1%)

end174.0ms (8.6%)

Profiling