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)

sample51.0ms (2.8%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify24.0ms (1.3%)

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 (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 253/1000 (*.f64 x 3/25))
✓	0.2b	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))
✓	0.3b	(*.f64 x 3/25)

series7.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

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

rewrite11.0ms (0.6%)

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))

simplify75.0ms (4.2%)

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

prune108.0ms (6%)

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

0.0b

Counts

106 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 1 (.f64 x (/.f64 (fma.f64 (.f64 x x) -9/625 64009/1000000) (fma.f64 x -3/25 253/1000))))
	21.5b	(-.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)))))
	0.4b	(-.f64 1 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (fma.f64 3/25 x 253/1000) (cbrt.f64 x))))
	0.1b	(-.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)))))

Compiler

Compiled 1595 to 1238 computations (22.4% saved)

localize7.0ms (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))
✓	0.2b	(.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 (1.6%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(.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)))
4.0ms	(*.f64 x (sqrt.f64 3/25))

rewrite24.0ms (1.4%)

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:

10.0ms	(.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))))
6.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))
4.0ms	(*.f64 x (sqrt.f64 3/25))
2.0ms	(+.f64 253/1000 (.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))

simplify108.0ms (6%)

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

prune136.0ms (7.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	142	5	147

Error

Counts

147 → 5

Alt Table

Status	Error	Program
	0.4b	(-.f64 1 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (fma.f64 3/25 x 253/1000) (cbrt.f64 x))))
	0.1b	(-.f64 1 (.f64 x (/.f64 (fma.f64 (.f64 x x) -9/625 64009/1000000) (fma.f64 x -3/25 253/1000))))
	21.5b	(-.f64 1 (.f64 (sqrt.f64 (.f64 x (+.f64 253/1000 (.f64 (.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25))))) (sqrt.f64 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))))
▶	0.1b	(-.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)))))

Compiler

Compiled 2670 to 2224 computations (16.7% saved)

localize7.0ms (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)
✓	0.2b	(*.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)

rewrite13.0ms (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:

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 (4.9%)

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

prune94.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	92	5	97

Error

Counts

97 → 5

Alt Table

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

Compiler

Compiled 1635 to 1294 computations (20.9% saved)

localize8.0ms (0.4%)

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))
	0.0b	(*.f64 x (sqrt.f64 3/25))
	0.1b	(*.f64 253/1000 x)
✓	0.3b	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))

series16.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

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

rewrite16.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`pow1_binary64`
17×	`pow-prod-down_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
8×	`cbrt-unprod_binary64`

Counts

2 → 50

Calls

2 calls:

7.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x))
6.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))

simplify66.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

648×	`fma-neg_binary64`
385×	`unswap-sqr_binary64`
332×	`distribute-lft-out_binary64`
325×	`fma-def_binary64`
308×	`cancel-sign-sub-inv_binary64`

Counts

74 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	692
1	190	622
2	698	548
3	1877	548
4	4887	548
5	5245	548

prune146.0ms (8.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	152	5	157

Error

Counts

157 → 5

Alt Table

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

Compiler

Compiled 3058 to 2418 computations (20.9% saved)

regimes256.0ms (14.2%)

Accuracy

Total 0.1b remaining (85.7%)

Threshold costs 0.1b (85.7%)

Counts

89 → 1

Compiler

Compiled 3962 to 3185 computations (19.6% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	22	20
2	31	20
3	42	20
4	55	20
5	66	20
6	71	20
7	73	20
8	71	20

end1.0ms (0%)

Compiler: Compiled 14 to 12 computations (14.3% saved)

sample481.0ms (26.8%)

Algorithm

1×

intervals

Results

246.0ms

8000×

body

128

valid

Compiler

Compiled 100 to 79 computations (21% saved)

Details

analyze4.0ms (0.2%)

sample51.0ms (2.8%)

simplify24.0ms (1.3%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series7.0ms (0.4%)

rewrite11.0ms (0.6%)

simplify75.0ms (4.2%)

prune108.0ms (6%)

localize7.0ms (0.4%)

series29.0ms (1.6%)

rewrite24.0ms (1.4%)

simplify108.0ms (6%)

prune136.0ms (7.6%)

localize7.0ms (0.4%)

series7.0ms (0.4%)

rewrite13.0ms (0.8%)

simplify88.0ms (4.9%)

prune94.0ms (5.2%)

localize8.0ms (0.4%)

series16.0ms (0.9%)

rewrite16.0ms (0.9%)

simplify66.0ms (3.7%)

prune146.0ms (8.1%)

regimes256.0ms (14.2%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample481.0ms (26.8%)

Profiling