Details

analyze6.0ms (0.3%)

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)

sample691.0ms (35.5%)

Results

645.0ms	8256×	body	128	valid
0.0ms	4×	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 (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 33 to 25 computations (24.2% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
✓	0.1b	(fma.f64 x -3/25 -253/1000)

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
2.0ms	(fma.f64 x -3/25 -253/1000)

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 x -3/25 -253/1000)
0.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

simplify73.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-l_binary64`
533×	`fma-neg_binary64`
477×	`associate-r_binary64`
446×	`unsub-neg_binary64`
418×	`times-frac_binary64`

Counts

44 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	455
1	77	344
2	166	341
3	592	341
4	2915	341
5	4504	341
6	5515	341

prune41.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	32	6	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	6	39

Error

0.0b

Counts

39 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1))) (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1)))
	12.1b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1) 3))
	0.1b	(fma.f64 x (+.f64 (*.f64 x -3/25) -253/1000) 1)
▶	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.4b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x -3/25 -253/1000)) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) 1)
	5.9b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)

Compiler

Compiled 551 to 429 computations (22.1% 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))

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))
1.0ms	(*.f64 253/1000 x)

rewrite32.0ms (1.6%)

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:

24.0ms	(*.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)

simplify87.0ms (4.5%)

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

prune146.0ms (7.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	92	6	98

Error

0.0b

Counts

98 → 6

Alt Table

Status	Error	Program
	12.1b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1) 3))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.3b	(-.f64 1 (+.f64 (.f64 (.f64 3/25 (.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)) (.f64 253/1000 x)))
▶	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))
	5.9b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))

Compiler

Compiled 1669 to 1328 computations (20.4% saved)

localize9.0ms (0.5%)

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)
✓	0.1b	(*.f64 (sqrt.f64 3/25) (pow.f64 x 2))
✓	0.1b	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))

series20.0ms (1%)

Counts

3 → 24

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))
7.0ms	(+.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))

rewrite26.0ms (1.3%)

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:

8.0ms	(+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x))
8.0ms	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))
5.0ms	(*.f64 (sqrt.f64 3/25) (pow.f64 x 2))

simplify92.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-neg_binary64`
382×	`unswap-sqr_binary64`
375×	`*-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

prune209.0ms (10.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	134	5	139

Error

Counts

139 → 5

Alt Table

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

Compiler

Compiled 2810 to 2356 computations (16.2% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series16.0ms (0.8%)

Counts

3 → 24

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 3/25) (.f64 (*.f64 (sqrt.f64 3/25) x) x))
4.0ms	(.f64 (.f64 (sqrt.f64 3/25) x) x)
3.0ms	(*.f64 (sqrt.f64 3/25) x)

rewrite20.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
19×	`pow1_binary64`
13×	`associate-l_binary64`
13×	`add-sqr-sqrt_binary64`

Counts

3 → 70

Calls

3 calls:

9.0ms	(.f64 (sqrt.f64 3/25) (.f64 (*.f64 (sqrt.f64 3/25) x) x))
5.0ms	(.f64 (.f64 (sqrt.f64 3/25) x) x)
4.0ms	(*.f64 (sqrt.f64 3/25) x)

simplify70.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

701×	`associate-/l/_binary64`
633×	`fma-def_binary64`
267×	`sqr-pow_binary64`
255×	`*-commutative_binary64`
206×	`distribute-rgt-in_binary64`

Counts

94 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	79	973
1	181	865
2	598	853
3	896	839
4	1517	828
5	2571	828
6	5061	828

prune119.0ms (6.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	113	5	118

Error

Counts

118 → 5

Alt Table

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

Compiler

Compiled 2322 to 1834 computations (21% saved)

regimes148.0ms (7.6%)

Accuracy

Total 0.1b remaining (91%)

Threshold costs 0.1b (91%)

Counts

49 → 1

Compiler

Compiled 1903 to 1545 computations (18.8% saved)

simplify3.0ms (0.2%)

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

end83.0ms (4.3%)

Compiler: Compiled 101 to 84 computations (16.8% saved)

Details

analyze6.0ms (0.3%)

sample691.0ms (35.5%)

simplify24.0ms (1.2%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify73.0ms (3.8%)

prune41.0ms (2.1%)

localize6.0ms (0.3%)

series7.0ms (0.4%)

rewrite32.0ms (1.6%)

simplify87.0ms (4.5%)

prune146.0ms (7.5%)

localize9.0ms (0.5%)

series20.0ms (1%)

rewrite26.0ms (1.3%)

simplify92.0ms (4.7%)

prune209.0ms (10.7%)

localize8.0ms (0.4%)

series16.0ms (0.8%)

rewrite20.0ms (1%)

simplify70.0ms (3.6%)

prune119.0ms (6.1%)

regimes148.0ms (7.6%)

simplify3.0ms (0.2%)

end83.0ms (4.3%)

Profiling