Details

analyze122.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample33.0ms (1.2%)

Algorithm

1×

intervals

Results

20.0ms

256×

body

128

valid

Compiler

Compiled 30 to 24 computations (20% saved)

simplify81.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
722×	`fma-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-in_binary64`
83×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	32	14
2	69	12
3	160	12
4	298	9
5	418	9
6	666	9
7	960	9
8	1262	9
9	1473	9
10	1531	9
11	1530	9
12	1536	9
13	1536	9
14	1401	9

prune7.0ms (0.3%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 65 to 50 computations (23.1% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 9 -12)
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)
3.0ms	(fma.f64 x 9 -12)

rewrite2.0ms (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:

1.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)
1.0ms	(fma.f64 x 9 -12)

simplify84.0ms (3%)

Algorithm

1×	egg-herbie

Rules

785×	`associate-+l+_binary64`
415×	`fma-neg_binary64`
321×	`distribute-lft-in_binary64`
321×	`distribute-rgt-in_binary64`
225×	`distribute-rgt-out_binary64`

Counts

44 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	431
1	63	344
2	120	342
3	378	342
4	1764	342
5	4979	342
6	5271	342

prune45.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	35	4	39

Error

0.0b

Counts

39 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	0.8b	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 455 to 350 computations (23.1% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series7.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

4.0ms	(*.f64 9 (pow.f64 x 2))
3.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64`

Counts

2 → 51

Calls

2 calls:

10.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
7.0ms	(*.f64 9 (pow.f64 x 2))

simplify111.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-l_binary64`
410×	`associate-r_binary64`
379×	`fma-neg_binary64`
297×	`cancel-sign-sub-inv_binary64`
252×	`fma-def_binary64`

Counts

57 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	880
1	216	651
2	609	587
3	2814	561
4	4082	561
5	4830	561

prune151.0ms (5.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	87	5	92

Error

Counts

92 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
▶	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
	0.4b	(fma.f64 (.f64 (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2)))) (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))))) (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2)))) (*.f64 x -12))
	13.4b	(-.f64 (+.f64 3 (cbrt.f64 (.f64 729 (pow.f64 x 6)))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 1614 to 1297 computations (19.6% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.3b	(.f64 (.f64 3 x) (*.f64 3 x))

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 (.f64 3 x) (*.f64 3 x))
2.0ms	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))

rewrite19.0ms (0.7%)

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 → 58

Calls

2 calls:

9.0ms	(.f64 (.f64 3 x) (*.f64 3 x))
6.0ms	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))

simplify73.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-r_binary64`
631×	`associate-+l+_binary64`
287×	`fma-def_binary64`
272×	`distribute-rgt-out_binary64`
228×	`fma-neg_binary64`

Counts

82 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	947
1	208	778
2	679	638
3	2522	638
4	5058	638

prune118.0ms (4.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	80	5	85

Error

Counts

85 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
✓	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
▶	0.4b	(fma.f64 (.f64 (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2)))) (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))))) (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2)))) (*.f64 x -12))
	13.4b	(-.f64 (+.f64 3 (cbrt.f64 (.f64 729 (pow.f64 x 6)))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 1580 to 1225 computations (22.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2)))) (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))))) (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2)))) (*.f64 x -12))
✓	0.2b	(cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2))))
✓	0.2b	(.f64 (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2)))) (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2)))))
	0.2b	(*.f64 9 (pow.f64 x 2))

series35.0ms (1.3%)

Counts

3 → 36

Calls

3 calls:

19.0ms

(fma.f64 (*.f64 (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2)))) (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2))))) (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2)))) (*.f64 x -12))

9.0ms

(*.f64 (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2)))) (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2)))))

7.0ms

(cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2))))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`cbrt-div_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 75

Calls

3 calls:

7.0ms

(*.f64 (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2)))) (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2)))))

2.0ms

(cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2))))

0.0ms

(fma.f64 (*.f64 (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2)))) (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2))))) (cbrt.f64 (+.f64 3 (*.f64 9 (pow.f64 x 2)))) (*.f64 x -12))

simplify121.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

751×	`fma-neg_binary64`
609×	`fma-def_binary64`
608×	`associate-l_binary64`
224×	`times-frac_binary64`
214×	`cancel-sign-sub-inv_binary64`

Counts

111 → 184

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	3787
1	538	3237
2	1469	2711
3	4782	2709
4	5389	2709

prune586.0ms (20.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	418	0	418
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	418	5	423

Error

Counts

423 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
✓	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.4b	(fma.f64 (.f64 (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2)))) (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))))) (cbrt.f64 (+.f64 3 (.f64 9 (pow.f64 x 2)))) (*.f64 x -12))
	13.4b	(-.f64 (+.f64 3 (cbrt.f64 (.f64 729 (pow.f64 x 6)))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 15977 to 13401 computations (16.1% saved)

regimes195.0ms (6.9%)

Accuracy

Total 0.1b remaining (85.7%)

Threshold costs 0.1b (85.7%)

Counts

43 → 1

Compiler

Compiled 2897 to 2378 computations (17.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample947.0ms (33.5%)

Algorithm

1×

intervals

Results

554.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 101 to 83 computations (17.8% saved)

Details

analyze122.0ms (4.3%)

sample33.0ms (1.2%)

simplify81.0ms (2.8%)

prune7.0ms (0.3%)

localize9.0ms (0.3%)

series6.0ms (0.2%)

rewrite2.0ms (0.1%)

simplify84.0ms (3%)

prune45.0ms (1.6%)

localize10.0ms (0.3%)

series7.0ms (0.2%)

rewrite21.0ms (0.8%)

simplify111.0ms (3.9%)

prune151.0ms (5.4%)

localize7.0ms (0.3%)

series5.0ms (0.2%)

rewrite19.0ms (0.7%)

simplify73.0ms (2.6%)

prune118.0ms (4.2%)

localize12.0ms (0.4%)

series35.0ms (1.3%)

rewrite15.0ms (0.5%)

simplify121.0ms (4.3%)

prune586.0ms (20.7%)

regimes195.0ms (6.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample947.0ms (33.5%)

Profiling