Details

analyze67.0ms (3.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
50%	50%	0.1%	6
62.4%	31.2%	6.3%	7
71.8%	21.9%	6.3%	8
76.5%	14%	9.5%	9
80.4%	10.1%	9.5%	10
82.3%	6.6%	11%	11
84.1%	4.9%	11%	12
85%	3.2%	11.8%	13
85.8%	2.4%	11.8%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample36.0ms (1.7%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 25 to 21 computations (16% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
13×	`distribute-lft-in_binary64`
13×	`distribute-rgt-in_binary64`
10×	`*-commutative_binary64`
9×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	10
1	18	10
2	32	8
3	56	8
4	68	8
5	74	8
6	66	8

prune5.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
▶	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 55 to 43 computations (21.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 x (/.f64 16 116)) 3)
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

series7.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

5.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
2.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

rewrite19.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`associate-l_binary64`

Counts

2 → 47

Calls

2 calls:

9.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)
8.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

simplify103.0ms (5%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
495×	`associate-r_binary64`
206×	`sqr-pow_binary64`
195×	`distribute-rgt-in_binary64`
194×	`distribute-lft-in_binary64`

Counts

83 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	921
1	206	672
2	611	666
3	1677	666
4	2385	666
5	3622	666
6	4778	666
7	4997	666
8	4869	666

prune372.0ms (18.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Error

0.0b

Counts

87 → 8

Alt Table

Status	Error	Program
	20.0b	(/.f64 (.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 (/.f64 16 116) 3)) 3) y) (+.f64 (.f64 x x) (+.f64 (.f64 (/.f64 16 116) (/.f64 16 116)) (*.f64 x (/.f64 16 116)))))
▶	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	16.0b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 3 x -12/29) 3)) y)
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 3 x -12/29))) (cbrt.f64 (.f64 y (fma.f64 3 x -12/29)))) (cbrt.f64 (*.f64 y (fma.f64 3 x -12/29))))
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	33.7b	(.f64 (.f64 (*.f64 (-.f64 x (/.f64 16 116)) 3) (sqrt.f64 y)) (sqrt.f64 y))

Compiler

Compiled 1439 to 1123 computations (22% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x 3 -12/29)
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)

series7.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

6.0ms	(*.f64 (fma.f64 x 3 -12/29) y)
2.0ms	(fma.f64 x 3 -12/29)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 (fma.f64 x 3 -12/29) y)
0.0ms	(fma.f64 x 3 -12/29)

simplify44.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

939×	`fma-def_binary64`
595×	`distribute-rgt-in_binary64`
593×	`distribute-lft-in_binary64`
497×	`associate-+r+_binary64`
408×	`associate-+l+_binary64`

Counts

66 → 60

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	691
1	91	531
2	246	531
3	644	531
4	2128	531
5	5282	531

prune37.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	63	5	68

Error

0.0b

Counts

68 → 5

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))
	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
▶	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 738 to 539 computations (27% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
✓	0.1b	(*.f64 12/29 y)
✓	0.3b	(.f64 3 (.f64 y x))

series12.0ms (0.6%)

Counts

3 → 15

Calls

3 calls:

6.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
4.0ms	(.f64 3 (.f64 y x))
1.0ms	(*.f64 12/29 y)

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

3 → 56

Calls

3 calls:

4.0ms	(.f64 3 (.f64 y x))
4.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
3.0ms	(*.f64 12/29 y)

simplify81.0ms (4%)

Algorithm

1×	egg-herbie

Rules

605×	`times-frac_binary64`
509×	`associate-l_binary64`
472×	`fma-neg_binary64`
366×	`associate-r_binary64`
288×	`distribute-rgt-in_binary64`

Counts

71 → 85

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	701
1	230	632
2	626	623
3	1846	614
4	3688	612
5	4571	612
6	5558	612

prune72.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	85	5	90

Error

Counts

90 → 5

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))
▶	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	0.4b	(-.f64 (.f64 3 (.f64 y x)) (.f64 (sqrt.f64 12/29) (.f64 (sqrt.f64 12/29) y)))

Compiler

Compiled 1267 to 831 computations (34.4% saved)

localize7.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 (-.f64 x (/.f64 16 116)) (*.f64 3 y))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`

Counts

1 → 25

Calls

1 calls:

8.0ms

(*.f64 (-.f64 x (/.f64 16 116)) (*.f64 3 y))

simplify81.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
545×	`associate-l_binary64`
389×	`associate-r_binary64`
207×	`unswap-sqr_binary64`
175×	`fma-neg_binary64`

Counts

49 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	656
1	172	447
2	499	447
3	1627	443
4	2444	443
5	3664	443
6	4975	443
7	4985	443

prune27.0ms (1.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	43	5	48

Error

Counts

48 → 5

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))
✓	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	0.4b	(-.f64 (.f64 3 (.f64 y x)) (.f64 (sqrt.f64 12/29) (.f64 (sqrt.f64 12/29) y)))

Compiler

Compiled 704 to 551 computations (21.7% saved)

regimes415.0ms (20.2%)

Accuracy

Total 0.2b remaining (94.6%)

Threshold costs 0.2b (94.6%)

Counts

65 → 1

Compiler

Compiled 5304 to 4121 computations (22.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	13	10
2	14	10
3	13	10

end0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample605.0ms (29.5%)

Algorithm

1×

intervals

Results

329.0ms	8000×	body	128	valid
5.0ms	76×	body	128	invalid

Compiler

Compiled 89 to 72 computations (19.1% saved)

Details

analyze67.0ms (3.3%)

sample36.0ms (1.7%)

simplify7.0ms (0.3%)

prune5.0ms (0.2%)

localize5.0ms (0.3%)

series7.0ms (0.3%)

rewrite19.0ms (0.9%)

simplify103.0ms (5%)

prune372.0ms (18.1%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite4.0ms (0.2%)

simplify44.0ms (2.2%)

prune37.0ms (1.8%)

localize5.0ms (0.3%)

series12.0ms (0.6%)

rewrite13.0ms (0.6%)

simplify81.0ms (4%)

prune72.0ms (3.5%)

localize7.0ms (0.4%)

series6.0ms (0.3%)

rewrite9.0ms (0.4%)

simplify81.0ms (3.9%)

prune27.0ms (1.3%)

regimes415.0ms (20.2%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample605.0ms (29.5%)

Profiling