Details

analyze1.3s (31.4%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	96.8%	3.2%	7
0%	96.8%	3.2%	8
0%	95.2%	4.8%	9
0%	95.2%	4.8%	10
0%	94.4%	5.6%	11
0%	94.4%	5.6%	12
0%	94%	6%	13
0%	94%	6%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample1.5s (37%)

Results

1.2s	8256×	body	128	valid
302.0ms	607×	body	8192	exit
3.0ms	33×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify12.0ms (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

prune3.0ms (0.1%)

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
▶	0.2b	(*.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)

localize4.0ms (0.1%)

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)

series9.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

8.0ms	(*.f64 (fma.f64 x 3 -12/29) y)
2.0ms	(fma.f64 x 3 -12/29)

rewrite4.0ms (0.1%)

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)

simplify45.0ms (1.1%)

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

prune47.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	52	8	60
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	52	10	62

Error

0.0b

Counts

62 → 10

Alt Table

Status	Error	Program
	17.7b	(.f64 (cbrt.f64 (.f64 (*.f64 (fma.f64 x 3 -12/29) (fma.f64 x 3 -12/29)) (fma.f64 x 3 -12/29))) y)
	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
▶	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	32.3b	(.f64 (.f64 (fma.f64 x 3 -12/29) (sqrt.f64 y)) (sqrt.f64 y))
	31.3b	(.f64 (sqrt.f64 (.f64 (fma.f64 x 3 -12/29) y)) (sqrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)))
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	29.7b	(*.f64 (log1p.f64 (expm1.f64 (fma.f64 x 3 -12/29))) y)
	1.4b	(.f64 (.f64 (fma.f64 x 3 -12/29) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))
	49.6b	(.f64 (sqrt.f64 (fma.f64 x 3 -12/29)) (.f64 (sqrt.f64 (fma.f64 x 3 -12/29)) y))
	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))

Compiler

Compiled 903 to 660 computations (26.9% saved)

localize7.0ms (0.2%)

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 (0.2%)

Counts

2 → 36

Calls

2 calls:

6.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
2.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

rewrite18.0ms (0.5%)

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)

simplify102.0ms (2.5%)

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

prune104.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	7	1	8
Picked	1	0	1
Done	0	1	1
Total	90	5	95

Error

Counts

95 → 5

Alt Table

Status	Error	Program
	18.0b	(.f64 (/.f64 (fma.f64 3 (pow.f64 x 3) -192/24389) (+.f64 (.f64 x x) (+.f64 (.f64 (/.f64 16 116) (/.f64 16 116)) (.f64 x (/.f64 16 116))))) y)
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
▶	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	0.5b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	19.5b	(/.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)))))

Compiler

Compiled 1374 to 1076 computations (21.7% saved)

localize5.0ms (0.1%)

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)
✓	0.2b	(.f64 3 (.f64 y x))

series13.0ms (0.3%)

Counts

3 → 15

Calls

3 calls:

6.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
5.0ms	(.f64 3 (.f64 y x))
1.0ms	(*.f64 12/29 y)

rewrite12.0ms (0.3%)

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

simplify86.0ms (2.1%)

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

prune58.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	86	4	90

Error

Counts

90 → 4

Alt Table

Status	Error	Program
▶	0.2b	(.f64 -1 (.f64 y (-.f64 12/29 (*.f64 3 x))))
	0.5b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
✓	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	19.5b	(/.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)))))

Compiler

Compiled 1275 to 840 computations (34.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 12/29 (*.f64 3 x))
✓	0.2b	(.f64 y (-.f64 12/29 (.f64 3 x)))

series7.0ms (0.2%)

Counts

2 → 15

Calls

2 calls:

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

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
5×	`distribute-lft-in_binary64`

Counts

2 → 52

Calls

2 calls:

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

simplify72.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-def_binary64`
306×	`*-commutative_binary64`
296×	`distribute-rgt-neg-out_binary64`
290×	`distribute-lft-neg-out_binary64`
287×	`associate-l_binary64`

Counts

67 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	944
1	185	746
2	519	608
3	1465	581
4	2446	581
5	4486	581
6	4919	581

prune76.0ms (1.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	91	4	95

Error

Counts

95 → 4

Alt Table

Status	Error	Program
✓	0.2b	(.f64 -1 (.f64 y (-.f64 12/29 (*.f64 3 x))))
	0.5b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
✓	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	19.5b	(/.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)))))

Compiler

Compiled 1417 to 1108 computations (21.8% saved)

regimes507.0ms (12.4%)

Accuracy

Total 0.2b remaining (89.9%)

Threshold costs 0.2b (89.9%)

Counts

92 → 1

Compiler

Compiled 7822 to 6165 computations (21.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	8	8
2	8	8

end73.0ms (1.8%)

Compiler: Compiled 82 to 66 computations (19.5% saved)

Details

analyze1.3s (31.4%)

sample1.5s (37%)

simplify12.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify45.0ms (1.1%)

prune47.0ms (1.1%)

localize7.0ms (0.2%)

series7.0ms (0.2%)

rewrite18.0ms (0.5%)

simplify102.0ms (2.5%)

prune104.0ms (2.6%)

localize5.0ms (0.1%)

series13.0ms (0.3%)

rewrite12.0ms (0.3%)

simplify86.0ms (2.1%)

prune58.0ms (1.4%)

localize5.0ms (0.1%)

series7.0ms (0.2%)

rewrite10.0ms (0.3%)

simplify72.0ms (1.8%)

prune76.0ms (1.9%)

regimes507.0ms (12.4%)

simplify3.0ms (0.1%)

end73.0ms (1.8%)

Profiling