Details

analyze67.0ms (3.5%)

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)

sample35.0ms (1.8%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 25 to 21 computations (16% saved)

simplify8.0ms (0.4%)

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 (0.2%)

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
	0.2b	(*.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)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 16 116))
✓	0.0b	(*.f64 (-.f64 x (/.f64 16 116)) 3)
✓	0.1b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

series9.0ms (0.5%)

Counts

3 → 48

Calls

3 calls:

6.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
2.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)
1.0ms	(-.f64 x (/.f64 16 116))

rewrite33.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
48×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
38×	`times-frac_binary64`

Counts

3 → 118

Calls

3 calls:

11.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
8.0ms	(-.f64 x (/.f64 16 116))
7.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

simplify104.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

914×	`fma-def_binary64`
591×	`times-frac_binary64`
420×	`associate-/l/_binary64`
297×	`*-commutative_binary64`
215×	`distribute-rgt-in_binary64`

Counts

166 → 175

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	241	1319
1	522	1059
2	1188	1053
3	2796	1052
4	4608	1052
5	4991	1052
6	3938	1052

prune164.0ms (8.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	170	5	175
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	170	7	177

Error

0.0b

Counts

177 → 7

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
	18.1b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 3 x -12/29))) y)
	16.7b	(/.f64 (.f64 (.f64 (-.f64 (.f64 x x) (.f64 (/.f64 16 116) (/.f64 16 116))) 3) y) (+.f64 x (/.f64 16 116)))
▶	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	19.7b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 3 x -12/29) 3)) y)

Compiler

Compiled 3802 to 3163 computations (16.8% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series11.0ms (0.6%)

Counts

2 → 36

Calls

2 calls:

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

simplify49.0ms (2.6%)

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

prune40.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	60	7	67

Error

0.0b

Counts

67 → 7

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
▶	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
	18.1b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 3 x -12/29))) y)
	16.7b	(/.f64 (.f64 (.f64 (-.f64 (.f64 x x) (.f64 (/.f64 16 116) (/.f64 16 116))) 3) y) (+.f64 x (/.f64 16 116)))
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	19.7b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 3 x -12/29) 3)) y)

Compiler

Compiled 780 to 575 computations (26.3% saved)

localize4.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x 4/29)
✓	0.1b	(*.f64 y (-.f64 x 4/29))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

series14.0ms (0.7%)

Counts

3 → 31

Calls

3 calls:

6.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
6.0ms	(*.f64 y (-.f64 x 4/29))
1.0ms	(-.f64 x 4/29)

rewrite29.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
63×	`prod-diff_binary64`
62×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`

Counts

3 → 154

Calls

3 calls:

7.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
6.0ms	(*.f64 y (-.f64 x 4/29))
5.0ms	(-.f64 x 4/29)

simplify97.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
499×	`neg-mul-1_binary64`
303×	`*-commutative_binary64`
245×	`distribute-rgt-neg-out_binary64`
242×	`distribute-lft-neg-out_binary64`

Counts

185 → 213

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	2017
1	312	1518
2	753	1518
3	1781	1515
4	3712	1515
5	4915	1515

prune161.0ms (8.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	211	2	213
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	213	7	220

Error

Counts

220 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y (-.f64 x 4/29))))
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	18.1b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 3 x -12/29))) y)
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
	16.7b	(/.f64 (.f64 (.f64 (-.f64 (.f64 x x) (.f64 (/.f64 16 116) (/.f64 16 116))) 3) y) (+.f64 x (/.f64 16 116)))
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
▶	0.3b	(.f64 (.f64 3 y) (-.f64 x 4/29))

Compiler

Compiled 3930 to 3034 computations (22.8% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x 4/29)
✓	0.3b	(.f64 (.f64 3 y) (-.f64 x 4/29))

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 (*.f64 3 y) (-.f64 x 4/29))

rewrite14.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`prod-diff_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

1 → 50

Calls

1 calls:

7.0ms

(*.f64 (*.f64 3 y) (-.f64 x 4/29))

simplify90.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
413×	`*-commutative_binary64`
330×	`sqr-pow_binary64`
258×	`exp-prod_binary64`
219×	`neg-mul-1_binary64`

Counts

74 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	818
1	251	682
2	694	682
3	1447	680
4	2211	680
5	3814	680
6	4938	680
7	4898	680

prune79.0ms (4.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	115	7	122

Error

Counts

122 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y (-.f64 x 4/29))))
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	18.1b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 3 x -12/29))) y)
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
	16.7b	(/.f64 (.f64 (.f64 (-.f64 (.f64 x x) (.f64 (/.f64 16 116) (/.f64 16 116))) 3) y) (+.f64 x (/.f64 16 116)))
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
✓	0.3b	(.f64 (.f64 3 y) (-.f64 x 4/29))

Compiler

Compiled 1969 to 1530 computations (22.3% saved)

regimes251.0ms (13.2%)

Accuracy

Total 0.2b remaining (94.9%)

Threshold costs 0.2b (94.9%)

Counts

47 → 1

Compiler

Compiled 3920 to 3172 computations (19.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
2	11	10

end0.0ms (0%)

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

sample604.0ms (31.9%)

Algorithm

1×

intervals

Results

308.0ms	8000×	body	128	valid
2.0ms	57×	body	128	invalid

Compiler

Compiled 109 to 89 computations (18.3% saved)

Details

analyze67.0ms (3.5%)

sample35.0ms (1.8%)

simplify8.0ms (0.4%)

prune3.0ms (0.2%)

localize7.0ms (0.4%)

series9.0ms (0.5%)

rewrite33.0ms (1.7%)

simplify104.0ms (5.5%)

prune164.0ms (8.6%)

localize4.0ms (0.2%)

series11.0ms (0.6%)

rewrite4.0ms (0.2%)

simplify49.0ms (2.6%)

prune40.0ms (2.1%)

localize4.0ms (0.2%)

series14.0ms (0.7%)

rewrite29.0ms (1.5%)

simplify97.0ms (5.1%)

prune161.0ms (8.5%)

localize7.0ms (0.4%)

series6.0ms (0.3%)

rewrite14.0ms (0.7%)

simplify90.0ms (4.8%)

prune79.0ms (4.2%)

regimes251.0ms (13.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample604.0ms (31.9%)

Profiling