Details

analyze211.0ms (5.8%)

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
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.3s (36.1%)

Results

1.2s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify60.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
556×	`cancel-sign-sub-inv_binary64`
552×	`unswap-sqr_binary64`
357×	`unsub-neg_binary64`
344×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	168	37
3	492	37
4	1604	33
5	2891	33
6	4309	33
7	5214	33

prune5.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)

Status

Error

Program

▶

0.0b

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	1.1b	(.f64 (.f64 b b) (+.f64 a 3))

series78.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

31.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
27.0ms	(pow.f64 (hypot.f64 a b) 4)
13.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
7.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 78

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify82.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-+l+_binary64`
469×	`distribute-rgt-in_binary64`
453×	`distribute-lft-in_binary64`
338×	`associate--l+_binary64`
219×	`cancel-sign-sub-inv_binary64`

Counts

174 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3413
1	464	3143
2	1556	3045
3	5074	3045

prune198.0ms (5.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	157	5	162
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	158	6	164

Error

Counts

164 → 6

Alt Table

Status	Error	Program
	11.2b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (.f64 4 (pow.f64 a 3)) 1))
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	53.3b	(+.f64 (.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b)))) (*.f64 (pow.f64 a 3) (-.f64 a 4)))
	10.4b	(+.f64 -1 (.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
	11.2b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

Compiler

Compiled 5064 to 2973 computations (41.3% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3))
✓	1.1b	(.f64 (+.f64 3 a) (.f64 b b))

series50.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

32.0ms

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))

10.0ms

(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))

7.0ms

(*.f64 (+.f64 3 a) (*.f64 b b))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
36×	`prod-diff_binary64`
31×	`add-cube-cbrt_binary64`
16×	`unpow-prod-down_binary64`

Counts

3 → 116

Calls

3 calls:

9.0ms

(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))

6.0ms

(*.f64 (+.f64 3 a) (*.f64 b b))

4.0ms

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))

simplify136.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

706×	`fma-neg_binary64`
672×	`distribute-rgt-in_binary64`
514×	`cancel-sign-sub-inv_binary64`
255×	`unswap-sqr_binary64`
176×	`distribute-rgt-out_binary64`

Counts

188 → 179

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	4373
1	532	3968
2	2022	3657
3	4999	3647
4	5258	3647

prune277.0ms (7.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	211	2	213
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	213	6	219

Error

Counts

219 → 6

Alt Table

Status	Error	Program
	11.2b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (.f64 4 (pow.f64 a 3)) 1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	53.3b	(+.f64 (.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b)))) (*.f64 (pow.f64 a 3) (-.f64 a 4)))
▶	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	10.4b	(fma.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (*.f64 a 4) 12)) -1)
	11.2b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

Compiler

Compiled 7528 to 4505 computations (40.2% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	0.0b	(-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
	1.1b	(.f64 (+.f64 3 a) (.f64 b b))

series35.0ms (1%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
11.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`fma-def_binary64`
8×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`unpow-prod-down_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

6.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify92.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

842×	`fma-neg_binary64`
752×	`fma-def_binary64`
567×	`associate-+l+_binary64`
336×	`associate--l+_binary64`
278×	`associate-+r+_binary64`

Counts

91 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	2281
1	314	2122
2	964	1866
3	4975	1852
4	5692	1852

prune288.0ms (7.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	218	6	224

Error

Counts

224 → 6

Alt Table

Status	Error	Program
	11.2b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (.f64 4 (pow.f64 a 3)) 1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	53.3b	(+.f64 (.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b)))) (*.f64 (pow.f64 a 3) (-.f64 a 4)))
✓	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
▶	10.4b	(fma.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (*.f64 a 4) 12)) -1)
	11.2b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

Compiler

Compiled 8443 to 4618 computations (45.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))
✓	0.1b	(fma.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (*.f64 a 4) 12)) -1)

series17.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (*.f64 a 4) 12)) -1)
5.0ms	(+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64`
3×	`sum-log_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

2 → 26

Calls

2 calls:

5.0ms	(+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))
0.0ms	(fma.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (*.f64 a 4) 12)) -1)

simplify88.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

366×	`sub-neg_binary64`
362×	`*-commutative_binary64`
320×	`exp-prod_binary64`
316×	`distribute-rgt-in_binary64`
313×	`unswap-sqr_binary64`

Counts

74 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1046
1	175	919
2	551	917
3	2152	913
4	3394	913
5	4903	913
6	5086	913

prune74.0ms (2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	65	6	71

Error

Counts

71 → 6

Alt Table

Status	Error	Program
	11.2b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (.f64 4 (pow.f64 a 3)) 1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	53.3b	(+.f64 (.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b)))) (*.f64 (pow.f64 a 3) (-.f64 a 4)))
✓	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
✓	10.4b	(fma.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (*.f64 a 4) 12)) -1)
	11.2b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

Compiler

Compiled 1269 to 762 computations (40% saved)

regimes389.0ms (10.7%)

Accuracy

Total 0.0b remaining (65.6%)

Threshold costs 0.0b (65.6%)

Counts

77 → 1

Compiler

Compiled 8161 to 5616 computations (31.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-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	16	33
1	21	33
2	25	33
3	27	33
4	28	33
5	28	33

end128.0ms (3.5%)

Compiler: Compiled 176 to 122 computations (30.7% saved)

Details

analyze211.0ms (5.8%)

sample1.3s (36.1%)

simplify60.0ms (1.7%)

prune5.0ms (0.1%)

localize13.0ms (0.4%)

series78.0ms (2.2%)

rewrite15.0ms (0.4%)

simplify82.0ms (2.2%)

prune198.0ms (5.4%)

localize14.0ms (0.4%)

series50.0ms (1.4%)

rewrite26.0ms (0.7%)

simplify136.0ms (3.8%)

prune277.0ms (7.6%)

localize15.0ms (0.4%)

series35.0ms (1%)

rewrite12.0ms (0.3%)

simplify92.0ms (2.5%)

prune288.0ms (7.9%)

localize8.0ms (0.2%)

series17.0ms (0.5%)

rewrite6.0ms (0.2%)

simplify88.0ms (2.4%)

prune74.0ms (2%)

regimes389.0ms (10.7%)

simplify3.0ms (0.1%)

end128.0ms (3.5%)

Profiling