Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.8s (25%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify111.0ms (1.6%)

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

prune9.0ms (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

16.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.8b	(+.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))
	18.1b	(-.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

▶

16.8b

(+.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))

18.1b

(-.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)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	3.7b	(.f64 (.f64 b b) (+.f64 a 3))
✓	7.2b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	11.0b	(+.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))

series159.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

77.0ms	(+.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))
49.0ms	(pow.f64 (hypot.f64 a b) 4)
21.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
12.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`

Counts

4 → 78

Calls

4 calls:

13.0ms	(.f64 (.f64 b b) (+.f64 a 3))
8.0ms	(+.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))
3.0ms	(pow.f64 (hypot.f64 a b) 4)
1.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify173.0ms (2.5%)

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 → 158

Iterations

Useful iterations: 2 (0.0ms)

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

prune413.0ms (5.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	157	3	160

Error

0.0b

Counts

160 → 3

Alt Table

Status	Error	Program
▶	0.7b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 3 (pow.f64 b 2)) -1))
	20.3b	(+.f64 (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 b b) (.f64 a a)) (pow.f64 a 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	18.1b	(-.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 4792 to 2812 computations (41.3% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.2b	(*.f64 3 (pow.f64 b 2))

series34.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

29.0ms	(hypot.f64 a b)
5.0ms	(*.f64 3 (pow.f64 b 2))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 39

Calls

2 calls:

9.0ms	(*.f64 3 (pow.f64 b 2))
1.0ms	(hypot.f64 a b)

simplify143.0ms (2%)

Algorithm

1×	egg-herbie

Rules

651×	`fma-neg_binary64`
375×	`unswap-sqr_binary64`
285×	`associate-l_binary64`
278×	`distribute-neg-frac_binary64`
265×	`associate-r_binary64`

Counts

63 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	874
1	263	793
2	693	766
3	2976	766
4	4411	766
5	4873	766
6	4940	766

prune233.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	119	3	122

Error

0.0b

Counts

122 → 3

Alt Table

Status	Error	Program
✓	0.7b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 3 (pow.f64 b 2)) -1))
	20.3b	(+.f64 (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 b b) (.f64 a a)) (pow.f64 a 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
▶	18.1b	(-.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 2651 to 1896 computations (28.5% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	3.7b	(.f64 (.f64 b b) (+.f64 3 a))
✓	9.1b	(+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (.f64 b b) (+.f64 3 a)))
✓	11.0b	(+.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)))))

series104.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

42.0ms	(+.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)))))
31.0ms	(+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (.f64 b b) (+.f64 3 a)))
19.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
11.0ms	(.f64 (.f64 b b) (+.f64 3 a))

rewrite78.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`associate-+l+_binary64`
25×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`

Counts

4 → 115

Calls

4 calls:

21.0ms	(+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (.f64 b b) (+.f64 3 a)))
16.0ms	(+.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)))))
12.0ms	(.f64 (.f64 b b) (+.f64 3 a))
7.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify220.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

480×	`cancel-sign-sub-inv_binary64`
443×	`fma-neg_binary64`
363×	`associate-l_binary64`
324×	`associate-r_binary64`
300×	`fma-def_binary64`

Counts

211 → 230

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	4568
1	750	4050
2	3046	3794
3	4865	3794
4	4919	3794

prune505.0ms (7.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	230	3	233

Error

0.0b

Counts

233 → 3

Alt Table

Status	Error	Program
✓	0.7b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 3 (pow.f64 b 2)) -1))
▶	20.3b	(+.f64 (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 b b) (.f64 a a)) (pow.f64 a 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
✓	18.1b	(-.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 8807 to 4597 computations (47.8% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.7b	(.f64 (.f64 b b) (+.f64 a 3))
	7.2b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	11.0b	(+.f64 (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 b b) (.f64 a a)) (pow.f64 a 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
✓	14.5b	(.f64 (.f64 b b) (*.f64 a a))

series80.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

55.0ms	(+.f64 (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 b b) (.f64 a a)) (pow.f64 a 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
25.0ms	(.f64 (.f64 b b) (*.f64 a a))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow-prod-down_binary64`
10×	`*-un-lft-identity_binary64`

Counts

2 → 53

Calls

2 calls:

13.0ms	(.f64 (.f64 b b) (*.f64 a a))
12.0ms	(+.f64 (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 b b) (.f64 a a)) (pow.f64 a 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))

simplify156.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

773×	`associate-l_binary64`
610×	`associate-r_binary64`
482×	`distribute-rgt-in_binary64`
464×	`distribute-lft-in_binary64`
408×	`fma-neg_binary64`

Counts

101 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	2635
1	360	2433
2	1359	2322
3	4912	2314
4	5170	2314

prune385.0ms (5.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	163	4	167

Error

Counts

167 → 4

Alt Table

Status	Error	Program
	47.5b	(/.f64 (+.f64 (pow.f64 (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 a 4))) 3) (pow.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) 3)) (fma.f64 (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 a 4))) (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 a 4))) (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) (-.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 a 4)))))))
✓	0.7b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 3 (pow.f64 b 2)) -1))
✓	20.3b	(+.f64 (+.f64 (pow.f64 b 4) (fma.f64 2 (.f64 (.f64 b b) (.f64 a a)) (pow.f64 a 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
✓	18.1b	(-.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 6704 to 3655 computations (45.5% saved)

regimes1.9s (27.5%)

Accuracy

Total 0.5b remaining (99.2%)

Threshold costs 0.5b (99.2%)

Counts

182 → 1

Compiler

Compiled 25020 to 17551 computations (29.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	15	20
2	15	20

end341.0ms (4.9%)

Compiler: Compiled 241 to 149 computations (38.2% saved)

Details

analyze2.0ms (0%)

sample1.8s (25%)

simplify111.0ms (1.6%)

prune9.0ms (0.1%)

localize28.0ms (0.4%)

series159.0ms (2.3%)

rewrite31.0ms (0.4%)

simplify173.0ms (2.5%)

prune413.0ms (5.9%)

localize16.0ms (0.2%)

series34.0ms (0.5%)

rewrite13.0ms (0.2%)

simplify143.0ms (2%)

prune233.0ms (3.3%)

localize26.0ms (0.4%)

series104.0ms (1.5%)

rewrite78.0ms (1.1%)

simplify220.0ms (3.1%)

prune505.0ms (7.2%)

localize33.0ms (0.5%)

series80.0ms (1.1%)

rewrite33.0ms (0.5%)

simplify156.0ms (2.2%)

prune385.0ms (5.5%)

regimes1.9s (27.5%)

simplify4.0ms (0.1%)

end341.0ms (4.9%)

Profiling