Details

analyze249.0ms (8.2%)

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)

sample32.0ms (1.1%)

Algorithm

1×

intervals

Results

24.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify65.0ms (2.2%)

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

prune8.0ms (0.3%)

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
	0.2b	(-.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)
▶	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))

Status

Error

Program

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)

▶

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))

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	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))
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.4b	(.f64 (.f64 b b) (+.f64 a 3))

rewrite17.0ms (0.6%)

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))
2.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

series129.0ms (4.3%)

Counts

4 → 96

Calls

4 calls:

46.0ms	(pow.f64 (hypot.f64 a b) 4)
42.0ms	(+.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))
22.0ms	(.f64 (.f64 b b) (+.f64 a 3))
19.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify102.0ms (3.4%)

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 → 315

Iterations

Useful iterations: 2 (0.0ms)

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

prune181.0ms (6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	314	1	315
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	314	3	317

Error

Counts

317 → 3

Alt Table

Status	Error	Program
	11.0b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -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)
✓	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))

Compiler

Compiled 4988 to 2916 computations (41.5% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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)))))
✓	0.1b	(.f64 (.f64 a a) (-.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.4b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite39.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
15×	`distribute-lft-in_binary64`

Counts

4 → 121

Calls

4 calls:

15.0ms	(.f64 (.f64 a a) (-.f64 1 a))
6.0ms	(+.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)))))
6.0ms	(.f64 (.f64 b b) (+.f64 3 a))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series92.0ms (3%)

Counts

4 → 84

Calls

4 calls:

40.0ms	(+.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)))))
25.0ms	(.f64 (.f64 b b) (+.f64 3 a))
17.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
10.0ms	(.f64 (.f64 a a) (-.f64 1 a))

simplify114.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-+l+_binary64`
383×	`associate-l_binary64`
299×	`associate-r_binary64`
268×	`cancel-sign-sub-inv_binary64`
211×	`unswap-sqr_binary64`

Counts

205 → 374

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	3743
1	600	3419
2	2388	3054
3	4882	3054

prune218.0ms (7.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	373	1	374
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	374	3	377

Error

Counts

377 → 3

Alt Table

Status	Error	Program
✓	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)
✓	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))
▶	11.0b	(-.f64 (fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4))) 1)

Compiler

Compiled 7651 to 3925 computations (48.7% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 a 3) (+.f64 a -4))
✓	0.1b	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4)))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64`
7×	`add-exp-log_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 48

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))
0.0ms	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4)))

series17.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))
7.0ms	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4)))

simplify92.0ms (3%)

Algorithm

1×	egg-herbie

Rules

626×	`exp-prod_binary64`
451×	`fma-neg_binary64`
446×	`fma-def_binary64`
368×	`*-commutative_binary64`
321×	`distribute-rgt-in_binary64`

Counts

72 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1006
1	213	941
2	933	923
3	2703	899
4	4465	899
5	5047	899

prune75.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	124	3	127

Error

Counts

127 → 3

Alt Table

Status	Error	Program
✓	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)
✓	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))
✓	11.0b	(-.f64 (fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4))) 1)

Compiler

Compiled 1501 to 1027 computations (31.6% saved)

regimes571.0ms (18.9%)

Accuracy

Total 0.0b remaining (55%)

Threshold costs 0.0b (55%)

Compiler

Compiled 12410 to 8892 computations (28.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	37
1	33	37
2	37	37
3	39	37
4	40	37
5	38	37

end1.0ms (0%)

Compiler: Compiled 27 to 19 computations (29.6% saved)

sample974.0ms (32.2%)

Algorithm

1×

intervals

Results

652.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 133 to 89 computations (33.1% saved)

Details

analyze249.0ms (8.2%)

sample32.0ms (1.1%)

simplify65.0ms (2.2%)

prune8.0ms (0.3%)

localize14.0ms (0.5%)

rewrite17.0ms (0.6%)

series129.0ms (4.3%)

simplify102.0ms (3.4%)

prune181.0ms (6%)

localize14.0ms (0.5%)

rewrite39.0ms (1.3%)

series92.0ms (3%)

simplify114.0ms (3.7%)

prune218.0ms (7.2%)

localize9.0ms (0.3%)

rewrite9.0ms (0.3%)

series17.0ms (0.6%)

simplify92.0ms (3%)

prune75.0ms (2.5%)

regimes571.0ms (18.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample974.0ms (32.2%)

Profiling