Details

analyze424.0ms (6.5%)

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
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)

sample59.0ms (0.9%)

Algorithm

1×

intervals

Results

42.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify81.0ms (1.2%)

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

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

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)

localize29.0ms (0.4%)

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)))
✓	1.1b	(.f64 (.f64 b b) (+.f64 a 3))

rewrite30.0ms (0.5%)

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:

13.0ms	(.f64 (.f64 b b) (+.f64 a 3))
7.0ms	(+.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)))

series258.0ms (4%)

Counts

4 → 96

Calls

4 calls:

99.0ms	(+.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))
77.0ms	(pow.f64 (hypot.f64 a b) 4)
45.0ms	(.f64 (.f64 b b) (+.f64 a 3))
36.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify165.0ms (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 → 315

Iterations

Useful iterations: 2 (0.0ms)

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

prune384.0ms (5.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	311	4	315
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	312	5	317

Error

0.0b

Counts

317 → 5

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
	43.6b	(.f64 (sqrt.f64 (+.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))) (sqrt.f64 (+.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))))
	15.1b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1)) 3))
	15.1b	(cbrt.f64 (.f64 (.f64 (+.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)) (+.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))) (+.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 5287 to 3101 computations (41.3% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
36×	`prod-diff_binary64`
33×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
13×	`cube-prod_binary64`

Counts

3 → 104

Calls

3 calls:

15.0ms

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

10.0ms

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

1.0ms

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

series148.0ms (2.3%)

Counts

3 → 72

Calls

3 calls:

70.0ms

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

39.0ms

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

38.0ms

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

simplify301.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

548×	`distribute-rgt-in_binary64`
515×	`fma-neg_binary64`
502×	`exp-prod_binary64`
458×	`cancel-sign-sub-inv_binary64`
247×	`unswap-sqr_binary64`

Counts

176 → 337

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	221	4043
1	447	3644
2	1699	3331
3	4274	3318
4	4869	3318
5	4953	3318
6	4906	3318

prune616.0ms (9.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	411	1	412
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	412	5	417

Error

0.0b

Counts

417 → 5

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
	43.6b	(.f64 (sqrt.f64 (+.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))) (sqrt.f64 (+.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))))
	15.1b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1)) 3))
	15.1b	(cbrt.f64 (.f64 (.f64 (+.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)) (+.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))) (+.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 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -1)

Compiler

Compiled 7093 to 4264 computations (39.9% saved)

localize34.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`unpow-prod-down_binary64`
6×	`pow-unpow_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 39

Calls

2 calls:

5.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))
1.0ms	(fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)))

series159.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

81.0ms	(fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)))
77.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

simplify178.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
596×	`fma-def_binary64`
403×	`cancel-sign-sub-inv_binary64`
379×	`associate-+l+_binary64`
310×	`distribute-lft-out_binary64`

Counts

87 → 160

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	111	2093
1	271	1834
2	726	1645
3	2797	1631
4	4509	1628
5	4941	1628

prune389.0ms (6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	435	0	435
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	435	5	440

Error

0.0b

Counts

440 → 5

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
	43.6b	(.f64 (sqrt.f64 (+.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))) (sqrt.f64 (+.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))))
	15.1b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1)) 3))
▶	15.1b	(cbrt.f64 (.f64 (.f64 (+.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)) (+.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))) (+.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 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -1)

Compiler

Compiled 8002 to 5047 computations (36.9% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.1b	(.f64 (.f64 b b) (+.f64 a 3))
	1.1b	(.f64 (.f64 b b) (+.f64 a 3))
	1.1b	(.f64 (.f64 b b) (+.f64 a 3))
✓	14.2b	(cbrt.f64 (.f64 (.f64 (+.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)) (+.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))) (+.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))))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`frac-times_binary64`
27×	`flip-+_binary64`
27×	`flip3-+_binary64`
26×	`cbrt-div_binary64`
14×	`associate-*l/_binary64`

Counts

1 → 38

Calls

1 calls:

18.0ms

(cbrt.f64 (*.f64 (*.f64 (+.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)) (+.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))) (+.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))))

series46.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

46.0ms

(cbrt.f64 (*.f64 (*.f64 (+.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)) (+.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))) (+.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))))

simplify209.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

676×	`associate-+l+_binary64`
458×	`*-commutative_binary64`
457×	`fma-neg_binary64`
386×	`associate-+r+_binary64`
325×	`associate--l+_binary64`

Counts

62 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	171	8493
1	472	6945
2	1872	6762
3	4150	6740
4	4913	6740

prune432.0ms (6.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	787	1	788
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	789	4	793

Error

0.0b

Counts

793 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
	43.6b	(.f64 (sqrt.f64 (+.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))) (sqrt.f64 (+.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 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -1)
	15.1b	(cbrt.f64 (pow.f64 (+.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))

Compiler

Compiled 18983 to 10619 computations (44.1% saved)

regimes1.2s (19%)

Accuracy

Total 0.0b remaining (41.1%)

Threshold costs 0.0b (41.1%)

Compiler

Compiled 15147 to 10845 computations (28.4% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-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	22	33
2	26	33
3	28	33
4	29	33
5	29	33

end2.0ms (0%)

Compiler: Compiled 25 to 17 computations (32% saved)

sample1.2s (18.5%)

Algorithm

1×

intervals

Results

818.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 191 to 128 computations (33% saved)

Details

analyze424.0ms (6.5%)

sample59.0ms (0.9%)

simplify81.0ms (1.2%)

prune9.0ms (0.1%)

localize29.0ms (0.4%)

rewrite30.0ms (0.5%)

series258.0ms (4%)

simplify165.0ms (2.5%)

prune384.0ms (5.9%)

localize26.0ms (0.4%)

rewrite38.0ms (0.6%)

series148.0ms (2.3%)

simplify301.0ms (4.6%)

prune616.0ms (9.4%)

localize34.0ms (0.5%)

rewrite9.0ms (0.1%)

series159.0ms (2.4%)

simplify178.0ms (2.7%)

prune389.0ms (6%)

localize21.0ms (0.3%)

rewrite25.0ms (0.4%)

series46.0ms (0.7%)

simplify209.0ms (3.2%)

prune432.0ms (6.6%)

regimes1.2s (19%)

simplify7.0ms (0.1%)

end2.0ms (0%)

sample1.2s (18.5%)

Profiling