Details

analyze269.0ms (6%)

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)

sample30.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify70.0ms (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 → 1

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 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 137 to 89 computations (35% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

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)))
0.6b	(.f64 (.f64 b b) (+.f64 a 3))

rewrite115.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

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:

7.0ms	(.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)))

Compiler

Compiled 2356 to 1295 computations (45% saved)

series219.0ms (4.9%)

Error

0.0b

Counts

4 → 56

Calls

4 calls:

78.0ms	(pow.f64 (hypot.f64 a b) 4)
65.0ms	(+.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))
26.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
16.0ms	(.f64 (.f64 b b) (+.f64 a 3))

Compiler

Compiled 2856 to 2144 computations (24.9% saved)

simplify91.0ms (2%)

Algorithm

1×	egg-herbie

Rules

644×	`associate-+l+_binary64`
497×	`distribute-rgt-in_binary64`
463×	`distribute-lft-in_binary64`
323×	`associate--l+_binary64`
190×	`cancel-sign-sub-inv_binary64`

Counts

134 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	3381
1	499	3158
2	1666	3083
3	5145	3083

prune78.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	101	5	106

Error

0.0b

Counts

106 → 5

Alt Table

Status	Error	Program
	10.4b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1)))
	0.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b)))) (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))))) (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))) -1))
	49.9b	(+.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 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 2092 to 1184 computations (43.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (hypot.f64 a b) 4)
0.1b	(fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4))
0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b)))
0.6b	(.f64 (+.f64 a 3) (.f64 b b))

rewrite113.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 64

Calls

4 calls:

8.0ms	(.f64 (+.f64 a 3) (.f64 b b))
2.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b)))
0.0ms	(fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4))

Compiler

Compiled 1834 to 1015 computations (44.7% saved)

series253.0ms (5.7%)

Error

0.0b

Counts

4 → 58

Calls

4 calls:

110.0ms	(fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4))
62.0ms	(pow.f64 (hypot.f64 a b) 4)
21.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b)))
17.0ms	(.f64 (+.f64 a 3) (.f64 b b))

Compiler

Compiled 2880 to 2170 computations (24.7% saved)

simplify123.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-neg_binary64`
547×	`associate-+r+_binary64`
532×	`associate-l_binary64`
439×	`associate-r_binary64`
285×	`distribute-rgt-in_binary64`

Counts

122 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	192	3189
1	454	2940
2	1390	2872
3	4394	2857
4	4955	2857

prune109.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	108	5	113

Error

Counts

113 → 5

Alt Table

Status	Error	Program
	10.4b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1)))
▶	0.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b)))) (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))))) (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))) -1))
	12.5b	(+.f64 -1 (fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (-.f64 a 4))))
	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 2014 to 1164 computations (42.2% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (+.f64 a 3) (.f64 b b))
7.5b	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))
7.5b	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))
7.5b	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))

rewrite154.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

10×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`cbrt-prod_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 63

Calls

4 calls:

8.0ms	(.f64 (+.f64 a 3) (.f64 b b))
1.0ms	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))
1.0ms	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))
1.0ms	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))

Compiler

Compiled 3914 to 2087 computations (46.7% saved)

series181.0ms (4.1%)

Error

Counts

4 → 35

Calls

4 calls:

34.0ms	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))
34.0ms	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))
33.0ms	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))
23.0ms	(.f64 (+.f64 a 3) (.f64 b b))

Compiler

Compiled 5372 to 3535 computations (34.2% saved)

simplify123.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

545×	`associate-l_binary64`
519×	`associate-r_binary64`
360×	`fma-def_binary64`
359×	`distribute-rgt-in_binary64`
357×	`distribute-lft-in_binary64`

Counts

98 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	3997
1	418	3916
2	1109	3854
3	3751	3817
4	5017	3817

prune124.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	86	5	91

Error

Counts

91 → 5

Alt Table

Status	Error	Program
	10.4b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1)))
✓	0.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b)))) (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))))) (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))) -1))
	12.5b	(+.f64 -1 (fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (-.f64 a 4))))
▶	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 3831 to 2074 computations (45.9% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (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)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.6b	(.f64 (.f64 b b) (+.f64 a 3))

rewrite137.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

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 → 79

Calls

4 calls:

7.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

Compiler

Compiled 2784 to 1301 computations (53.3% saved)

series165.0ms (3.7%)

Error

Counts

4 → 56

Calls

4 calls:

56.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
36.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
22.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
16.0ms	(.f64 (.f64 b b) (+.f64 a 3))

Compiler

Compiled 3016 to 2192 computations (27.3% saved)

simplify121.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-neg_binary64`
571×	`distribute-rgt-in_binary64`
532×	`distribute-lft-in_binary64`
331×	`associate--l+_binary64`
190×	`cancel-sign-sub-inv_binary64`

Counts

135 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	3582
1	504	3315
2	1684	3111
3	4671	3095
4	5100	3095

prune77.0ms (1.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	95	5	100

Error

Counts

100 → 5

Alt Table

Status	Error	Program
	10.4b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))) -1)))
✓	0.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b)))) (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (.f64 b b))))) (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))))) -1))
	12.5b	(fma.f64 (*.f64 a a) 4 (fma.f64 (pow.f64 a 3) (-.f64 a 4) -1))
✓	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (+.f64 a 3) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 1703 to 948 computations (44.3% saved)

regimes729.0ms (16.4%)

Accuracy

Total 0.0b remaining (84.9%)

Threshold costs 0.0b (84.9%)

Compiler

Compiled 17025 to 11653 computations (31.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	30
1	22	30
2	25	30
3	27	30
4	28	30
5	27	30

end1.0ms (0%)

Compiler: Compiled 23 to 16 computations (30.4% saved)

sample1.1s (24.5%)

Algorithm

1×

intervals

Results

677.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 251 to 157 computations (37.5% saved)

Details

analyze269.0ms (6%)

sample30.0ms (0.7%)

simplify70.0ms (1.6%)

prune5.0ms (0.1%)

localize18.0ms (0.4%)

rewrite115.0ms (2.6%)

series219.0ms (4.9%)

simplify91.0ms (2%)

prune78.0ms (1.7%)

localize18.0ms (0.4%)

rewrite113.0ms (2.5%)

series253.0ms (5.7%)

simplify123.0ms (2.8%)

prune109.0ms (2.4%)

localize22.0ms (0.5%)

rewrite154.0ms (3.5%)

series181.0ms (4.1%)

simplify123.0ms (2.8%)

prune124.0ms (2.8%)

localize17.0ms (0.4%)

rewrite137.0ms (3.1%)

series165.0ms (3.7%)

simplify121.0ms (2.7%)

prune77.0ms (1.7%)

regimes729.0ms (16.4%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (24.5%)

Profiling