Details

analyze258.0ms (6.4%)

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)

sample29.0ms (0.7%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify58.0ms (1.4%)

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 (0.3%)

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

series119.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

38.0ms	(+.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))
37.0ms	(pow.f64 (hypot.f64 a b) 4)
35.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite18.0ms (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:

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))
6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
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)))

simplify84.0ms (2.1%)

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

prune262.0ms (6.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	158	4	162
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	159	5	164

Error

Counts

164 → 5

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))
	8.9b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.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)))
	12.4b	(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))))
▶	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.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))

Compiler

Compiled 5203 to 3042 computations (41.5% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
✓	0.0b	(.f64 a (+.f64 4 (.f64 2 a)))
✓	0.1b	(*.f64 (pow.f64 a 3) (-.f64 a 4))
✓	0.7b	(.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (*.f64 2 a)))))

series35.0ms (0.9%)

Counts

4 → 60

Calls

4 calls:

25.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (*.f64 2 a)))))
4.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
3.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
3.0ms	(.f64 a (+.f64 4 (.f64 2 a)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
16×	`associate-l_binary64`

Counts

4 → 126

Calls

4 calls:

9.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (*.f64 2 a)))))
8.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
4.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
0.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

simplify117.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

483×	`associate-l_binary64`
452×	`fma-neg_binary64`
443×	`associate-r_binary64`
240×	`cancel-sign-sub-inv_binary64`
217×	`unswap-sqr_binary64`

Counts

186 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	3659
1	703	2717
2	3163	2701
3	4741	2695
4	4886	2695

prune348.0ms (8.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	219	4	223

Error

Counts

223 → 4

Alt Table

Status	Error	Program
	4.3b	(+.f64 (/.f64 (.f64 (.f64 b b) (fma.f64 (-.f64 4 (.f64 2 a)) (-.f64 144 (pow.f64 b 4)) (.f64 (fma.f64 a 16 (.f64 -4 (pow.f64 a 3))) (-.f64 12 (.f64 b b))))) (.f64 (-.f64 12 (.f64 b b)) (-.f64 4 (.f64 2 a)))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -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))
▶	0.1b	(+.f64 (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12)))) (fma.f64 (.f64 a a) 4 (+.f64 (.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))

Compiler

Compiled 9314 to 5915 computations (36.5% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
	0.1b	(*.f64 (pow.f64 a 3) (-.f64 a 4))
✓	0.1b	(*.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12)))
✓	0.2b	(.f64 b (.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12))))

series38.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(.f64 b (.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12))))
17.0ms	(*.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 46

Calls

2 calls:

4.0ms	(.f64 b (.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12))))
3.0ms	(*.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12)))

simplify90.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

478×	`fma-def_binary64`
401×	`distribute-rgt-in_binary64`
395×	`distribute-lft-in_binary64`
393×	`associate-+l+_binary64`
349×	`+-commutative_binary64`

Counts

94 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	2369
1	231	1708
2	771	1632
3	2837	1630
4	4372	1630
5	5008	1630

prune340.0ms (8.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	198	4	202

Error

Counts

202 → 4

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))
▶	0.1b	(+.f64 (.f64 b (pow.f64 (+.f64 (.f64 (+.f64 (.f64 a (fma.f64 2 a 4)) 12) b) (pow.f64 b 3)) 1)) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
✓	0.1b	(+.f64 (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12)))) (fma.f64 (.f64 a a) 4 (+.f64 (.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))

Compiler

Compiled 7365 to 4801 computations (34.8% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (+.f64 (.f64 a (fma.f64 2 a 4)) 12) b) (pow.f64 b 3))
	0.1b	(*.f64 (pow.f64 a 3) (-.f64 a 4))
✓	0.1b	(.f64 (+.f64 (.f64 a (fma.f64 2 a 4)) 12) b)
✓	0.2b	(.f64 b (pow.f64 (+.f64 (.f64 (+.f64 (*.f64 a (fma.f64 2 a 4)) 12) b) (pow.f64 b 3)) 1))

series55.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

25.0ms

(*.f64 b (pow.f64 (+.f64 (*.f64 (+.f64 (*.f64 a (fma.f64 2 a 4)) 12) b) (pow.f64 b 3)) 1))

15.0ms

(+.f64 (*.f64 (+.f64 (*.f64 a (fma.f64 2 a 4)) 12) b) (pow.f64 b 3))

14.0ms

(*.f64 (+.f64 (*.f64 a (fma.f64 2 a 4)) 12) b)

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 66

Calls

3 calls:

13.0ms

(*.f64 b (pow.f64 (+.f64 (*.f64 (+.f64 (*.f64 a (fma.f64 2 a 4)) 12) b) (pow.f64 b 3)) 1))

7.0ms

(+.f64 (*.f64 (+.f64 (*.f64 a (fma.f64 2 a 4)) 12) b) (pow.f64 b 3))

5.0ms

(*.f64 (+.f64 (*.f64 a (fma.f64 2 a 4)) 12) b)

simplify111.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
412×	`exp-prod_binary64`
392×	`*-commutative_binary64`
379×	`fma-neg_binary64`
327×	`cancel-sign-sub-inv_binary64`

Counts

138 → 136

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	148	3046
1	371	2447
2	1443	2298
3	3419	2296
4	4718	2295
5	4973	2295

prune349.0ms (8.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	222	4	226

Error

Counts

226 → 4

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))
✓	0.1b	(+.f64 (.f64 b (pow.f64 (+.f64 (.f64 (+.f64 (.f64 a (fma.f64 2 a 4)) 12) b) (pow.f64 b 3)) 1)) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
✓	0.1b	(+.f64 (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12)))) (fma.f64 (.f64 a a) 4 (+.f64 (.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))

Compiler

Compiled 9350 to 6606 computations (29.3% saved)

regimes560.0ms (13.8%)

Accuracy

Total 0.0b remaining (76.7%)

Threshold costs 0.0b (76.7%)

Counts

99 → 1

Compiler

Compiled 14413 to 10106 computations (29.9% 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	17	33
1	24	33
2	27	33
3	29	33
4	30	33
5	29	33

end1.0ms (0%)

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

sample1.0s (25.8%)

Algorithm

1×

intervals

Results

703.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 179 to 120 computations (33% saved)

Details

analyze258.0ms (6.4%)

sample29.0ms (0.7%)

simplify58.0ms (1.4%)

prune5.0ms (0.1%)

localize13.0ms (0.3%)

series119.0ms (2.9%)

rewrite18.0ms (0.4%)

simplify84.0ms (2.1%)

prune262.0ms (6.4%)

localize18.0ms (0.5%)

series35.0ms (0.9%)

rewrite31.0ms (0.8%)

simplify117.0ms (2.9%)

prune348.0ms (8.6%)

localize18.0ms (0.4%)

series38.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify90.0ms (2.2%)

prune340.0ms (8.4%)

localize20.0ms (0.5%)

series55.0ms (1.4%)

rewrite28.0ms (0.7%)

simplify111.0ms (2.7%)

prune349.0ms (8.6%)

regimes560.0ms (13.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.0s (25.8%)

Profiling