Details

analyze403.0ms (5.8%)

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)

sample53.0ms (0.8%)

Algorithm

1×

intervals

Results

39.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify67.0ms (1%)

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)

localize30.0ms (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)))
✓	1.3b	(.f64 (.f64 b b) (+.f64 a 3))

series175.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

69.0ms	(pow.f64 (hypot.f64 a b) 4)
68.0ms	(+.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))
21.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
16.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite32.0ms (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:

12.0ms	(.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)
2.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify149.0ms (2.2%)

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

prune336.0ms (4.9%)

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

0.0b

Counts

164 → 5

Alt Table

Status	Error	Program
▶	0.9b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 a b)) 8) (pow.f64 (cbrt.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))
✓	0.0b	(+.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))
	18.1b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	48.9b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))) (.f64 4 (pow.f64 a 3)))
	9.4b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

Compiler

Compiled 5003 to 2940 computations (41.2% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (hypot.f64 a b))
✓	0.8b	(pow.f64 (cbrt.f64 (hypot.f64 a b)) 4)
✓	1.1b	(pow.f64 (cbrt.f64 (hypot.f64 a b)) 8)
	1.3b	(.f64 (.f64 b b) (+.f64 a 3))

series438.0ms (6.4%)

Counts

3 → 72

Calls

3 calls:

202.0ms	(pow.f64 (cbrt.f64 (hypot.f64 a b)) 8)
161.0ms	(pow.f64 (cbrt.f64 (hypot.f64 a b)) 4)
74.0ms	(cbrt.f64 (hypot.f64 a b))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`unpow-prod-down_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`cbrt-prod_binary64`

Counts

3 → 59

Calls

3 calls:

7.0ms	(pow.f64 (cbrt.f64 (hypot.f64 a b)) 8)
4.0ms	(pow.f64 (cbrt.f64 (hypot.f64 a b)) 4)
1.0ms	(cbrt.f64 (hypot.f64 a b))

simplify208.0ms (3%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-def_binary64`
469×	`*-commutative_binary64`
419×	`cancel-sign-sub-inv_binary64`
380×	`fma-neg_binary64`
272×	`sqr-pow_binary64`

Counts

131 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	3154
1	652	3042
2	1812	2959
3	3932	2954
4	4980	2954
5	4899	2954

prune516.0ms (7.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	233	5	238

Error

0.0b

Counts

238 → 5

Alt Table

Status	Error	Program
✓	0.9b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 a b)) 8) (pow.f64 (cbrt.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))
✓	0.0b	(+.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))
	18.1b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	48.9b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))) (.f64 4 (pow.f64 a 3)))
▶	9.4b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

Compiler

Compiled 9922 to 5673 computations (42.8% saved)

localize16.0ms (0.2%)

Local error

Found 2 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))

series13.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
6.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 73

Calls

2 calls:

18.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
1.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

simplify136.0ms (2%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-neg_binary64`
528×	`exp-prod_binary64`
509×	`unswap-sqr_binary64`
356×	`*-commutative_binary64`
319×	`fma-def_binary64`

Counts

97 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1505
1	247	1218
2	905	1214
3	2380	1177
4	4398	1177
5	5146	1177

prune244.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	113	4	117

Error

0.0b

Counts

117 → 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))
▶	9.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1))) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)))
	20.2b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1) 3))
	48.9b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))) (.f64 4 (pow.f64 a 3)))

Compiler

Compiled 2744 to 1944 computations (29.2% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)
✓	0.1b	(.f64 (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (*.f64 a (+.f64 -4 a)) 4) -1)))
✓	0.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1))) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)))
✓	0.1b	(cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1))

series44.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

17.0ms	(cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1))
13.0ms	(.f64 (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (*.f64 a (+.f64 -4 a)) 4) -1)))
8.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1))) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)))
6.0ms	(fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
15×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

15.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1))) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)))
9.0ms	(.f64 (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)) (cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (*.f64 a (+.f64 -4 a)) 4) -1)))
2.0ms	(fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1)
1.0ms	(cbrt.f64 (fma.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 -4 a)) 4) -1))

simplify267.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-neg_binary64`
446×	`cancel-sign-sub-inv_binary64`
323×	`fma-def_binary64`
269×	`unswap-sqr_binary64`
230×	`exp-prod_binary64`

Counts

151 → 184

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	153	3901
1	362	3500
2	991	3010
3	2687	2939
4	4558	2839
5	4972	2839
6	4919	2839

prune661.0ms (9.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	278	2	280
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	280	4	284

Error

Counts

284 → 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))
	48.9b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))) (.f64 4 (pow.f64 a 3)))
	20.2b	(cbrt.f64 (pow.f64 (fma.f64 a (*.f64 a (fma.f64 a (+.f64 a -4) 4)) -1) 3))
	9.4b	(fma.f64 a (*.f64 a (fma.f64 a (+.f64 a -4) 4)) -1)

Compiler

Compiled 12441 to 8337 computations (33% saved)

regimes1.1s (15.9%)

Accuracy

Total 0.0b remaining (39.5%)

Threshold costs 0.0b (39.5%)

Counts

103 → 1

Compiler

Compiled 12110 to 8843 computations (27% saved)

simplify5.0ms (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	16	33
1	21	33
2	25	33
3	27	33
4	28	33
5	28	33

end1.0ms (0%)

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

sample1.9s (26.8%)

Algorithm

1×

intervals

Results

1.3s	8000×	body	128	valid
1.0ms	4×	body	128	invalid

Compiler

Compiled 140 to 99 computations (29.3% saved)

Details

analyze403.0ms (5.8%)

sample53.0ms (0.8%)

simplify67.0ms (1%)

prune9.0ms (0.1%)

localize30.0ms (0.4%)

series175.0ms (2.5%)

rewrite32.0ms (0.5%)

simplify149.0ms (2.2%)

prune336.0ms (4.9%)

localize33.0ms (0.5%)

series438.0ms (6.4%)

rewrite16.0ms (0.2%)

simplify208.0ms (3%)

prune516.0ms (7.5%)

localize16.0ms (0.2%)

series13.0ms (0.2%)

rewrite28.0ms (0.4%)

simplify136.0ms (2%)

prune244.0ms (3.5%)

localize21.0ms (0.3%)

series44.0ms (0.6%)

rewrite47.0ms (0.7%)

simplify267.0ms (3.9%)

prune661.0ms (9.6%)

regimes1.1s (15.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.9s (26.8%)

Profiling