Details

analyze252.0ms (5.5%)

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)

sample1.4s (30.5%)

Results

1.3s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify57.0ms (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

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)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	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))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	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))

series95.0ms (2.1%)

Counts

4 → 96

Calls

4 calls:

39.0ms	(pow.f64 (hypot.f64 a b) 4)
37.0ms	(+.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))
11.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
7.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite19.0ms (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:

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))
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)))

simplify83.0ms (1.8%)

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

prune240.0ms (5.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	160	4	164

Error

Counts

164 → 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)
	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)
	1.4b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (neg.f64 (pow.f64 a 3)) -1))
	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 5016 to 2935 computations (41.5% saved)

localize14.0ms (0.3%)

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	(pow.f64 (hypot.f64 a b) 4)
✓	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))
✓	0.6b	(.f64 (+.f64 3 a) (.f64 b b))

series63.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

38.0ms

(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))

17.0ms

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

8.0ms

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

rewrite21.0ms (0.5%)

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:

6.0ms

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

6.0ms

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

0.0ms

(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))

simplify176.0ms (3.8%)

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 → 163

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

prune278.0ms (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	197	4	201

Error

Counts

201 → 4

Alt Table

Status	Error	Program
	1.4b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (neg.f64 (pow.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 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
✓	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)
▶	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 6807 to 4085 computations (40% saved)

localize17.0ms (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))
✓	0.0b	(.f64 a (+.f64 4 (.f64 2 a)))
✓	0.1b	(*.f64 (pow.f64 a 3) (-.f64 a 4))
✓	1.4b	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))

series28.0ms (0.6%)

Counts

4 → 60

Calls

4 calls:

20.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
3.0ms	(*.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))
2.0ms	(.f64 a (+.f64 4 (.f64 2 a)))

rewrite33.0ms (0.7%)

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:

11.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
7.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
7.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
0.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

simplify110.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

480×	`associate-l_binary64`
455×	`fma-neg_binary64`
439×	`associate-r_binary64`
393×	`exp-prod_binary64`
239×	`cancel-sign-sub-inv_binary64`

Counts

186 → 217

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	3597
1	700	2721
2	3127	2717
3	4515	2687
4	4898	2687

prune285.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	217	4	221

Error

Counts

221 → 4

Alt Table

Status	Error	Program
	1.4b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (neg.f64 (pow.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 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
✓	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)
✓	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 9157 to 5824 computations (36.4% saved)

localize15.0ms (0.3%)

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

series35.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
12.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`add-exp-log_binary64`
3×	`pow1_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0ms	(fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))

simplify108.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
590×	`unswap-sqr_binary64`
584×	`exp-prod_binary64`
403×	`cancel-sign-sub-inv_binary64`
388×	`fma-neg_binary64`

Counts

78 → 80

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	91	1929
1	234	1778
2	662	1532
3	2661	1532
4	4198	1529
5	4851	1529
6	5149	1529

prune264.0ms (5.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	201	4	205

Error

Counts

205 → 4

Alt Table

Status	Error	Program
	1.4b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (neg.f64 (pow.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 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
✓	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)
✓	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 7544 to 4138 computations (45.1% saved)

regimes873.0ms (19%)

Accuracy

Total 0.0b remaining (61.8%)

Threshold costs 0.0b (61.8%)

Counts

159 → 1

Compiler

Compiled 21004 to 14658 computations (30.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-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	22	49
1	32	49
2	35	49
3	37	49
4	38	49
5	37	49

end104.0ms (2.3%)

Compiler: Compiled 175 to 116 computations (33.7% saved)

Details

analyze252.0ms (5.5%)

sample1.4s (30.5%)

simplify57.0ms (1.2%)

prune5.0ms (0.1%)

localize14.0ms (0.3%)

series95.0ms (2.1%)

rewrite19.0ms (0.4%)

simplify83.0ms (1.8%)

prune240.0ms (5.2%)

localize14.0ms (0.3%)

series63.0ms (1.4%)

rewrite21.0ms (0.5%)

simplify176.0ms (3.8%)

prune278.0ms (6%)

localize17.0ms (0.4%)

series28.0ms (0.6%)

rewrite33.0ms (0.7%)

simplify110.0ms (2.4%)

prune285.0ms (6.2%)

localize15.0ms (0.3%)

series35.0ms (0.8%)

rewrite5.0ms (0.1%)

simplify108.0ms (2.3%)

prune264.0ms (5.7%)

regimes873.0ms (19%)

simplify3.0ms (0.1%)

end104.0ms (2.3%)

Profiling