Details

analyze182.0ms (5.2%)

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 (39.4%)

Results

1.3s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify58.0ms (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 → 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)

localize15.0ms (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))
✓	0.0b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.6b	(.f64 (.f64 b b) (+.f64 a 3))

series103.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

46.0ms	(pow.f64 (hypot.f64 a b) 4)
36.0ms	(+.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)))
9.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite18.0ms (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:

9.0ms	(.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))
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 (2.4%)

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

prune181.0ms (5.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	160	4	164

Error

Counts

164 → 4

Alt Table

Status	Error	Program
	12.1b	(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
▶	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)
✓	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))

Compiler

Compiled 4937 to 2886 computations (41.5% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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)))))
✓	0.1b	(.f64 (.f64 a a) (-.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.6b	(.f64 (.f64 b b) (+.f64 3 a))

series56.0ms (1.6%)

Counts

4 → 84

Calls

4 calls:

31.0ms	(+.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)))))
14.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
15×	`distribute-lft-in_binary64`

Counts

4 → 121

Calls

4 calls:

8.0ms	(.f64 (.f64 a a) (-.f64 1 a))
8.0ms	(+.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)))))
6.0ms	(.f64 (.f64 b b) (+.f64 3 a))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify127.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-+l+_binary64`
383×	`associate-l_binary64`
299×	`associate-r_binary64`
268×	`cancel-sign-sub-inv_binary64`
211×	`unswap-sqr_binary64`

Counts

205 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	3743
1	600	3419
2	2388	3054
3	4882	3054

prune244.0ms (6.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	209	4	213

Error

Counts

213 → 4

Alt Table

Status	Error	Program
▶	12.1b	(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
✓	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)
✓	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))

Compiler

Compiled 7747 to 3979 computations (48.6% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (*.f64 b b) 12 (pow.f64 b 4))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(fma.f64 (*.f64 b b) 12 (pow.f64 b 4))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (*.f64 b b) 12 (pow.f64 b 4))

simplify59.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

704×	`distribute-rgt-in_binary64`
639×	`distribute-rgt-out_binary64`
576×	`distribute-lft-out_binary64`
334×	`associate-l_binary64`
287×	`associate-r_binary64`

Counts

22 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	277
1	32	254
2	73	254
3	239	254
4	1207	254
5	4884	254
6	4984	254

prune29.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	23	4	27

Error

Counts

27 → 4

Alt Table

Status	Error	Program
✓	12.1b	(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
✓	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)
✓	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))

Compiler

Compiled 454 to 301 computations (33.7% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.2b	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)
	0.6b	(.f64 (.f64 b b) (+.f64 a 3))
✓	27.9b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3))

series71.0ms (2%)

Counts

2 → 48

Calls

2 calls:

36.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3))
35.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`unpow-prod-down_binary64`
20×	`cbrt-prod_binary64`
14×	`cube-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

2 → 66

Calls

2 calls:

3.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3))
2.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)

simplify152.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
554×	`unswap-sqr_binary64`
435×	`log-prod_binary64`
406×	`sqr-pow_binary64`
400×	`exp-prod_binary64`

Counts

114 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1921
1	267	1844
2	801	1704
3	1600	1642
4	2717	1642
5	4642	1642
6	4942	1642
7	4845	1642

prune195.0ms (5.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	164	4	168

Error

Counts

168 → 4

Alt Table

Status	Error	Program
✓	12.1b	(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
✓	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)
✓	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))

Compiler

Compiled 5324 to 3235 computations (39.2% saved)

regimes370.0ms (10.5%)

Accuracy

Total 0.0b remaining (54.3%)

Threshold costs 0.0b (54.3%)

Counts

68 → 1

Compiler

Compiled 7712 to 5509 computations (28.6% 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

end104.0ms (3%)

Compiler: Compiled 146 to 99 computations (32.2% saved)

Details

analyze182.0ms (5.2%)

sample1.4s (39.4%)

simplify58.0ms (1.6%)

prune5.0ms (0.1%)

localize15.0ms (0.4%)

series103.0ms (2.9%)

rewrite18.0ms (0.5%)

simplify84.0ms (2.4%)

prune181.0ms (5.1%)

localize16.0ms (0.4%)

series56.0ms (1.6%)

rewrite32.0ms (0.9%)

simplify127.0ms (3.6%)

prune244.0ms (6.9%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify59.0ms (1.7%)

prune29.0ms (0.8%)

localize17.0ms (0.5%)

series71.0ms (2%)

rewrite8.0ms (0.2%)

simplify152.0ms (4.3%)

prune195.0ms (5.5%)

regimes370.0ms (10.5%)

simplify3.0ms (0.1%)

end104.0ms (3%)

Profiling