Details

analyze202.0ms (4.6%)

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)

sample1.4s (31.7%)

Results

1.3s	8256×	body	128	valid
1.0ms	4×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify64.0ms (1.5%)

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
	0.2b	(-.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))

Status

Error

Program

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))

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)))
✓	0.5b	(.f64 (.f64 b b) (+.f64 a 3))

series102.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

42.0ms	(+.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))
38.0ms	(pow.f64 (hypot.f64 a b) 4)
13.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
9.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite21.0ms (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 (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)))

simplify82.0ms (1.9%)

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

prune182.0ms (4.2%)

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
	12.9b	(+.f64 -1 (.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))))
✓	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))
	39.7b	(.f64 (sqrt.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))) (sqrt.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))))
▶	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 4993 to 2914 computations (41.6% saved)

localize15.0ms (0.3%)

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))
✓	0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.5b	(.f64 (.f64 b b) (+.f64 3 a))

series55.0ms (1.3%)

Counts

4 → 84

Calls

4 calls:

30.0ms	(+.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)))))
12.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
10.0ms	(.f64 (.f64 b b) (+.f64 3 a))
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite33.0ms (0.7%)

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:

10.0ms	(.f64 (.f64 a a) (-.f64 1 a))
6.0ms	(+.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))
3.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify93.0ms (2.1%)

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

prune228.0ms (5.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	209	4	213

Error

Counts

213 → 4

Alt Table

Status	Error	Program
	12.9b	(+.f64 -1 (.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))))
✓	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)
▶	0.2b	(-.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4)))) 1)

Compiler

Compiled 7799 to 3997 computations (48.7% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b)))
✓	0.3b	(.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4))))
✓	0.5b	(.f64 (+.f64 3 a) (.f64 b b))
✓	7.3b	(sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4)))

series130.0ms (3%)

Counts

4 → 96

Calls

4 calls:

74.0ms	(sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4)))
35.0ms	(.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4))))
11.0ms	(fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b)))
9.0ms	(.f64 (+.f64 3 a) (.f64 b b))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
21×	`sqrt-prod_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 102

Calls

4 calls:

8.0ms	(.f64 (+.f64 3 a) (.f64 b b))
5.0ms	(.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4))))
1.0ms	(sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4)))
0.0ms	(fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b)))

simplify145.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

536×	`cancel-sign-sub-inv_binary64`
380×	`fma-def_binary64`
360×	`associate-r_binary64`
279×	`times-frac_binary64`
265×	`associate-+r+_binary64`

Counts

198 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	7316
1	975	6626
2	3699	6452
3	5326	6452

prune590.0ms (13.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	336	4	340

Error

Counts

340 → 4

Alt Table

Status	Error	Program
▶	12.9b	(+.f64 -1 (.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))))
✓	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)
✓	0.2b	(-.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4)))) 1)

Compiler

Compiled 21514 to 12048 computations (44% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 -1 (.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))))
✓	0.5b	(.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12)))

series32.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(+.f64 -1 (.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))))
13.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 43

Calls

2 calls:

8.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12)))
3.0ms	(+.f64 -1 (.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))))

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary64`
615×	`fma-neg_binary64`
455×	`cancel-sign-sub-inv_binary64`
388×	`unswap-sqr_binary64`
259×	`*-commutative_binary64`

Counts

91 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	1572
1	268	1396
2	1068	1391
3	2882	1389
4	5006	1389

prune90.0ms (2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	84	4	88

Error

Counts

88 → 4

Alt Table

Status	Error	Program
✓	12.9b	(+.f64 -1 (.f64 (.f64 b b) (+.f64 (.f64 b b) (+.f64 (.f64 a 4) 12))))
✓	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)
✓	0.2b	(-.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 (hypot.f64 a b) 4)))) 1)

Compiler

Compiled 1976 to 1191 computations (39.7% saved)

regimes679.0ms (15.5%)

Accuracy

Total 0.0b remaining (60.3%)

Threshold costs 0.0b (60.3%)

Counts

129 → 1

Compiler

Compiled 18380 to 12391 computations (32.6% saved)

simplify2.0ms (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

end94.0ms (2.2%)

Compiler: Compiled 172 to 108 computations (37.2% saved)

Details

analyze202.0ms (4.6%)

sample1.4s (31.7%)

simplify64.0ms (1.5%)

prune5.0ms (0.1%)

localize13.0ms (0.3%)

series102.0ms (2.3%)

rewrite21.0ms (0.5%)

simplify82.0ms (1.9%)

prune182.0ms (4.2%)

localize15.0ms (0.3%)

series55.0ms (1.3%)

rewrite33.0ms (0.7%)

simplify93.0ms (2.1%)

prune228.0ms (5.2%)

localize16.0ms (0.4%)

series130.0ms (3%)

rewrite24.0ms (0.6%)

simplify145.0ms (3.3%)

prune590.0ms (13.5%)

localize8.0ms (0.2%)

series32.0ms (0.7%)

rewrite13.0ms (0.3%)

simplify66.0ms (1.5%)

prune90.0ms (2%)

regimes679.0ms (15.5%)

simplify2.0ms (0.1%)

end94.0ms (2.2%)

Profiling