Details

analyze170.0ms (3.6%)

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)

sample1.3s (27.5%)

Results

1.2s	8256×	body	128	valid
1.0ms	8×	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
	0.2b	(-.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)

localize14.0ms (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))

series89.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

35.0ms	(+.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))
34.0ms	(pow.f64 (hypot.f64 a b) 4)
12.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite16.0ms (0.3%)

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:

6.0ms	(.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))
3.0ms	(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 (1.7%)

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

prune213.0ms (4.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	159	5	164

Error

Counts

164 → 5

Alt Table

Status	Error	Program
	25.0b	(+.f64 (log.f64 (exp.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))
	11.6b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
	39.0b	(.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)
✓	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 5045 to 2954 computations (41.4% 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 (1.2%)

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 (0.7%)

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:

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)))))
7.0ms	(.f64 (.f64 a a) (-.f64 1 a))
6.0ms	(.f64 (.f64 b b) (+.f64 3 a))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify95.0ms (2%)

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

prune268.0ms (5.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	209	5	214

Error

Counts

214 → 5

Alt Table

Status	Error	Program
	25.0b	(+.f64 (log.f64 (exp.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 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (*.f64 (pow.f64 a 3) (+.f64 a -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)
	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)
✓	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 7887 to 4059 computations (48.5% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series52.0ms (1.1%)

Counts

4 → 72

Calls

4 calls:

25.0ms	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (*.f64 (pow.f64 a 3) (+.f64 a -4))))
19.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
5.0ms	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4)))
3.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64`
12×	`associate-*r/_binary64`
11×	`*-un-lft-identity_binary64`

Counts

4 → 94

Calls

4 calls:

10.0ms	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (*.f64 (pow.f64 a 3) (+.f64 a -4))))
9.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
6.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))
0.0ms	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4)))

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Rules

425×	`cancel-sign-sub-inv_binary64`
420×	`associate-l_binary64`
384×	`associate-r_binary64`
344×	`fma-def_binary64`
308×	`fma-neg_binary64`

Counts

166 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	237	4248
1	754	3437
2	3460	3422
3	5035	3422

prune302.0ms (6.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	174	5	179

Error

Counts

179 → 5

Alt Table

Status	Error	Program
	25.0b	(+.f64 (log.f64 (exp.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 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (*.f64 (pow.f64 a 3) (+.f64 a -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)
▶	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)
✓	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 7563 to 4738 computations (37.4% saved)

localize17.0ms (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))
✓	8.3b	(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)))

series123.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

69.0ms	(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)))
33.0ms	(.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))))
13.0ms	(fma.f64 a (-.f64 a (.f64 a a)) (.f64 (+.f64 3 a) (*.f64 b b)))
7.0ms	(.f64 (+.f64 3 a) (.f64 b b))

rewrite23.0ms (0.5%)

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:

6.0ms	(.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)))

simplify148.0ms (3.1%)

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

prune653.0ms (13.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	336	5	341

Error

Counts

341 → 5

Alt Table

Status	Error	Program
	25.0b	(+.f64 (log.f64 (exp.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 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (*.f64 (pow.f64 a 3) (+.f64 a -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)
✓	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)
✓	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 21541 to 12068 computations (44% saved)

regimes764.0ms (16%)

Accuracy

Total 0.0b remaining (73.8%)

Threshold costs 0.0b (73.8%)

Counts

136 → 1

Compiler

Compiled 21369 to 14403 computations (32.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-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	18	35
1	27	35
2	30	35
3	32	35
4	33	35
5	32	35

end121.0ms (2.5%)

Compiler: Compiled 218 to 141 computations (35.3% saved)

Details

analyze170.0ms (3.6%)

sample1.3s (27.5%)

simplify57.0ms (1.2%)

prune5.0ms (0.1%)

localize14.0ms (0.3%)

series89.0ms (1.9%)

rewrite16.0ms (0.3%)

simplify82.0ms (1.7%)

prune213.0ms (4.5%)

localize15.0ms (0.3%)

series55.0ms (1.2%)

rewrite32.0ms (0.7%)

simplify95.0ms (2%)

prune268.0ms (5.6%)

localize18.0ms (0.4%)

series52.0ms (1.1%)

rewrite30.0ms (0.6%)

simplify97.0ms (2%)

prune302.0ms (6.3%)

localize17.0ms (0.4%)

series123.0ms (2.6%)

rewrite23.0ms (0.5%)

simplify148.0ms (3.1%)

prune653.0ms (13.7%)

regimes764.0ms (16%)

simplify2.0ms (0.1%)

end121.0ms (2.5%)

Profiling