Details

analyze176.0ms (3%)

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 (22.3%)

Results

1.2s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify59.0ms (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

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 (0.2%)

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))

series92.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

36.0ms	(pow.f64 (hypot.f64 a b) 4)
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))
11.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
10.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite15.0ms (0.2%)

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))
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)))

simplify76.0ms (1.3%)

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

prune230.0ms (3.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	157	5	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	5	164

Error

0.0b

Counts

164 → 5

Alt Table

Status	Error	Program
	0.2b	(+.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)))
▶	0.0b	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	15.8b	(/.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))) (-.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)))
	25.5b	(log.f64 (exp.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))))

Compiler

Compiled 5204 to 3043 computations (41.5% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.2b	(.f64 a (.f64 a (*.f64 b b)))
✓	0.6b	(.f64 a (.f64 b b))
	0.6b	(.f64 (.f64 b b) (+.f64 a 3))

series22.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(.f64 a (.f64 a (*.f64 b b)))
8.0ms	(.f64 a (.f64 b b))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms	(.f64 a (.f64 a (*.f64 b b)))
4.0ms	(.f64 a (.f64 b b))

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-l_binary64`
566×	`fma-def_binary64`
511×	`unswap-sqr_binary64`
413×	`*-commutative_binary64`
369×	`associate-r_binary64`

Counts

92 → 51

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	979
1	125	850
2	375	826
3	1084	808
4	2147	797
5	3407	797
6	4998	797

prune213.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	124	5	129

Error

0.0b

Counts

129 → 5

Alt Table

Status	Error	Program
▶	0.2b	(+.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)))
✓	0.0b	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	15.8b	(/.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))) (-.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)))
	25.5b	(log.f64 (exp.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))))

Compiler

Compiled 5193 to 2757 computations (46.9% saved)

localize16.0ms (0.3%)

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 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
✓	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))
✓	0.9b	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))

series59.0ms (1%)

Counts

4 → 72

Calls

4 calls:

31.0ms	(+.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)))
21.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
3.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
3.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
15×	`distribute-lft-in_binary64`

Counts

4 → 119

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 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
9.0ms	(*.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)))))
0.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

simplify103.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

432×	`fma-neg_binary64`
429×	`associate-l_binary64`
399×	`associate-r_binary64`
397×	`cancel-sign-sub-inv_binary64`
332×	`fma-def_binary64`

Counts

191 → 218

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	4782
1	798	3757
2	3511	3728
3	5034	3728

prune359.0ms (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	219	4	223

Error

0.0b

Counts

223 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 (.f64 (.f64 b b) (sqrt.f64 (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a)))))) (sqrt.f64 (+.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)))
✓	0.0b	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	25.5b	(log.f64 (exp.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))))

Compiler

Compiled 9517 to 6098 computations (35.9% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
	0.1b	(*.f64 (pow.f64 a 3) (-.f64 a 4))
✓	0.4b	(.f64 (.f64 (.f64 b b) (sqrt.f64 (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a)))))) (sqrt.f64 (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a))))))
✓	0.7b	(.f64 (.f64 b b) (sqrt.f64 (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a))))))

series96.0ms (1.6%)

Counts

3 → 72

Calls

3 calls:

48.0ms

(*.f64 (*.f64 b b) (sqrt.f64 (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a))))))

30.0ms

(sqrt.f64 (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))

19.0ms

(*.f64 (*.f64 (*.f64 b b) (sqrt.f64 (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))) (sqrt.f64 (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a))))))

rewrite70.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`associate-*r/_binary64`
96×	`sqrt-div_binary64`
80×	`flip-+_binary64`
80×	`flip3-+_binary64`
64×	`frac-add_binary64`

Counts

3 → 126

Calls

3 calls:

17.0ms

(*.f64 (*.f64 (*.f64 b b) (sqrt.f64 (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))) (sqrt.f64 (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a))))))

10.0ms

(*.f64 (*.f64 b b) (sqrt.f64 (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a))))))

5.0ms

(sqrt.f64 (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))

simplify170.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

652×	`associate-l_binary64`
502×	`fma-def_binary64`
475×	`associate-r_binary64`
197×	`*-commutative_binary64`
139×	`associate-/r*_binary64`

Counts

198 → 298

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	527	12360
1	1656	10617
2	5136	10617

prune864.0ms (14.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	465	0	465
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	465	4	469

Error

0.0b

Counts

469 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 (.f64 (.f64 b b) (sqrt.f64 (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a)))))) (sqrt.f64 (+.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)))
✓	0.0b	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	25.5b	(log.f64 (exp.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))))

Compiler

Compiled 35352 to 23585 computations (33.3% saved)

regimes1.7s (27.7%)

Accuracy

Total 0.0b remaining (69.6%)

Threshold costs 0.0b (69.6%)

Counts

254 → 1

Compiler

Compiled 44131 to 30561 computations (30.7% saved)

simplify3.0ms (0%)

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

end175.0ms (2.9%)

Compiler: Compiled 214 to 139 computations (35% saved)

Details

analyze176.0ms (3%)

sample1.3s (22.3%)

simplify59.0ms (1%)

prune5.0ms (0.1%)

localize14.0ms (0.2%)

series92.0ms (1.5%)

rewrite15.0ms (0.2%)

simplify76.0ms (1.3%)

prune230.0ms (3.9%)

localize22.0ms (0.4%)

series22.0ms (0.4%)

rewrite12.0ms (0.2%)

simplify71.0ms (1.2%)

prune213.0ms (3.6%)

localize16.0ms (0.3%)

series59.0ms (1%)

rewrite37.0ms (0.6%)

simplify103.0ms (1.7%)

prune359.0ms (6%)

localize18.0ms (0.3%)

series96.0ms (1.6%)

rewrite70.0ms (1.2%)

simplify170.0ms (2.8%)

prune864.0ms (14.5%)

regimes1.7s (27.7%)

simplify3.0ms (0%)

end175.0ms (2.9%)

Profiling