Details

analyze171.0ms (4.5%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (37.7%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1167×	`fma-def_binary64`
1073×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	43	18
3	75	18
4	123	16
5	213	16
6	302	16
7	472	16
8	1009	13
9	1328	13
10	1542	13
11	1559	13
12	1556	13
13	1556	13
14	1453	13

prune3.0ms (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
	4.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	2.1b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (fma.f64 x z -4))
✓	2.1b	(/.f64 (-.f64 x (fma.f64 x z -4)) y)

series22.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

17.0ms	(/.f64 (-.f64 x (fma.f64 x z -4)) y)
4.0ms	(-.f64 x (fma.f64 x z -4))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
9×	`prod-diff_binary64`

Counts

2 → 71

Calls

2 calls:

5.0ms	(/.f64 (-.f64 x (fma.f64 x z -4)) y)
3.0ms	(-.f64 x (fma.f64 x z -4))

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

531×	`fma-neg_binary64`
446×	`associate-l_binary64`
420×	`div-sub_binary64`
358×	`associate-r_binary64`
297×	`fma-def_binary64`

Counts

131 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2146
1	314	2027
2	864	1648
3	3571	1648
4	4943	1648

prune108.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	122	5	127

Error

0.0b

Counts

127 → 5

Alt Table

Status	Error	Program
	4.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	2.2b	(fabs.f64 (*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y)))
	2.2b	(fabs.f64 (/.f64 1 (/.f64 y (fma.f64 x (-.f64 1 z) 4))))
	61.5b	(fabs.f64 (*.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x z -4))) (sqrt.f64 y)) (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x z -4))) (sqrt.f64 y))))
	34.8b	(fabs.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y)) (sqrt.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))))

Compiler

Compiled 2449 to 1496 computations (38.9% saved)

localize27.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (fma.f64 x z -4))
✓	2.2b	(*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y))

series18.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

18.0ms

(*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 44

Calls

1 calls:

8.0ms

(*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y))

simplify94.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

845×	`fma-def_binary64`
306×	`fma-neg_binary64`
290×	`associate-/l*_binary64`
272×	`associate-l_binary64`
230×	`div-sub_binary64`

Counts

80 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1400
1	243	1310
2	689	1046
3	2012	1046
4	4555	1046
5	4996	1046
6	4951	1046

prune112.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	135	5	140

Error

0.0b

Counts

140 → 5

Alt Table

Status	Error	Program
	4.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	2.2b	(fabs.f64 (*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y)))
▶	2.2b	(fabs.f64 (/.f64 1 (/.f64 y (fma.f64 x (-.f64 1 z) 4))))
	3.1b	(fabs.f64 (.f64 (.f64 (-.f64 x (fma.f64 x z -4)) (*.f64 (cbrt.f64 (/.f64 1 y)) (cbrt.f64 (/.f64 1 y)))) (cbrt.f64 (/.f64 1 y))))
	34.8b	(fabs.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y)) (sqrt.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))))

Compiler

Compiled 2782 to 1814 computations (34.8% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 y (fma.f64 x (-.f64 1 z) 4)))
✓	2.3b	(/.f64 y (fma.f64 x (-.f64 1 z) 4))

series59.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

43.0ms	(/.f64 y (fma.f64 x (-.f64 1 z) 4))
16.0ms	(/.f64 1 (/.f64 y (fma.f64 x (-.f64 1 z) 4)))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 y (fma.f64 x (-.f64 1 z) 4)))
3.0ms	(/.f64 y (fma.f64 x (-.f64 1 z) 4))

simplify135.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

790×	`times-frac_binary64`
344×	`fma-neg_binary64`
238×	`cancel-sign-sub-inv_binary64`
167×	`distribute-neg-in_binary64`
146×	`associate-r_binary64`

Counts

179 → 192

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	279	4414
1	740	4133
2	2707	4037
3	4932	4036
4	5089	4036

prune170.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	192	5	197

Error

0.0b

Counts

197 → 5

Alt Table

Status	Error	Program
▶	2.2b	(fabs.f64 (/.f64 1 (*.f64 y (/.f64 1 (fma.f64 x (-.f64 1 z) 4)))))
✓	2.2b	(fabs.f64 (*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y)))
	4.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	2.2b	(fabs.f64 (/.f64 1 (/.f64 y (fma.f64 x (-.f64 1 z) 4))))
	34.8b	(fabs.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y)) (sqrt.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))))

Compiler

Compiled 4706 to 3213 computations (31.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (*.f64 y (/.f64 1 (fma.f64 x (-.f64 1 z) 4))))
✓	0.3b	(/.f64 1 (fma.f64 x (-.f64 1 z) 4))
✓	2.2b	(*.f64 y (/.f64 1 (fma.f64 x (-.f64 1 z) 4)))

series83.0ms (2.2%)

Counts

3 → 96

Calls

3 calls:

46.0ms	(*.f64 y (/.f64 1 (fma.f64 x (-.f64 1 z) 4)))
21.0ms	(/.f64 1 (fma.f64 x (-.f64 1 z) 4))
16.0ms	(/.f64 1 (*.f64 y (/.f64 1 (fma.f64 x (-.f64 1 z) 4))))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-exp-log_binary64`
28×	`add-sqr-sqrt_binary64`
23×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`

Counts

3 → 113

Calls

3 calls:

6.0ms	(*.f64 y (/.f64 1 (fma.f64 x (-.f64 1 z) 4)))
6.0ms	(/.f64 1 (*.f64 y (/.f64 1 (fma.f64 x (-.f64 1 z) 4))))
3.0ms	(/.f64 1 (fma.f64 x (-.f64 1 z) 4))

simplify148.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

356×	`fma-neg_binary64`
279×	`associate-/r*_binary64`
242×	`fma-def_binary64`
227×	`associate-r_binary64`
225×	`associate-+r+_binary64`

Counts

209 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	4899
1	1100	4529
2	4286	4419
3	4995	4419
4	5055	4419

prune197.0ms (5.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	236	5	241

Error

0.0b

Counts

241 → 5

Alt Table

Status	Error	Program
✓	2.2b	(fabs.f64 (/.f64 1 (*.f64 y (/.f64 1 (fma.f64 x (-.f64 1 z) 4)))))
✓	2.2b	(fabs.f64 (*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y)))
	4.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	2.2b	(fabs.f64 (/.f64 1 (/.f64 y (fma.f64 x (-.f64 1 z) 4))))
	34.8b	(fabs.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y)) (sqrt.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))))

Compiler

Compiled 5890 to 4224 computations (28.3% saved)

regimes610.0ms (16.1%)

Accuracy

Total 2.2b remaining (98.9%)

Threshold costs 0b (0%)

Counts

73 → 2

Compiler

Compiled 5307 to 3891 computations (26.7% saved)

bsearch7.0ms (0.2%)

Steps

Iters	Range		Point
1	-2.7643915924426e-110	-3.3279532268001096e-115	-9.558233736210092e-113

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
9×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	37
1	38	37
2	53	37
3	66	37
4	79	37
5	84	37
6	85	37
7	83	37

end158.0ms (4.2%)

Compiler: Compiled 138 to 97 computations (29.7% saved)

Details

analyze171.0ms (4.5%)

sample1.4s (37.7%)

simplify64.0ms (1.7%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series22.0ms (0.6%)

rewrite13.0ms (0.3%)

simplify80.0ms (2.1%)

prune108.0ms (2.8%)

localize27.0ms (0.7%)

series18.0ms (0.5%)

rewrite15.0ms (0.4%)

simplify94.0ms (2.5%)

prune112.0ms (3%)

localize9.0ms (0.2%)

series59.0ms (1.5%)

rewrite16.0ms (0.4%)

simplify135.0ms (3.6%)

prune170.0ms (4.5%)

localize9.0ms (0.2%)

series83.0ms (2.2%)

rewrite21.0ms (0.6%)

simplify148.0ms (3.9%)

prune197.0ms (5.2%)

regimes610.0ms (16.1%)

bsearch7.0ms (0.2%)

simplify7.0ms (0.2%)

end158.0ms (4.2%)

Profiling