Details

analyze73.0ms (2.5%)

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
0%	99.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
87.4%	12.5%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample843.0ms (29.3%)

Infinites

21.5% of outputs are infinite.

Results

566.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify32.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

377×	`fma-neg_binary64`
309×	`fma-def_binary64`
112×	`cancel-sign-sub-inv_binary64`
77×	`distribute-rgt-in_binary64`
56×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
✓	0.0b	(/.f64 (-.f64 y x) z)

series106.0ms (3.7%)

Counts

2 → 64

Calls

2 calls:

81.0ms	(/.f64 (-.f64 y x) z)
25.0ms	(+.f64 x (/.f64 (-.f64 y x) z))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 58

Calls

2 calls:

7.0ms	(+.f64 x (/.f64 (-.f64 y x) z))
4.0ms	(/.f64 (-.f64 y x) z)

simplify85.0ms (3%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
598×	`times-frac_binary64`
572×	`associate-/l*_binary64`
274×	`div-sub_binary64`
243×	`distribute-rgt-in_binary64`

Counts

122 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1378
1	273	1269
2	636	1260
3	1893	1260
4	4435	1260
5	5003	1260

prune43.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Error

Counts

82 → 4

Alt Table

Status	Error	Program
	32.3b	(+.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 y x)) (.f64 (.f64 z z) z))))
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
▶	0.1b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
	30.9b	(+.f64 x (*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z)))

Compiler

Compiled 1189 to 354 computations (70.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
✓	0.0b	(/.f64 z (-.f64 y x))
✓	0.3b	(/.f64 1 (/.f64 z (-.f64 y x)))

series43.0ms (1.5%)

Counts

3 → 96

Calls

3 calls:

20.0ms	(/.f64 z (-.f64 y x))
12.0ms	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
11.0ms	(/.f64 1 (/.f64 z (-.f64 y x)))

rewrite46.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
107×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
72×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

3 → 167

Calls

3 calls:

18.0ms	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
10.0ms	(/.f64 1 (/.f64 z (-.f64 y x)))
4.0ms	(/.f64 z (-.f64 y x))

simplify156.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

492×	`fma-neg_binary64`
390×	`times-frac_binary64`
376×	`fma-def_binary64`
319×	`associate-/l*_binary64`
287×	`distribute-rgt-in_binary64`

Counts

263 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	4146
1	447	3761
2	1281	3568
3	4164	3568
4	4962	3568
5	5190	3568

prune146.0ms (5.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	229	4	233

Error

Counts

233 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
	30.9b	(+.f64 x (*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z)))
▶	21.8b	(+.f64 x (.f64 (/.f64 (-.f64 (.f64 y y) (*.f64 x x)) z) (/.f64 1 (+.f64 y x))))
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))

Compiler

Compiled 4152 to 1542 computations (62.9% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 y x))
✓	3.4b	(-.f64 (.f64 y y) (.f64 x x))
✓	5.6b	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) z)
✓	15.7b	(.f64 (/.f64 (-.f64 (.f64 y y) (*.f64 x x)) z) (/.f64 1 (+.f64 y x)))

series73.0ms (2.5%)

Counts

4 → 120

Calls

4 calls:

31.0ms	(.f64 (/.f64 (-.f64 (.f64 y y) (*.f64 x x)) z) (/.f64 1 (+.f64 y x)))
27.0ms	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) z)
8.0ms	(/.f64 1 (+.f64 y x))
7.0ms	(-.f64 (.f64 y y) (.f64 x x))

rewrite42.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`times-frac_binary64`
55×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 159

Calls

4 calls:

18.0ms	(.f64 (/.f64 (-.f64 (.f64 y y) (*.f64 x x)) z) (/.f64 1 (+.f64 y x)))
5.0ms	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) z)
4.0ms	(/.f64 1 (+.f64 y x))
3.0ms	(-.f64 (.f64 y y) (.f64 x x))

simplify136.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

560×	`times-frac_binary64`
387×	`distribute-rgt-in_binary64`
376×	`distribute-lft-in_binary64`
302×	`fma-def_binary64`
172×	`fma-neg_binary64`

Counts

279 → 259

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	4577
1	557	4160
2	1767	3797
3	4980	3797
4	5027	3797

prune137.0ms (4.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	259	4	263

Error

Counts

263 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
▶	30.9b	(+.f64 x (*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z)))
✓	21.8b	(+.f64 x (.f64 (/.f64 (-.f64 (.f64 y y) (*.f64 x x)) z) (/.f64 1 (+.f64 y x))))
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))

Compiler

Compiled 6427 to 1861 computations (71% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 y x))
✓	0.0b	(+.f64 x (*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z)))
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 y x)) z)
✓	0.1b	(*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z))

series107.0ms (3.7%)

Counts

4 → 92

Calls

4 calls:

35.0ms	(/.f64 (sqrt.f64 (-.f64 y x)) z)
27.0ms	(sqrt.f64 (-.f64 y x))
24.0ms	(+.f64 x (*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z)))
21.0ms	(*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z))

rewrite36.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64`
52×	`times-frac_binary64`
50×	`sqrt-prod_binary64`
40×	`add-cube-cbrt_binary64`

Counts

4 → 148

Calls

4 calls:

13.0ms	(*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z))
5.0ms	(/.f64 (sqrt.f64 (-.f64 y x)) z)
3.0ms	(sqrt.f64 (-.f64 y x))
2.0ms	(+.f64 x (*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z)))

simplify122.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

501×	`fma-def_binary64`
443×	`times-frac_binary64`
318×	`distribute-rgt-in_binary64`
293×	`distribute-lft-in_binary64`
281×	`fma-neg_binary64`

Counts

240 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	3745
1	607	3433
2	1927	3375
3	4657	3375
4	4982	3375

prune142.0ms (4.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	257	4	261

Error

Counts

261 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
✓	30.9b	(+.f64 x (*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z)))
✓	21.8b	(+.f64 x (.f64 (/.f64 (-.f64 (.f64 y y) (*.f64 x x)) z) (/.f64 1 (+.f64 y x))))
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))

Compiler

Compiled 5640 to 1518 computations (73.1% saved)

regimes408.0ms (14.2%)

Accuracy

Total 0.0b remaining (57.7%)

Threshold costs 0.0b (57.7%)

Counts

28 → 1

Compiler

Compiled 1584 to 1018 computations (35.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	15	10
3	17	10
4	18	10
5	18	10

end58.0ms (2%)

Compiler: Compiled 78 to 46 computations (41% saved)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

Details

analyze73.0ms (2.5%)

sample843.0ms (29.3%)

simplify32.0ms (1.1%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series106.0ms (3.7%)

rewrite14.0ms (0.5%)

simplify85.0ms (3%)

prune43.0ms (1.5%)

localize6.0ms (0.2%)

series43.0ms (1.5%)

rewrite46.0ms (1.6%)

simplify156.0ms (5.4%)

prune146.0ms (5.1%)

localize11.0ms (0.4%)

series73.0ms (2.5%)

rewrite42.0ms (1.5%)

simplify136.0ms (4.7%)

prune137.0ms (4.7%)

localize7.0ms (0.2%)

series107.0ms (3.7%)

rewrite36.0ms (1.3%)

simplify122.0ms (4.2%)

prune142.0ms (4.9%)

regimes408.0ms (14.2%)

simplify2.0ms (0.1%)

end58.0ms (2%)

Profiling

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10