Details

analyze58.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample335.0ms (8.1%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
6.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify117.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series28.0ms (0.7%)

Counts

3 → 56

Calls

3 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
11.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 102

Calls

3 calls:

10.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify85.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
423×	`distribute-rgt-in_binary64`
385×	`distribute-lft-in_binary64`
346×	`associate-/l/_binary64`
288×	`fma-neg_binary64`

Counts

158 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	2119
1	364	1923
2	1597	1729
3	4495	1728
4	4950	1728

prune181.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	163	6	169
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	165	6	171

Error

0.0b

Counts

171 → 6

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	32.0b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	14.5b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	37.2b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	0.6b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
▶	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)

Compiler

Compiled 3431 to 1927 computations (43.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 m (*.f64 m m))
✓	0.1b	(/.f64 v (-.f64 m (*.f64 m m)))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
✓	0.3b	(/.f64 1 (/.f64 v (-.f64 m (*.f64 m m))))

series65.0ms (1.6%)

Counts

4 → 84

Calls

4 calls:

36.0ms	(/.f64 v (-.f64 m (*.f64 m m)))
14.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
13.0ms	(/.f64 1 (/.f64 v (-.f64 m (*.f64 m m))))
3.0ms	(-.f64 m (*.f64 m m))

rewrite56.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
127×	`add-sqr-sqrt_binary64`
107×	`*-un-lft-identity_binary64`
76×	`add-cube-cbrt_binary64`
27×	`difference-of-squares_binary64`

Counts

4 → 210

Calls

4 calls:

23.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
8.0ms	(/.f64 1 (/.f64 v (-.f64 m (*.f64 m m))))
5.0ms	(/.f64 v (-.f64 m (*.f64 m m)))
2.0ms	(-.f64 m (*.f64 m m))

simplify176.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

375×	`fma-neg_binary64`
361×	`fma-def_binary64`
342×	`distribute-rgt-in_binary64`
332×	`times-frac_binary64`
314×	`distribute-lft-in_binary64`

Counts

294 → 330

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	5283
1	491	4765
2	1492	4639
3	4301	4639
4	5170	4639

prune303.0ms (7.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	328	2	330
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	329	7	336

Error

0.0b

Counts

336 → 7

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (-.f64 (/.f64 1 (.f64 v (/.f64 1 (-.f64 m (*.f64 m m))))) 1) m)
	37.2b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	0.8b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	32.0b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	9.7b	(.f64 (+.f64 (/.f64 1 (/.f64 (sqrt.f64 v) (sqrt.f64 (-.f64 m (.f64 m m))))) 1) (.f64 m (+.f64 -1 (/.f64 (sqrt.f64 (-.f64 m (.f64 m m))) (sqrt.f64 v)))))
	0.6b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)

Compiler

Compiled 7458 to 3068 computations (58.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 m (*.f64 m m)))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (.f64 v (/.f64 1 (-.f64 m (*.f64 m m))))) 1) m)
✓	0.3b	(/.f64 1 (.f64 v (/.f64 1 (-.f64 m (.f64 m m)))))
✓	0.3b	(.f64 v (/.f64 1 (-.f64 m (.f64 m m))))

series67.0ms (1.6%)

Counts

4 → 84

Calls

4 calls:

37.0ms	(.f64 v (/.f64 1 (-.f64 m (.f64 m m))))
14.0ms	(.f64 (-.f64 (/.f64 1 (.f64 v (/.f64 1 (-.f64 m (*.f64 m m))))) 1) m)
13.0ms	(/.f64 1 (.f64 v (/.f64 1 (-.f64 m (.f64 m m)))))
3.0ms	(/.f64 1 (-.f64 m (*.f64 m m)))

rewrite43.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary64`
48×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
35×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`

Counts

4 → 158

Calls

4 calls:

13.0ms	(.f64 (-.f64 (/.f64 1 (.f64 v (/.f64 1 (-.f64 m (*.f64 m m))))) 1) m)
8.0ms	(.f64 v (/.f64 1 (-.f64 m (.f64 m m))))
7.0ms	(/.f64 1 (.f64 v (/.f64 1 (-.f64 m (.f64 m m)))))
4.0ms	(/.f64 1 (-.f64 m (*.f64 m m)))

simplify113.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

959×	`fma-neg_binary64`
503×	`times-frac_binary64`
381×	`fma-def_binary64`
254×	`distribute-rgt-in_binary64`
235×	`associate-/r*_binary64`

Counts

242 → 261

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	3615
1	472	3190
2	1447	3174
3	4232	3098
4	5094	3098

prune232.0ms (5.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	259	2	261
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	260	8	268

Error

Counts

268 → 8

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (-.f64 (/.f64 1 (.f64 v (/.f64 1 (-.f64 m (*.f64 m m))))) 1) m)
	37.2b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	37.2b	(.f64 (sqrt.f64 (-.f64 (/.f64 1 (.f64 v (/.f64 1 (-.f64 m (.f64 m m))))) 1)) (.f64 m (sqrt.f64 (fma.f64 (/.f64 (-.f64 1 m) v) m -1))))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
	32.0b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	16.2b	(.f64 (-.f64 (/.f64 1 (.f64 v (cbrt.f64 (.f64 (.f64 (/.f64 1 (-.f64 m (.f64 m m))) (/.f64 1 (-.f64 m (.f64 m m)))) (/.f64 1 (-.f64 m (*.f64 m m))))))) 1) m)
	9.7b	(.f64 (+.f64 (/.f64 1 (/.f64 (sqrt.f64 v) (sqrt.f64 (-.f64 m (.f64 m m))))) 1) (.f64 m (+.f64 -1 (/.f64 (sqrt.f64 (-.f64 m (.f64 m m))) (sqrt.f64 v)))))
▶	0.6b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

Compiler

Compiled 5821 to 3150 computations (45.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
✓	0.4b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

series46.0ms (1.1%)

Counts

2 → 32

Calls

2 calls:

25.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
21.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

2 → 55

Calls

2 calls:

14.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
10.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))

simplify86.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-neg_binary64`
546×	`associate-/l*_binary64`
487×	`fma-def_binary64`
357×	`times-frac_binary64`
305×	`associate-/r/_binary64`

Counts

87 → 98

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	1884
1	250	1638
2	727	1451
3	1939	1448
4	4767	1448
5	5248	1448

prune163.0ms (4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	215	8	223

Error

Counts

223 → 8

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (-.f64 (/.f64 1 (.f64 v (/.f64 1 (-.f64 m (*.f64 m m))))) 1) m)
	37.2b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	37.2b	(.f64 (sqrt.f64 (-.f64 (/.f64 1 (.f64 v (/.f64 1 (-.f64 m (.f64 m m))))) 1)) (.f64 m (sqrt.f64 (fma.f64 (/.f64 (-.f64 1 m) v) m -1))))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
	32.0b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	9.7b	(.f64 (+.f64 (/.f64 1 (/.f64 (sqrt.f64 v) (sqrt.f64 (-.f64 m (.f64 m m))))) 1) (.f64 m (+.f64 -1 (/.f64 (sqrt.f64 (-.f64 m (.f64 m m))) (sqrt.f64 v)))))
✓	0.6b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	17.2b	(-.f64 (/.f64 (*.f64 m m) v) m)

Compiler

Compiled 4965 to 2546 computations (48.7% saved)

regimes974.0ms (23.7%)

Accuracy

Total 0.2b remaining (83.6%)

Threshold costs 0.2b (83.6%)

Counts

273 → 1

Compiler

Compiled 17279 to 11304 computations (34.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	19	19
2	25	19
3	29	19
4	32	19
5	33	19
6	31	19

end0.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

sample893.0ms (21.7%)

Algorithm

1×

intervals

Results

332.0ms	8000×	body	128	valid
186.0ms	8064×	pre	128	true
3.0ms	64×	body	128	invalid

Compiler

Compiled 192 to 126 computations (34.4% saved)

Details

analyze58.0ms (1.4%)

sample335.0ms (8.1%)

simplify117.0ms (2.8%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series28.0ms (0.7%)

rewrite29.0ms (0.7%)

simplify85.0ms (2.1%)

prune181.0ms (4.4%)

localize7.0ms (0.2%)

series65.0ms (1.6%)

rewrite56.0ms (1.3%)

simplify176.0ms (4.3%)

prune303.0ms (7.4%)

localize9.0ms (0.2%)

series67.0ms (1.6%)

rewrite43.0ms (1.1%)

simplify113.0ms (2.7%)

prune232.0ms (5.6%)

localize9.0ms (0.2%)

series46.0ms (1.1%)

rewrite28.0ms (0.7%)

simplify86.0ms (2.1%)

prune163.0ms (4%)

regimes974.0ms (23.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample893.0ms (21.7%)

Profiling