Details

analyze68.0ms (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)

sample1.2s (25.5%)

Results

922.0ms	8256×	body	128	valid
7.0ms	62×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify119.0ms (2.5%)

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)
	0.3b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (0.1%)

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)

series25.0ms (0.5%)

Counts

3 → 56

Calls

3 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite27.0ms (0.6%)

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:

9.0ms	(.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 (1.8%)

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

prune166.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	162	7	169
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	163	8	171

Error

0.0b

Counts

171 → 8

Alt Table

Status	Error	Program
▶	0.6b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	7.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	21.4b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
	11.5b	(.f64 (-.f64 (/.f64 (exp.f64 (log.f64 (-.f64 m (.f64 m m)))) v) 1) m)
	31.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
	13.9b	(/.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))

Compiler

Compiled 3516 to 1988 computations (43.5% saved)

localize8.0ms (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))
✓	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

series46.0ms (0.9%)

Counts

2 → 32

Calls

2 calls:

24.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
22.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

rewrite28.0ms (0.6%)

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:

13.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
11.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))

simplify86.0ms (1.8%)

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

prune180.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	213	2	215
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	216	7	223

Error

Counts

223 → 7

Alt Table

Status	Error	Program
▶	0.7b	(.f64 (.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))) (sqrt.f64 (sqrt.f64 m)))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	7.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	21.4b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
	4.2b	(*.f64 (-.f64 (/.f64 (-.f64 (pow.f64 m 3/2) (pow.f64 m 5/2)) v) (sqrt.f64 m)) (sqrt.f64 m))
	31.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))

Compiler

Compiled 5117 to 2652 computations (48.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (sqrt.f64 m))
✓	0.3b	(.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m))))
✓	0.3b	(.f64 (.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))) (sqrt.f64 (sqrt.f64 m)))
✓	0.4b	(*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))

series154.0ms (3.2%)

Counts

4 → 56

Calls

4 calls:

93.0ms	(.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m))))
25.0ms	(*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))
18.0ms	(sqrt.f64 (sqrt.f64 m))
18.0ms	(.f64 (.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))) (sqrt.f64 (sqrt.f64 m)))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary64`
35×	`add-sqr-sqrt_binary64`
31×	`pow1_binary64`
20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 117

Calls

4 calls:

11.0ms	(.f64 (.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))) (sqrt.f64 (sqrt.f64 m)))
7.0ms	(.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m))))
7.0ms	(*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))
1.0ms	(sqrt.f64 (sqrt.f64 m))

simplify110.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-def_binary64`
557×	`fma-neg_binary64`
385×	`associate-/l*_binary64`
339×	`*-commutative_binary64`
200×	`associate-l_binary64`

Counts

173 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	3065
1	306	2592
2	992	2389
3	2345	2383
4	4598	2383
5	4937	2383

prune140.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	192	7	199

Error

Counts

199 → 7

Alt Table

Status	Error	Program
✓	0.7b	(.f64 (.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))) (sqrt.f64 (sqrt.f64 m)))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	7.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	21.4b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
	4.2b	(*.f64 (-.f64 (/.f64 (-.f64 (pow.f64 m 3/2) (pow.f64 m 5/2)) v) (sqrt.f64 m)) (sqrt.f64 m))
	31.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
▶	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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))

Compiler

Compiled 4765 to 2033 computations (57.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m)
✓	0.2b	(.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
✓	0.3b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
✓	0.4b	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))

series207.0ms (4.3%)

Counts

4 → 96

Calls

4 calls:

79.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
64.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m)
44.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
20.0ms	(.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))

rewrite88.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`cbrt-div_binary64`
56×	`add-sqr-sqrt_binary64`
55×	`cbrt-prod_binary64`
42×	`*-un-lft-identity_binary64`
36×	`associate-*l/_binary64`

Counts

4 → 165

Calls

4 calls:

27.0ms	(.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
18.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
10.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m)
6.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

simplify239.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-def_binary64`
432×	`associate-l_binary64`
280×	`times-frac_binary64`
256×	`associate-/l*_binary64`
207×	`associate-/r*_binary64`

Counts

261 → 360

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	564	13854
1	1733	13068
2	4909	12488
3	5357	12488

prune700.0ms (14.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	494	2	496
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	496	7	503

Error

Counts

503 → 7

Alt Table

Status	Error	Program
✓	0.7b	(.f64 (.f64 (fma.f64 (-.f64 1 m) (/.f64 m v) -1) (*.f64 (sqrt.f64 m) (sqrt.f64 (sqrt.f64 m)))) (sqrt.f64 (sqrt.f64 m)))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	7.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	13.3b	(.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))
	0.2b	(fma.f64 (/.f64 (-.f64 m (*.f64 m m)) v) m (neg.f64 m))
	4.2b	(*.f64 (-.f64 (/.f64 (-.f64 (pow.f64 m 3/2) (pow.f64 m 5/2)) v) (sqrt.f64 m)) (sqrt.f64 m))
✓	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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))

Compiler

Compiled 30547 to 21571 computations (29.4% saved)

regimes948.0ms (19.6%)

Accuracy

Total 0.1b remaining (87.3%)

Threshold costs 0.1b (87.3%)

Counts

261 → 1

Compiler

Compiled 17797 to 11579 computations (34.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	24	16
4	25	16
5	25	16

end111.0ms (2.3%)

Compiler: Compiled 176 to 114 computations (35.2% saved)

Details

analyze68.0ms (1.4%)

sample1.2s (25.5%)

simplify119.0ms (2.5%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series25.0ms (0.5%)

rewrite27.0ms (0.6%)

simplify85.0ms (1.8%)

prune166.0ms (3.4%)

localize8.0ms (0.2%)

series46.0ms (0.9%)

rewrite28.0ms (0.6%)

simplify86.0ms (1.8%)

prune180.0ms (3.7%)

localize10.0ms (0.2%)

series154.0ms (3.2%)

rewrite34.0ms (0.7%)

simplify110.0ms (2.3%)

prune140.0ms (2.9%)

localize10.0ms (0.2%)

series207.0ms (4.3%)

rewrite88.0ms (1.8%)

simplify239.0ms (4.9%)

prune700.0ms (14.5%)

regimes948.0ms (19.6%)

simplify2.0ms (0%)

end111.0ms (2.3%)

Profiling