Details

analyze182.0ms (4.9%)

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
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
46.8%	53.1%	0.1%	7
60.9%	39%	0.1%	8
67.9%	31.2%	0.9%	9
74.5%	22.2%	3.2%	10
77.9%	17.2%	5%	11
81.1%	11.8%	7.1%	12
82.7%	9%	8.3%	13
84.3%	6.1%	9.7%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.1s (28.5%)

Results

932.0ms	8256×	body	128	valid
24.0ms	250×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify88.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1151×	`distribute-rgt-in_binary64`
1143×	`distribute-lft-in_binary64`
971×	`fma-def_binary64`
653×	`associate-/l*_binary64`
535×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	22	14
2	30	14
3	75	14
4	112	14
5	222	14
6	406	14
7	419	14
8	783	14
9	937	14
10	1259	14
11	1611	14
12	1778	14
13	2015	14
14	2939	14
15	3245	14
16	5075	14

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

9.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.8b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Compiler

Compiled 47 to 27 computations (42.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (/.f64 x y) x)
✓	9.2b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

series22.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
9.0ms	(fma.f64 x (/.f64 x y) x)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

2 → 45

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
0.0ms	(fma.f64 x (/.f64 x y) x)

simplify86.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1032×	`fma-neg_binary64`
526×	`cancel-sign-sub-inv_binary64`
338×	`sub-neg_binary64`
265×	`distribute-rgt-in_binary64`
240×	`associate-/l/_binary64`

Counts

93 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1641
1	245	1554
2	714	1484
3	2409	1453
4	4439	1453
5	5061	1453

prune51.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	3	75

Error

0.0b

Counts

75 → 3

Alt Table

Status	Error	Program
	34.5b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
	29.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
▶	9.9b	(*.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1)))

Compiler

Compiled 1353 to 608 computations (55.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
	0.1b	(fma.f64 x (/.f64 x y) x)
✓	9.3b	(*.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1)))

series16.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

14.0ms	(*.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1)))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

2 → 82

Calls

2 calls:

8.0ms	(*.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1)))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify124.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

892×	`fma-neg_binary64`
598×	`cancel-sign-sub-inv_binary64`
402×	`sub-neg_binary64`
234×	`associate--l+_binary64`
202×	`associate-+l+_binary64`

Counts

118 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1920
1	315	1752
2	953	1660
3	3141	1647
4	4191	1647
5	4999	1647
6	4986	1647

prune100.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	149	3	152

Error

0.0b

Counts

152 → 3

Alt Table

Status	Error	Program
	34.5b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
▶	29.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
✓	9.9b	(*.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1)))

Compiler

Compiled 2805 to 1466 computations (47.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.3b	(/.f64 (pow.f64 x 3) y)
✓	6.7b	(+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2))
✓	8.4b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
✓	8.8b	(/.f64 (pow.f64 x 2) y)

series89.0ms (2.4%)

Counts

4 → 28

Calls

4 calls:

38.0ms	(+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2))
21.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
16.0ms	(/.f64 (pow.f64 x 3) y)
14.0ms	(/.f64 (pow.f64 x 2) y)

rewrite87.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`*-un-lft-identity_binary64`
96×	`times-frac_binary64`
81×	`add-sqr-sqrt_binary64`
79×	`add-cube-cbrt_binary64`
40×	`fma-def_binary64`

Counts

4 → 236

Calls

4 calls:

38.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
20.0ms	(+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2))
4.0ms	(/.f64 (pow.f64 x 3) y)
3.0ms	(/.f64 (pow.f64 x 2) y)

simplify193.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

563×	`fma-neg_binary64`
258×	`associate-l_binary64`
257×	`associate-r_binary64`
239×	`distribute-rgt-in_binary64`
226×	`distribute-lft-in_binary64`

Counts

264 → 290

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	6184
1	806	5182
2	3883	5111
3	4992	5111
4	4927	5111

prune299.0ms (8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	287	3	290
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	287	6	293

Error

Counts

293 → 6

Alt Table

Status	Error	Program
✓	9.9b	(*.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1)))
▶	29.3b	(-.f64 (+.f64 (/.f64 x (/.f64 y x)) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
	34.5b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
	29.5b	(-.f64 (+.f64 (.f64 (.f64 x (cbrt.f64 x)) (/.f64 (pow.f64 (cbrt.f64 x) 2) y)) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
✓	29.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
	29.4b	(-.f64 (+.f64 (/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) x) (cbrt.f64 y)) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))

Compiler

Compiled 10243 to 6455 computations (37% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.4b	(+.f64 (/.f64 x (/.f64 y x)) (+.f64 (pow.f64 x 3) x))
	6.3b	(/.f64 (pow.f64 x 3) y)
	6.7b	(+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2))
✓	8.4b	(-.f64 (+.f64 (/.f64 x (/.f64 y x)) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))

series37.0ms (1%)

Counts

2 → 48

Calls

2 calls:

25.0ms	(-.f64 (+.f64 (/.f64 x (/.f64 y x)) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
11.0ms	(+.f64 (/.f64 x (/.f64 y x)) (+.f64 (pow.f64 x 3) x))

rewrite87.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
52×	`add-sqr-sqrt_binary64`
50×	`add-cube-cbrt_binary64`
44×	`fma-def_binary64`

Counts

2 → 139

Calls

2 calls:

46.0ms	(-.f64 (+.f64 (/.f64 x (/.f64 y x)) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
23.0ms	(+.f64 (/.f64 x (/.f64 y x)) (+.f64 (pow.f64 x 3) x))

simplify144.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

443×	`cancel-sign-sub-inv_binary64`
438×	`fma-neg_binary64`
244×	`distribute-rgt-in_binary64`
231×	`distribute-lft-in_binary64`
209×	`times-frac_binary64`

Counts

187 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	5624
1	650	4578
2	2903	4186
3	4863	4186
4	5001	4186

prune331.0ms (8.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	311	1	312
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	313	5	318

Error

Counts

318 → 5

Alt Table

Status	Error	Program
✓	9.9b	(*.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1)))
✓	29.3b	(-.f64 (+.f64 (/.f64 x (/.f64 y x)) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
	34.5b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
✓	29.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))
	29.9b	(-.f64 (fma.f64 (/.f64 1 y) (/.f64 x (/.f64 1 x)) (+.f64 (pow.f64 x 3) x)) (+.f64 (/.f64 (pow.f64 x 3) y) (pow.f64 x 2)))

Compiler

Compiled 11188 to 6114 computations (45.4% saved)

regimes548.0ms (14.6%)

Accuracy

Total 0.1b remaining (81.3%)

Threshold costs 0.1b (81.3%)

Counts

100 → 3

Compiler

Compiled 5237 to 3398 computations (35.1% saved)

bsearch40.0ms (1.1%)

Steps

Iters	Range		Point
10	335951.5849647527	2.3616874415881426e+24	16483647715.548288
8	-5.384553914211595e+40	-1.1243591615808811e+38	-1.1391710068553142e+38

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`*-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	29	41
2	35	41
3	37	41
4	38	41
5	36	41

end94.0ms (2.5%)

Compiler: Compiled 157 to 104 computations (33.8% saved)

Details

analyze182.0ms (4.9%)

sample1.1s (28.5%)

simplify88.0ms (2.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series22.0ms (0.6%)

rewrite6.0ms (0.2%)

simplify86.0ms (2.3%)

prune51.0ms (1.3%)

localize7.0ms (0.2%)

series16.0ms (0.4%)

rewrite16.0ms (0.4%)

simplify124.0ms (3.3%)

prune100.0ms (2.7%)

localize11.0ms (0.3%)

series89.0ms (2.4%)

rewrite87.0ms (2.3%)

simplify193.0ms (5.2%)

prune299.0ms (8%)

localize11.0ms (0.3%)

series37.0ms (1%)

rewrite87.0ms (2.3%)

simplify144.0ms (3.8%)

prune331.0ms (8.8%)

regimes548.0ms (14.6%)

bsearch40.0ms (1.1%)

simplify3.0ms (0.1%)

end94.0ms (2.5%)

Profiling