Details

analyze167.0ms (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)

sample935.0ms (27.3%)

Results

797.0ms	8256×	body	128	valid
24.0ms	265×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify86.0ms (2.5%)

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

9.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.6b	(/.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)
✓	8.9b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

series20.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
8.0ms	(fma.f64 x (/.f64 x y) x)

rewrite13.0ms (0.4%)

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:

10.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
0.0ms	(fma.f64 x (/.f64 x y) x)

simplify81.0ms (2.4%)

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

prune44.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	4	75

Error

0.0b

Counts

75 → 4

Alt Table

Status	Error	Program
▶	13.4b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
✓	9.6b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
	37.5b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
	34.4b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))) (sqrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))))

Compiler

Compiled 1375 to 615 computations (55.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 1 x))
✓	0.0b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
✓	17.4b	(/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y))

series34.0ms (1%)

Counts

3 → 39

Calls

3 calls:

17.0ms	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
15.0ms	(/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y))
2.0ms	(/.f64 x (+.f64 1 x))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`

Counts

3 → 105

Calls

3 calls:

17.0ms	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
5.0ms	(/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y))
3.0ms	(/.f64 x (+.f64 1 x))

simplify86.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

767×	`associate-/l*_binary64`
470×	`fma-def_binary64`
453×	`associate-/r*_binary64`
358×	`fma-neg_binary64`
236×	`associate-/l/_binary64`

Counts

144 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2261
1	516	2167
2	1565	1981
3	4725	1981
4	4964	1981

prune131.0ms (3.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	202	3	205

Error

0.0b

Counts

205 → 3

Alt Table

Status	Error	Program
	34.4b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))) (sqrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))))
▶	2.4b	(+.f64 (/.f64 (*.f64 x (/.f64 x (+.f64 x 1))) y) (/.f64 x (+.f64 1 x)))
	4.4b	(+.f64 (/.f64 x (/.f64 (fma.f64 x y y) x)) (/.f64 x (+.f64 1 x)))

Compiler

Compiled 4422 to 2790 computations (36.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(+.f64 (/.f64 (*.f64 x (/.f64 x (+.f64 x 1))) y) (/.f64 x (+.f64 1 x)))
✓	0.0b	(*.f64 x (/.f64 x (+.f64 x 1)))
✓	5.5b	(/.f64 (*.f64 x (/.f64 x (+.f64 x 1))) y)

series34.0ms (1%)

Counts

4 → 72

Calls

4 calls:

16.0ms	(/.f64 (*.f64 x (/.f64 x (+.f64 x 1))) y)
14.0ms	(+.f64 (/.f64 (*.f64 x (/.f64 x (+.f64 x 1))) y) (/.f64 x (+.f64 1 x)))
2.0ms	(/.f64 x (+.f64 x 1))
2.0ms	(*.f64 x (/.f64 x (+.f64 x 1)))

rewrite42.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
31×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 122

Calls

4 calls:

12.0ms	(+.f64 (/.f64 (*.f64 x (/.f64 x (+.f64 x 1))) y) (/.f64 x (+.f64 1 x)))
8.0ms	(/.f64 (*.f64 x (/.f64 x (+.f64 x 1))) y)
6.0ms	(*.f64 x (/.f64 x (+.f64 x 1)))
3.0ms	(/.f64 x (+.f64 x 1))

simplify146.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-def_binary64`
461×	`fma-neg_binary64`
460×	`associate-/r*_binary64`
366×	`associate-/r/_binary64`
294×	`associate--l+_binary64`

Counts

194 → 215

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	223	3050
1	587	2759
2	2030	2644
3	4528	2631
4	4954	2631
5	4991	2631
6	4959	2631

prune150.0ms (4.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	213	2	215
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	214	4	218

Error

0.0b

Counts

218 → 4

Alt Table

Status	Error	Program
	35.6b	(fma.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (/.f64 x (+.f64 x 1)) (sqrt.f64 y)) (/.f64 x (+.f64 1 x)))
▶	0.6b	(fma.f64 (/.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 y)) (/.f64 x (+.f64 1 x)))
✓	2.4b	(+.f64 (/.f64 (*.f64 x (/.f64 x (+.f64 x 1))) y) (/.f64 x (+.f64 1 x)))
	4.4b	(+.f64 (/.f64 x (/.f64 (fma.f64 x y y) x)) (/.f64 x (+.f64 1 x)))

Compiler

Compiled 4706 to 2792 computations (40.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
✓	0.3b	(/.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 y))
✓	0.6b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)

series593.0ms (17.3%)

Counts

4 → 72

Calls

4 calls:

450.0ms	(/.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
71.0ms	(/.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 y))
37.0ms	(cbrt.f64 y)
35.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))

rewrite36.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
151×	`*-un-lft-identity_binary64`
117×	`add-sqr-sqrt_binary64`
109×	`add-cube-cbrt_binary64`
76×	`cbrt-prod_binary64`

Counts

4 → 227

Calls

4 calls:

7.0ms	(/.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 y))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
4.0ms	(/.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)

simplify168.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

689×	`associate-/r/_binary64`
440×	`fma-neg_binary64`
390×	`fma-def_binary64`
251×	`associate-/r*_binary64`
241×	`associate-/l*_binary64`

Counts

299 → 360

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	5885
1	736	5447
2	2631	5316
3	4650	5316
4	4949	5316

prune313.0ms (9.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	395	1	396
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	395	5	400

Error

Counts

400 → 5

Alt Table

Status	Error	Program
	35.6b	(fma.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (/.f64 x (+.f64 x 1)) (sqrt.f64 y)) (/.f64 x (+.f64 1 x)))
✓	0.6b	(fma.f64 (/.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 y)) (/.f64 x (+.f64 1 x)))
	0.8b	(fma.f64 (/.f64 x (.f64 (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (pow.f64 (cbrt.f64 (cbrt.f64 y)) 4))) (/.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 y)) (/.f64 x (+.f64 1 x)))
✓	2.4b	(+.f64 (/.f64 (*.f64 x (/.f64 x (+.f64 x 1))) y) (/.f64 x (+.f64 1 x)))
	4.4b	(+.f64 (/.f64 x (/.f64 (fma.f64 x y y) x)) (/.f64 x (+.f64 1 x)))

Compiler

Compiled 12080 to 5561 computations (54% saved)

regimes193.0ms (5.6%)

Accuracy

Total 0.0b remaining (59.8%)

Threshold costs 0.0b (59.8%)

Counts

68 → 1

Compiler

Compiled 3431 to 2159 computations (37.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	14	20
2	12	20

end82.0ms (2.4%)

Compiler: Compiled 138 to 83 computations (39.9% saved)

Details

analyze167.0ms (4.9%)

sample935.0ms (27.3%)

simplify86.0ms (2.5%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series20.0ms (0.6%)

rewrite13.0ms (0.4%)

simplify81.0ms (2.4%)

prune44.0ms (1.3%)

localize7.0ms (0.2%)

series34.0ms (1%)

rewrite31.0ms (0.9%)

simplify86.0ms (2.5%)

prune131.0ms (3.8%)

localize8.0ms (0.2%)

series34.0ms (1%)

rewrite42.0ms (1.2%)

simplify146.0ms (4.3%)

prune150.0ms (4.4%)

localize11.0ms (0.3%)

series593.0ms (17.3%)

rewrite36.0ms (1%)

simplify168.0ms (4.9%)

prune313.0ms (9.1%)

regimes193.0ms (5.6%)

simplify2.0ms (0.1%)

end82.0ms (2.4%)

Profiling