Details

analyze224.0ms (6.3%)

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)

sample962.0ms (27%)

Results

823.0ms	8256×	body	128	valid
29.0ms	294×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify83.0ms (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

8.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.3b	(/.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)
✓	7.8b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

series19.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
7.0ms	(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:

3.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
0.0ms	(fma.f64 x (/.f64 x y) x)

simplify81.0ms (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

prune80.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	5	75

Error

0.0b

Counts

75 → 5

Alt Table

Status	Error	Program
▶	0.1b	(.f64 1 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1))))
	15.2b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
	31.0b	(*.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))))
	8.5b	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
	8.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (/.f64 (fma.f64 x (/.f64 x y) x) (cbrt.f64 (+.f64 x 1))))

Compiler

Compiled 1449 to 668 computations (53.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series18.0ms (0.5%)

Counts

3 → 51

Calls

3 calls:

12.0ms	(*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))
4.0ms	(+.f64 (/.f64 x y) 1)
2.0ms	(/.f64 x (+.f64 x 1))

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

3 → 106

Calls

3 calls:

12.0ms	(*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))
5.0ms	(+.f64 (/.f64 x y) 1)
3.0ms	(/.f64 x (+.f64 x 1))

simplify120.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

440×	`fma-def_binary64`
386×	`associate-/l*_binary64`
386×	`times-frac_binary64`
344×	`distribute-rgt-in_binary64`
313×	`fma-neg_binary64`

Counts

157 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2330
1	444	2167
2	1466	2015
3	4449	2015
4	4896	2015
5	4995	2015
6	4966	2015

prune195.0ms (5.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	161	5	166

Error

0.0b

Counts

166 → 5

Alt Table

Status	Error	Program
	18.2b	(.f64 1 (.f64 (*.f64 (+.f64 (/.f64 x y) 1) (sqrt.f64 (/.f64 x (+.f64 x 1)))) (sqrt.f64 (/.f64 x (+.f64 x 1)))))
	19.4b	(.f64 1 (/.f64 (fma.f64 x (pow.f64 (/.f64 x y) 3) x) (.f64 (+.f64 x 1) (+.f64 1 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) 1))))))
▶	8.4b	(.f64 1 (.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1))))
	15.2b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
	8.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (/.f64 (fma.f64 x (/.f64 x y) x) (cbrt.f64 (+.f64 x 1))))

Compiler

Compiled 3462 to 2119 computations (38.8% saved)

localize9.0ms (0.3%)

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)
✓	7.8b	(*.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1)))

series13.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

11.0ms	(*.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1)))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite17.0ms (0.5%)

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:

9.0ms	(*.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1)))
3.0ms	(/.f64 1 (+.f64 x 1))

simplify108.0ms (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

prune130.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	149	5	154

Error

0.0b

Counts

154 → 5

Alt Table

Status	Error	Program
	18.2b	(.f64 1 (.f64 (*.f64 (+.f64 (/.f64 x y) 1) (sqrt.f64 (/.f64 x (+.f64 x 1)))) (sqrt.f64 (/.f64 x (+.f64 x 1)))))
	19.4b	(.f64 1 (/.f64 (fma.f64 x (pow.f64 (/.f64 x y) 3) x) (.f64 (+.f64 x 1) (+.f64 1 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) 1))))))
✓	8.4b	(.f64 1 (.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1))))
	15.2b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
▶	8.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (/.f64 (fma.f64 x (/.f64 x y) x) (cbrt.f64 (+.f64 x 1))))

Compiler

Compiled 3223 to 1846 computations (42.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
✓	0.3b	(cbrt.f64 (+.f64 x 1))
✓	1.7b	(/.f64 (fma.f64 x (/.f64 x y) x) (cbrt.f64 (+.f64 x 1)))
✓	6.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (/.f64 (fma.f64 x (/.f64 x y) x) (cbrt.f64 (+.f64 x 1))))

series102.0ms (2.9%)

Counts

4 → 72

Calls

4 calls:

76.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (cbrt.f64 (+.f64 x 1)))
15.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (/.f64 (fma.f64 x (/.f64 x y) x) (cbrt.f64 (+.f64 x 1))))
6.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
4.0ms	(cbrt.f64 (+.f64 x 1))

rewrite55.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
74×	`add-sqr-sqrt_binary64`
59×	`cbrt-prod_binary64`
57×	`times-frac_binary64`
53×	`add-exp-log_binary64`

Counts

4 → 203

Calls

4 calls:

19.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (/.f64 (fma.f64 x (/.f64 x y) x) (cbrt.f64 (+.f64 x 1))))
7.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
6.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (cbrt.f64 (+.f64 x 1)))
2.0ms	(cbrt.f64 (+.f64 x 1))

simplify214.0ms (6%)

Algorithm

1×	egg-herbie

Rules

436×	`cancel-sign-sub-inv_binary64`
355×	`fma-neg_binary64`
250×	`sub-neg_binary64`
216×	`associate-r_binary64`
178×	`associate-l_binary64`

Counts

275 → 356

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	384	8065
1	1032	6727
2	3632	6343
3	4774	6294
4	4975	6294
5	4911	6294

prune405.0ms (11.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	440	0	440
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	440	5	445

Error

0.0b

Counts

445 → 5

Alt Table

Status	Error	Program
	18.2b	(.f64 1 (.f64 (*.f64 (+.f64 (/.f64 x y) 1) (sqrt.f64 (/.f64 x (+.f64 x 1)))) (sqrt.f64 (/.f64 x (+.f64 x 1)))))
	19.4b	(.f64 1 (/.f64 (fma.f64 x (pow.f64 (/.f64 x y) 3) x) (.f64 (+.f64 x 1) (+.f64 1 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) 1))))))
✓	8.4b	(.f64 1 (.f64 (fma.f64 x (/.f64 x y) x) (/.f64 1 (+.f64 x 1))))
	15.2b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
✓	8.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (/.f64 (fma.f64 x (/.f64 x y) x) (cbrt.f64 (+.f64 x 1))))

Compiler

Compiled 14836 to 9391 computations (36.7% saved)

regimes580.0ms (16.3%)

Accuracy

Total 0.0b remaining (65.1%)

Threshold costs 0.0b (65.1%)

Counts

187 → 1

Compiler

Compiled 10229 to 7058 computations (31% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	17	16
2	16	16

end85.0ms (2.4%)

Compiler: Compiled 135 to 93 computations (31.1% saved)

Details

analyze224.0ms (6.3%)

sample962.0ms (27%)

simplify83.0ms (2.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series19.0ms (0.5%)

rewrite6.0ms (0.2%)

simplify81.0ms (2.3%)

prune80.0ms (2.2%)

localize7.0ms (0.2%)

series18.0ms (0.5%)

rewrite32.0ms (0.9%)

simplify120.0ms (3.4%)

prune195.0ms (5.5%)

localize9.0ms (0.3%)

series13.0ms (0.4%)

rewrite17.0ms (0.5%)

simplify108.0ms (3%)

prune130.0ms (3.7%)

localize10.0ms (0.3%)

series102.0ms (2.9%)

rewrite55.0ms (1.5%)

simplify214.0ms (6%)

prune405.0ms (11.4%)

regimes580.0ms (16.3%)

simplify2.0ms (0.1%)

end85.0ms (2.4%)

Profiling