Details

analyze257.0ms (7.7%)

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)

sample20.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify84.0ms (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

11.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.1b	(/.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)
✓	10.4b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

series20.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
8.0ms	(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)

simplify82.0ms (2.5%)

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

prune56.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Error

0.0b

Counts

75 → 4

Alt Table

Status	Error	Program
	36.0b	(*.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))))
	14.3b	(*.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (fma.f64 x x -1)) (-.f64 x 1))
	14.0b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
▶	0.0b	(.f64 1 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1))))

Compiler

Compiled 1405 to 634 computations (54.9% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series14.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

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

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

2 → 79

Calls

2 calls:

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

simplify123.0ms (3.7%)

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

115 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	2083
1	435	1938
2	1460	1787
3	4441	1787
4	4887	1787
5	4995	1787
6	4966	1787

prune113.0ms (3.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	130	4	134

Error

Counts

134 → 4

Alt Table

Status	Error	Program
✓	0.0b	(.f64 1 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1))))
▶	0.8b	(.f64 1 (.f64 (.f64 (+.f64 (/.f64 x y) 1) (.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1))))) (cbrt.f64 (/.f64 x (+.f64 x 1)))))
	18.1b	(.f64 1 (/.f64 (.f64 (-.f64 (.f64 (/.f64 x y) (/.f64 x y)) (.f64 1 1)) x) (*.f64 (-.f64 (/.f64 x y) 1) (+.f64 x 1))))
	14.0b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))

Compiler

Compiled 2807 to 1736 computations (38.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 (/.f64 x y) 1) (.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1)))))
✓	0.2b	(.f64 (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1))))) (cbrt.f64 (/.f64 x (+.f64 x 1))))
✓	0.3b	(*.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1))))
✓	0.3b	(cbrt.f64 (/.f64 x (+.f64 x 1)))

series225.0ms (6.8%)

Counts

4 → 72

Calls

4 calls:

185.0ms	(.f64 (+.f64 (/.f64 x y) 1) (.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1)))))
16.0ms	(.f64 (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1))))) (cbrt.f64 (/.f64 x (+.f64 x 1))))
14.0ms	(*.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1))))
10.0ms	(cbrt.f64 (/.f64 x (+.f64 x 1)))

rewrite94.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`cbrt-prod_binary64`
118×	`*-un-lft-identity_binary64`
90×	`times-frac_binary64`
87×	`add-sqr-sqrt_binary64`
62×	`add-cube-cbrt_binary64`

Counts

4 → 227

Calls

4 calls:

27.0ms	(.f64 (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1))))) (cbrt.f64 (/.f64 x (+.f64 x 1))))
18.0ms	(*.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1))))
16.0ms	(.f64 (+.f64 (/.f64 x y) 1) (.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1)))))
3.0ms	(cbrt.f64 (/.f64 x (+.f64 x 1)))

simplify230.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

493×	`associate-l_binary64`
457×	`associate-r_binary64`
432×	`fma-neg_binary64`
276×	`sub-neg_binary64`
226×	`*-commutative_binary64`

Counts

299 → 398

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	436	8593
1	1130	7903
2	3996	7493
3	4895	7493
4	4961	7493

prune465.0ms (14%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	511	1	512
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	512	4	516

Error

Counts

516 → 4

Alt Table

Status	Error	Program
✓	0.0b	(.f64 1 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1))))
✓	0.8b	(.f64 1 (.f64 (.f64 (+.f64 (/.f64 x y) 1) (.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1))))) (cbrt.f64 (/.f64 x (+.f64 x 1)))))
	18.1b	(.f64 1 (/.f64 (.f64 x (fma.f64 (/.f64 x y) (/.f64 x y) -1)) (*.f64 (+.f64 x 1) (+.f64 -1 (/.f64 x y)))))
▶	14.0b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))

Compiler

Compiled 18681 to 12908 computations (30.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 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)))
✓	0.0b	(*.f64 (+.f64 1 x) y)
✓	16.4b	(/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y))

series40.0ms (1.2%)

Counts

4 → 51

Calls

4 calls:

19.0ms	(+.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))
4.0ms	(*.f64 (+.f64 1 x) y)
2.0ms	(/.f64 x (+.f64 1 x))

rewrite38.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`

Counts

4 → 128

Calls

4 calls:

18.0ms	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
6.0ms	(/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y))
4.0ms	(*.f64 (+.f64 1 x) y)
4.0ms	(/.f64 x (+.f64 1 x))

simplify98.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-def_binary64`
489×	`associate-/r*_binary64`
378×	`fma-neg_binary64`
352×	`associate-*l/_binary64`
270×	`associate-/l/_binary64`

Counts

179 → 243

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	2557
1	542	2313
2	1716	2223
3	4630	2223
4	4998	2223

prune211.0ms (6.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	242	1	243
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	243	4	247

Error

Counts

247 → 4

Alt Table

Status	Error	Program
✓	0.0b	(.f64 1 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1))))
✓	0.8b	(.f64 1 (.f64 (.f64 (+.f64 (/.f64 x y) 1) (.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (cbrt.f64 (/.f64 x (+.f64 x 1))))) (cbrt.f64 (/.f64 x (+.f64 x 1)))))
	6.0b	(+.f64 (/.f64 x (/.f64 (*.f64 (+.f64 1 x) y) x)) (/.f64 x (+.f64 1 x)))
✓	14.0b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))

Compiler

Compiled 5217 to 3302 computations (36.7% saved)

regimes409.0ms (12.3%)

Accuracy

Total 0.0b remaining (74.4%)

Threshold costs 0.0b (74.4%)

Counts

136 → 1

Compiler

Compiled 7835 to 5240 computations (33.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	14	22
2	13	22

end1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample676.0ms (20.4%)

Algorithm

1×

intervals

Results

341.0ms	8000×	body	128	valid
10.0ms	251×	body	128	invalid

Compiler

Compiled 112 to 79 computations (29.5% saved)

Details

analyze257.0ms (7.7%)

sample20.0ms (0.6%)

simplify84.0ms (2.5%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series20.0ms (0.6%)

rewrite6.0ms (0.2%)

simplify82.0ms (2.5%)

prune56.0ms (1.7%)

localize8.0ms (0.2%)

series14.0ms (0.4%)

rewrite20.0ms (0.6%)

simplify123.0ms (3.7%)

prune113.0ms (3.4%)

localize11.0ms (0.3%)

series225.0ms (6.8%)

rewrite94.0ms (2.8%)

simplify230.0ms (6.9%)

prune465.0ms (14%)

localize8.0ms (0.2%)

series40.0ms (1.2%)

rewrite38.0ms (1.1%)

simplify98.0ms (2.9%)

prune211.0ms (6.3%)

regimes409.0ms (12.3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample676.0ms (20.4%)

Profiling