Details

analyze89.0ms (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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 18 to 8 computations (55.6% saved)

sample895.0ms (29.9%)

Results

863.0ms	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 53 to 23 computations (56.6% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
4×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	15	15
2	30	11
3	49	11
4	63	11
5	67	11
6	65	11

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
▶	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 79 to 36 computations (54.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series20.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
8.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-log-exp_binary64`
9×	`sum-log_binary64`
6×	`fma-def_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

2 → 37

Calls

2 calls:

6.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
6.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))

simplify75.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

520×	`cancel-sign-sub-inv_binary64`
492×	`fma-neg_binary64`
453×	`fma-def_binary64`
414×	`distribute-rgt-out_binary64`
376×	`distribute-rgt-in_binary64`

Counts

85 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	1132
1	186	1028
2	588	941
3	2530	937
4	4456	937
5	4891	937

prune54.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Error

0.0b

Counts

69 → 5

Alt Table

Status	Error	Program
	42.7b	(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) 3) (pow.f64 (.f64 y y) 3)) (+.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (-.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (*.f64 y y)))))
	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	0.9b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y)) (*.f64 y y))
▶	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))
	33.8b	(/.f64 (-.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (.f64 y y) (.f64 y y))) (-.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y)))

Compiler

Compiled 1747 to 381 computations (78.2% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))

series8.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(fma.f64 3 (*.f64 y y) (*.f64 x x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 3 (*.f64 y y) (*.f64 x x))

simplify59.0ms (2%)

Algorithm

1×	egg-herbie

Rules

912×	`fma-def_binary64`
466×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`
356×	`unswap-sqr_binary64`
324×	`*-commutative_binary64`

Counts

34 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	394
1	32	371
2	65	371
3	184	371
4	793	371
5	3022	371
6	4320	371
7	5097	371

prune19.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	23	5	28

Error

0.0b

Counts

28 → 5

Alt Table

Status	Error	Program
	42.7b	(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) 3) (pow.f64 (.f64 y y) 3)) (+.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (-.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (*.f64 y y)))))
▶	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	0.9b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y)) (*.f64 y y))
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))
	33.8b	(/.f64 (-.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (.f64 y y) (.f64 y y))) (-.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y)))

Compiler

Compiled 614 to 217 computations (64.7% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

series7.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

simplify58.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
466×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`
356×	`unswap-sqr_binary64`
323×	`*-commutative_binary64`

Counts

34 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	394
1	35	371
2	66	371
3	184	371
4	793	371
5	3022	371
6	4320	371
7	5097	371

prune20.0ms (0.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	24	5	29

Error

0.0b

Counts

29 → 5

Alt Table

Status	Error	Program
	42.7b	(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) 3) (pow.f64 (.f64 y y) 3)) (+.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (-.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (*.f64 y y)))))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
▶	0.9b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y)) (*.f64 y y))
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))
	33.8b	(/.f64 (-.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (.f64 y y) (.f64 y y))) (-.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y)))

Compiler

Compiled 613 to 229 computations (62.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y)) (*.f64 y y))
✓	0.2b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y))
✓	0.4b	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
✓	6.2b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series900.0ms (30.1%)

Counts

4 → 96

Calls

4 calls:

411.0ms	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y))
409.0ms	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y)) (*.f64 y y))
42.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
38.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`cbrt-div_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 92

Calls

4 calls:

14.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
2.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y)) (*.f64 y y))
0.0ms	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y))

simplify135.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
641×	`fma-neg_binary64`
474×	`*-commutative_binary64`
233×	`unswap-sqr_binary64`
223×	`cancel-sign-sub-inv_binary64`

Counts

188 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	4291
1	529	3993
2	1625	3769
3	4002	3698
4	4902	3698
5	5025	3698

prune165.0ms (5.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	278	6	284

Error

Counts

284 → 6

Alt Table

Status	Error	Program
✓	0.9b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y)) (*.f64 y y))
	0.9b	(fma.f64 (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y))) (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y))) (*.f64 y y))
	3.2b	(expm1.f64 (log1p.f64 (fma.f64 y y (fma.f64 2 (.f64 y y) (.f64 x x)))))
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))
	33.8b	(/.f64 (-.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (.f64 y y) (.f64 y y))) (-.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y)))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 11776 to 2450 computations (79.2% saved)

regimes328.0ms (11%)

Accuracy

Total 0.1b remaining (87.2%)

Threshold costs 0.1b (87.2%)

Counts

76 → 1

Compiler

Compiled 9162 to 3804 computations (58.5% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	11	22
2	11	22

end76.0ms (2.5%)

Compiler: Compiled 219 to 65 computations (70.3% saved)

Details

analyze89.0ms (3%)

sample895.0ms (29.9%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series20.0ms (0.7%)

rewrite15.0ms (0.5%)

simplify75.0ms (2.5%)

prune54.0ms (1.8%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite1.0ms (0%)

simplify59.0ms (2%)

prune19.0ms (0.6%)

localize5.0ms (0.2%)

series7.0ms (0.2%)

rewrite1.0ms (0%)

simplify58.0ms (1.9%)

prune20.0ms (0.7%)

localize9.0ms (0.3%)

series900.0ms (30.1%)

rewrite26.0ms (0.9%)

simplify135.0ms (4.5%)

prune165.0ms (5.5%)

regimes328.0ms (11%)

simplify5.0ms (0.2%)

end76.0ms (2.5%)

Profiling