Details

analyze16.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.4s (34.9%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify80.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

917×	`times-frac_binary64`
816×	`unsub-neg_binary64`
772×	`fma-def_binary64`
484×	`fma-neg_binary64`
376×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	24	20
2	55	20
3	112	20
4	271	20
5	657	20
6	1234	20
7	2620	20
8	3288	20
9	4652	20
10	5075	20

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

21.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	21.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
	21.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Compiler

Compiled 97 to 45 computations (53.6% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	20.7b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series25.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
6.0ms	(+.f64 (.f64 x x) (.f64 y y))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
5×	`flip-+_binary64`
5×	`flip3-+_binary64`

Counts

2 → 47

Calls

2 calls:

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

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

949×	`distribute-rgt-in_binary64`
893×	`distribute-lft-in_binary64`
607×	`fma-def_binary64`
132×	`cancel-sign-sub-inv_binary64`
127×	`div-sub_binary64`

Counts

95 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	1718
1	414	1552
2	1742	1514
3	5985	1514

prune52.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	100	4	104

Error

0.0b

Counts

104 → 4

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	21.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
	40.4b	1
	21.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Compiler

Compiled 2435 to 581 computations (76.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x y)
✓	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))
✓	0.0b	(/.f64 (-.f64 x y) (hypot.f64 x y))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

series65.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

26.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
19.0ms	(hypot.f64 x y)
10.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
10.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
40×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 146

Calls

4 calls:

14.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
5.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
4.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
0.0ms	(hypot.f64 x y)

simplify441.0ms (10.6%)

Algorithm

1×	egg-herbie

Rules

776×	`times-frac_binary64`
614×	`fma-neg_binary64`
593×	`fma-def_binary64`
222×	`sub-neg_binary64`
164×	`associate-*l/_binary64`

Counts

242 → 259

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	5087
1	854	4676
2	2705	4565
3	4842	4565
4	5181	4565

prune291.0ms (7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	297	4	301
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	300	5	305

Error

Counts

305 → 5

Alt Table

Status	Error	Program
	41.5b	(.f64 (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
▶	0.0b	(/.f64 (*.f64 (-.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y))) (hypot.f64 x y))
✓	21.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
	1.4b	(.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) (/.f64 (cbrt.f64 (+.f64 x y)) (hypot.f64 x y)))
	1.2b	(.f64 (/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (.f64 (cbrt.f64 (hypot.f64 x y)) (cbrt.f64 (hypot.f64 x y)))) (/.f64 (+.f64 x y) (cbrt.f64 (hypot.f64 x y))))

Compiler

Compiled 7556 to 1955 computations (74.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 x y)
✓	0.0b	(/.f64 (*.f64 (-.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y))) (hypot.f64 x y))
	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))
✓	0.0b	(*.f64 (-.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y)))

series52.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(/.f64 (*.f64 (-.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y))) (hypot.f64 x y))
24.0ms	(*.f64 (-.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y)))

rewrite58.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
16×	`times-frac_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

42.0ms	(/.f64 (*.f64 (-.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y))) (hypot.f64 x y))
11.0ms	(*.f64 (-.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y)))

simplify188.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

438×	`distribute-rgt-in_binary64`
421×	`fma-def_binary64`
416×	`distribute-lft-in_binary64`
208×	`fma-neg_binary64`
169×	`cancel-sign-sub-inv_binary64`

Counts

121 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	2838
1	578	2523
2	2102	2474
3	4722	2450
4	4990	2450
5	5000	2450
6	4958	2450

prune201.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	306	1	307
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	308	4	312

Error

Counts

312 → 4

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (*.f64 (-.f64 x y) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3))) (hypot.f64 x y))
	1.2b	(.f64 (/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (.f64 (cbrt.f64 (hypot.f64 x y)) (cbrt.f64 (hypot.f64 x y)))) (/.f64 (+.f64 x y) (cbrt.f64 (hypot.f64 x y))))
	41.5b	(.f64 (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	21.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Compiler

Compiled 7332 to 2162 computations (70.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3))
✓	0.0b	(*.f64 (-.f64 x y) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3)))
✓	0.1b	(pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3)

series51.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

21.0ms	(*.f64 (-.f64 x y) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3)))
17.0ms	(pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3)
12.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3))

rewrite49.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`*-un-lft-identity_binary64`
82×	`cbrt-prod_binary64`
74×	`times-frac_binary64`
73×	`add-sqr-sqrt_binary64`
56×	`add-cube-cbrt_binary64`

Counts

3 → 175

Calls

3 calls:

19.0ms	(*.f64 (-.f64 x y) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3)))
6.0ms	(pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3)
5.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3))

simplify248.0ms (6%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-def_binary64`
375×	`unswap-sqr_binary64`
261×	`cancel-sign-sub-inv_binary64`
233×	`fma-neg_binary64`
166×	`sub-neg_binary64`

Counts

247 → 256

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	5120
1	730	4682
2	2721	4554
3	4609	4554
4	4981	4554

prune217.0ms (5.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	317	0	317
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	317	4	321

Error

Counts

321 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 (-.f64 x y) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) 3))) (hypot.f64 x y))
	1.2b	(.f64 (/.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (.f64 (cbrt.f64 (hypot.f64 x y)) (cbrt.f64 (hypot.f64 x y)))) (/.f64 (+.f64 x y) (cbrt.f64 (hypot.f64 x y))))
	41.5b	(.f64 (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	21.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Compiler

Compiled 8248 to 2879 computations (65.1% saved)

regimes435.0ms (10.5%)

Accuracy

Total 0.0b remaining (38.4%)

Threshold costs 0.0b (38.4%)

Counts

149 → 1

Compiler

Compiled 8449 to 4514 computations (46.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	16	27
2	21	27
3	23	27
4	24	27
5	24	27

end78.0ms (1.9%)

Compiler: Compiled 130 to 65 computations (50% saved)

Details

analyze16.0ms (0.4%)

sample1.4s (34.9%)

simplify80.0ms (1.9%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series25.0ms (0.6%)

rewrite18.0ms (0.4%)

simplify56.0ms (1.3%)

prune52.0ms (1.3%)

localize8.0ms (0.2%)

series65.0ms (1.6%)

rewrite35.0ms (0.8%)

simplify441.0ms (10.6%)

prune291.0ms (7%)

localize8.0ms (0.2%)

series52.0ms (1.3%)

rewrite58.0ms (1.4%)

simplify188.0ms (4.5%)

prune201.0ms (4.8%)

localize11.0ms (0.3%)

series51.0ms (1.2%)

rewrite49.0ms (1.2%)

simplify248.0ms (6%)

prune217.0ms (5.2%)

regimes435.0ms (10.5%)

simplify4.0ms (0.1%)

end78.0ms (1.9%)

Profiling