Details

analyze18.0ms (0.5%)

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 (41.9%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify88.0ms (2.6%)

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

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

20.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Compiler

Compiled 63 to 27 computations (57.1% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	20.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series23.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

23.0ms

(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (*.f64 y y)))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`frac-times_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 31

Calls

1 calls:

7.0ms

(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (*.f64 y y)))

simplify45.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

801×	`distribute-rgt-in_binary64`
770×	`distribute-lft-in_binary64`
413×	`times-frac_binary64`
375×	`fma-def_binary64`
71×	`cancel-sign-sub-inv_binary64`

Counts

55 → 60

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1375
1	328	1210
2	1274	1172
3	5121	1172

prune48.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	4	61

Error

0.0b

Counts

61 → 4

Alt Table

Status	Error	Program
	21.0b	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (fma.f64 x x (.f64 y y))))
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	20.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y))) 3))
	41.8b	1

Compiler

Compiled 1513 to 443 computations (70.7% 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)))

series66.0ms (2%)

Counts

4 → 96

Calls

4 calls:

30.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
15.0ms	(hypot.f64 x y)
10.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
10.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))

rewrite39.0ms (1.1%)

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:

13.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
10.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
4.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
0.0ms	(hypot.f64 x y)

simplify146.0ms (4.3%)

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

prune199.0ms (5.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	298	3	301
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	301	4	305

Error

Counts

305 → 4

Alt Table

Status	Error	Program
	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	20.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y))) 3))
	0.0b	(/.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y)) (hypot.f64 x y))
▶	0.0b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3))

Compiler

Compiled 7493 to 1942 computations (74.1% saved)

localize10.0ms (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	(pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3)
	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)))

series44.0ms (1.3%)

Counts

1 → 24

Calls

1 calls:

44.0ms

(pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
5×	`rem-cube-cbrt_binary64`
5×	`pow-exp_binary64`
4×	`cbrt-undiv_binary64`

Counts

1 → 33

Calls

1 calls:

9.0ms

(pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3)

simplify70.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

712×	`associate-l_binary64`
709×	`fma-def_binary64`
370×	`associate-*l/_binary64`
330×	`associate-*r/_binary64`
237×	`times-frac_binary64`

Counts

57 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1343
1	251	1232
2	850	1175
3	4811	1163
4	5468	1163

prune205.0ms (6.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	270	4	274

Error

Counts

274 → 4

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	20.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y))) 3))
	0.0b	(/.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y)) (hypot.f64 x y))
✓	0.0b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3))

Compiler

Compiled 7397 to 2201 computations (70.2% saved)

localize9.0ms (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	(/.f64 (hypot.f64 x y) (-.f64 x y))
✓	0.0b	(/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y)))
✓	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))

series49.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

29.0ms	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
10.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))
10.0ms	(/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y)))

rewrite79.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

275×	`times-frac_binary64`
211×	`add-sqr-sqrt_binary64`
188×	`*-un-lft-identity_binary64`
128×	`add-cube-cbrt_binary64`
68×	`associate-l_binary64`

Counts

3 → 277

Calls

3 calls:

30.0ms	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
7.0ms	(/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y)))
4.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))

simplify192.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

638×	`distribute-rgt-in_binary64`
457×	`fma-def_binary64`
186×	`associate-*l/_binary64`
175×	`associate-r_binary64`
169×	`cancel-sign-sub-inv_binary64`

Counts

349 → 439

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	8487
1	810	7567
2	2955	7421
3	5314	7421

prune337.0ms (10%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	500	0	500
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	500	4	504

Error

Counts

504 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	20.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y))) 3))
	0.0b	(/.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y)) (hypot.f64 x y))
✓	0.0b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3))

Compiler

Compiled 14005 to 3569 computations (74.5% saved)

regimes163.0ms (4.9%)

Accuracy

Total 0.0b remaining (55%)

Threshold costs 0.0b (55%)

Counts

60 → 1

Compiler

Compiled 3069 to 1741 computations (43.3% saved)

simplify3.0ms (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

end80.0ms (2.4%)

Compiler: Compiled 115 to 62 computations (46.1% saved)

Details

analyze18.0ms (0.5%)

sample1.4s (41.9%)

simplify88.0ms (2.6%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series23.0ms (0.7%)

rewrite10.0ms (0.3%)

simplify45.0ms (1.3%)

prune48.0ms (1.4%)

localize8.0ms (0.2%)

series66.0ms (2%)

rewrite39.0ms (1.1%)

simplify146.0ms (4.3%)

prune199.0ms (5.9%)

localize10.0ms (0.3%)

series44.0ms (1.3%)

rewrite12.0ms (0.4%)

simplify70.0ms (2.1%)

prune205.0ms (6.1%)

localize9.0ms (0.3%)

series49.0ms (1.5%)

rewrite79.0ms (2.3%)

simplify192.0ms (5.7%)

prune337.0ms (10%)

regimes163.0ms (4.9%)

simplify3.0ms (0.1%)

end80.0ms (2.4%)

Profiling