Details

analyze16.0ms (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)

sample1.8s (59.4%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify77.0ms (2.5%)

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

19.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Compiler

Compiled 63 to 27 computations (57.1% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	18.7b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series18.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

17.0ms

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

rewrite11.0ms (0.4%)

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 (1.5%)

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

prune32.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	3	61

Error

0.0b

Counts

61 → 3

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	49.0b	(fma.f64 (/.f64 (.f64 y y) (.f64 x x)) -2 1)
	24.2b	(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)

Compiler

Compiled 1485 to 431 computations (71% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)))

series73.0ms (2.4%)

Counts

3 → 72

Calls

3 calls:

53.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
11.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
9.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))

rewrite35.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
19×	`associate-l_binary64`

Counts

3 → 136

Calls

3 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))

simplify108.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

614×	`times-frac_binary64`
493×	`distribute-rgt-in_binary64`
464×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`
176×	`sub-neg_binary64`

Counts

208 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4519
1	735	4135
2	2321	4033
3	5136	4033

prune108.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	215	4	219

Error

Counts

219 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	49.0b	(fma.f64 (/.f64 (.f64 y y) (.f64 x x)) -2 1)
	24.2b	(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
▶	0.0b	(/.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y)) (hypot.f64 x y))

Compiler

Compiled 5338 to 1135 computations (78.7% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series44.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

25.0ms	(/.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y)) (hypot.f64 x y))
19.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y))

rewrite40.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
19×	`associate-l_binary64`
19×	`times-frac_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 77

Calls

2 calls:

9.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y))
8.0ms	(/.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y)) (hypot.f64 x y))

simplify76.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

561×	`distribute-rgt-in_binary64`
534×	`distribute-lft-in_binary64`
502×	`fma-def_binary64`
179×	`cancel-sign-sub-inv_binary64`
146×	`div-sub_binary64`

Counts

125 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	2926
1	681	2611
2	2241	2563
3	5365	2563

prune120.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	212	4	216

Error

Counts

216 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	49.0b	(fma.f64 (/.f64 (.f64 y y) (.f64 x x)) -2 1)
▶	24.2b	(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	0.0b	(/.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y)) (hypot.f64 x y))

Compiler

Compiled 5033 to 1333 computations (73.5% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	18.8b	(/.f64 (.f64 x x) (.f64 y y))

series35.0ms (1.2%)

Counts

1 → 24

Calls

1 calls:

35.0ms

(/.f64 (*.f64 x x) (*.f64 y y))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
4×	`cbrt-unprod_binary64`
4×	`cbrt-undiv_binary64`
4×	`div-exp_binary64`

Counts

1 → 23

Calls

1 calls:

5.0ms

(/.f64 (*.f64 x x) (*.f64 y y))

simplify92.0ms (3%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-neg_binary64`
528×	`times-frac_binary64`
339×	`unswap-sqr_binary64`
327×	`associate-/l*_binary64`
288×	`*-commutative_binary64`

Counts

47 → 35

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	49	635
1	120	501
2	410	476
3	1765	453
4	2660	453
5	3835	363
6	4877	360
7	4953	360
8	4920	360

prune29.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	35	4	39

Error

Counts

39 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	49.0b	(fma.f64 (/.f64 (.f64 y y) (.f64 x x)) -2 1)
✓	24.2b	(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	0.0b	(/.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y)) (hypot.f64 x y))

Compiler

Compiled 570 to 255 computations (55.3% saved)

regimes173.0ms (5.7%)

Accuracy

Total 0.0b remaining (54.9%)

Threshold costs 0.0b (54.9%)

Counts

48 → 1

Compiler

Compiled 2044 to 1274 computations (37.7% saved)

simplify2.0ms (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	9	22
1	13	22
2	18	22
3	20	22
4	21	22
5	21	22

end60.0ms (2%)

Compiler: Compiled 92 to 48 computations (47.8% saved)

Details

analyze16.0ms (0.5%)

sample1.8s (59.4%)

simplify77.0ms (2.5%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series18.0ms (0.6%)

rewrite11.0ms (0.4%)

simplify45.0ms (1.5%)

prune32.0ms (1%)

localize8.0ms (0.2%)

series73.0ms (2.4%)

rewrite35.0ms (1.1%)

simplify108.0ms (3.5%)

prune108.0ms (3.6%)

localize11.0ms (0.4%)

series44.0ms (1.4%)

rewrite40.0ms (1.3%)

simplify76.0ms (2.5%)

prune120.0ms (3.9%)

localize6.0ms (0.2%)

series35.0ms (1.2%)

rewrite6.0ms (0.2%)

simplify92.0ms (3%)

prune29.0ms (1%)

regimes173.0ms (5.7%)

simplify2.0ms (0.1%)

end60.0ms (2%)

Profiling