Details

analyze126.0ms (7.6%)

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
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample796.0ms (47.8%)

Symmetry

(sort x y)

Results

764.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4
2	12	4

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (0.2%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(hypot.f64 x y)

Compiler

Compiled 23 to 13 computations (43.5% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x y)

series9.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(hypot.f64 x y)

rewrite32.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

329×	`log1p-expm1-u_binary64`
329×	`expm1-log1p-u_binary64`
294×	`add-log-exp_binary64`
293×	`add-exp-log_binary64`
288×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	79	4
2	919	4

Stop Event

1×	node limit

Counts

1 → 38

Calls

1 calls:

31.0ms

(hypot.f64 x y)

simplify30.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

568×	`fma-neg_binary64`
537×	`cancel-sign-sub-inv_binary64`
312×	`distribute-rgt-neg-in_binary64`
310×	`distribute-lft-neg-in_binary64`
266×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	488
1	162	470
2	523	454
3	2395	454

Stop Event

1×	node limit

Counts

62 → 68

prune31.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	2	69

Error

Counts

69 → 2

Alt Table

Status	Error	Program
▶	1.5b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3))
✓	0.0b	(hypot.f64 x y)

Compiler

Compiled 849 to 470 computations (44.6% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (hypot.f64 x y)))
✓	0.5b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3))
✓	0.6b	(cbrt.f64 (hypot.f64 x y))
✓	0.7b	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3)

series104.0ms (6.2%)

Counts

4 → 80

Calls

4 calls:

49.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3)
26.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x y)))
20.0ms	(cbrt.f64 (hypot.f64 x y))
9.0ms	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3))

rewrite49.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

630×	`log1p-expm1-u_binary64`
630×	`expm1-log1p-u_binary64`
314×	`log-prod_binary64`
128×	`log-pow_binary64`
127×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	189	23
2	1951	23

Stop Event

1×	node limit

Counts

4 → 108

Calls

4 calls:

48.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x y)))
48.0ms	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3))
48.0ms	(cbrt.f64 (hypot.f64 x y))
48.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3)

simplify58.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

708×	`times-frac_binary64`
410×	`cancel-sign-sub-inv_binary64`
216×	`fma-neg_binary64`
204×	`distribute-rgt-neg-in_binary64`
202×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	2388
1	738	2336
2	2465	2330

Stop Event

1×	node limit

Counts

188 → 214

prune199.0ms (11.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	374	0	374
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	374	2	376

Error

Counts

376 → 2

Alt Table

Status	Error	Program
✓	1.5b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x y))) 3))
✓	0.0b	(hypot.f64 x y)

Compiler

Compiled 9095 to 5188 computations (43% saved)

regimes170.0ms (10.2%)

Accuracy

Total 0.0b remaining (25%)

Threshold costs 0.0b (25%)

Counts

28 → 1

Compiler

Compiled 2288 to 1578 computations (31% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4

Stop Event

1×

saturated

end42.0ms (2.5%)

Remove: (sort x y)
Compiler: Compiled 42 to 25 computations (40.5% saved)

Details

analyze126.0ms (7.6%)

sample796.0ms (47.8%)

simplify7.0ms (0.4%)

prune4.0ms (0.2%)

localize2.0ms (0.1%)

series9.0ms (0.5%)

rewrite32.0ms (1.9%)

simplify30.0ms (1.8%)

prune31.0ms (1.9%)

localize7.0ms (0.4%)

series104.0ms (6.2%)

rewrite49.0ms (3%)

simplify58.0ms (3.5%)

prune199.0ms (11.9%)

regimes170.0ms (10.2%)

simplify2.0ms (0.1%)

end42.0ms (2.5%)

Profiling