Details

analyze243.0ms (3.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

26.0ms

256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify152.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1333×	`fma-def_binary64`
773×	`distribute-rgt-out_binary64`
559×	`hypot-def_binary64`
453×	`associate-l_binary64`
451×	`count-2_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	4
2	25	4
3	46	4
4	98	4
5	245	4
6	763	4
7	1382	4
8	2673	4
9	3450	4
10	4144	4
11	4482	4
12	4395	4
13	4766	4
14	4993	4
15	4742	4

prune6.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 20 to 12 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 x x)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-cbrt-cube_binary64`
3×	`log1p-expm1-u_binary64`

Counts

1 → 31

Calls

1 calls:

18.0ms

(hypot.f64 x x)

series54.0ms (0.8%)

Counts

1 → 12

Calls

1 calls:

54.0ms

(hypot.f64 x x)

simplify232.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1233×	`sqr-pow_binary64`
530×	`pow-sqr_binary64`
482×	`cube-prod_binary64`
435×	`fabs-mul_binary64`
374×	`unswap-sqr_binary64`

Counts

43 → 52

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	236
1	45	227
2	67	227
3	82	227
4	111	227
5	191	227
6	397	227
7	727	227
8	762	227
9	925	227
10	1102	227
11	1345	227
12	1674	227
13	2076	227
14	2488	227
15	3029	227
16	3317	227
17	3480	227
18	3590	227
19	3637	227
20	3686	227
21	4300	227
22	4946	227
23	4680	227

prune28.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	6	53

Error

0.0b

Counts

53 → 6

Alt Table

Status	Error	Program
	32.8b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
	5.7b	(exp.f64 (log.f64 (hypot.f64 x x)))
▶	0.6b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	1.4b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 282 to 124 computations (56% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.2b	(sqrt.f64 (hypot.f64 x x))
✓	0.6b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cube-cbrt_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`pow1_binary64`
6×	`add-cbrt-cube_binary64`
6×	`log1p-expm1-u_binary64`

Counts

2 → 75

Calls

2 calls:

25.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
21.0ms	(sqrt.f64 (hypot.f64 x x))

series48.0ms (0.7%)

Counts

2 → 0

Calls

2 calls:

30.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
18.0ms	(sqrt.f64 (hypot.f64 x x))

simplify117.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-def_binary64`
852×	`exp-sum_binary64`
568×	`distribute-rgt-in_binary64`
490×	`distribute-lft-in_binary64`
392×	`exp-prod_binary64`

Counts

75 → 110

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	423
1	81	398
2	178	398
3	686	349
4	1433	347
5	4019	347
6	5622	347

prune70.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	162	6	168

Error

0.0b

Counts

168 → 6

Alt Table

Status	Error	Program
	32.8b	(*.f64 (sqrt.f64 2) x)
▶	1.3b	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
✓	0.1b	(hypot.f64 x x)
	5.7b	(exp.f64 (log.f64 (hypot.f64 x x)))
✓	0.6b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 1122 to 514 computations (54.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
	0.6b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
✓	0.6b	(cbrt.f64 (hypot.f64 x x))
✓	0.6b	(cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 2))

rewrite72.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cube-cbrt_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`pow1/3_binary64`
9×	`log1p-expm1-u_binary64`
9×	`expm1-log1p-u_binary64`

Counts

3 → 101

Calls

3 calls:

23.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
21.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 2))
20.0ms	(cbrt.f64 (hypot.f64 x x))

series2.1s (32.5%)

Counts

3 → 36

Calls

3 calls:

741.0ms	(cbrt.f64 (hypot.f64 x x))
705.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 2))
680.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)

simplify239.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

501×	`distribute-rgt-in_binary64`
427×	`exp-prod_binary64`
419×	`log-prod_binary64`
380×	`distribute-lft-in_binary64`
309×	`*-commutative_binary64`

Counts

137 → 222

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	97	1560
1	172	1195
2	299	1101
3	1085	917
4	2171	917
5	4260	913
6	4852	913
7	4966	913
8	4859	913

prune143.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	285	6	291

Error

0.0b

Counts

291 → 6

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
▶	1.4b	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 2))
	32.8b	(*.f64 (sqrt.f64 2) x)
	5.7b	(exp.f64 (log.f64 (hypot.f64 x x)))
✓	0.6b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 2993 to 1451 computations (51.5% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)
	0.6b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	0.6b	(cbrt.f64 (hypot.f64 x x))
	0.6b	(cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 2))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cube-cbrt_binary64`
4×	`pow-to-exp_binary64`
4×	`unpow2_binary64`
3×	`add-exp-log_binary64`
3×	`sqr-pow_binary64`

Counts

1 → 40

Calls

1 calls:

23.0ms

(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)

series767.0ms (11.7%)

Counts

1 → 12

Calls

1 calls:

767.0ms

(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)

simplify151.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-def_binary64`
548×	`unswap-sqr_binary64`
442×	`exp-prod_binary64`
293×	`distribute-rgt-in_binary64`
286×	`log-prod_binary64`

Counts

52 → 87

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	564
1	112	494
2	197	453
3	740	346
4	1891	344
5	4275	344
6	4887	344
7	4979	344
8	4842	344

prune158.0ms (2.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	352	1	353
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	353	6	359

Error

0.0b

Counts

359 → 6

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
✓	1.4b	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 2))
	32.8b	(*.f64 (sqrt.f64 2) x)
	3.2b	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x)))) 2))
✓	0.6b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 3586 to 1847 computations (48.5% saved)

regimes313.0ms (4.8%)

Accuracy

Total 0.1b remaining (69%)

Threshold costs 0.1b (69%)

Compiler

Compiled 2286 to 1590 computations (30.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end1.0ms (0%)

Compiler: Compiled 4 to 2 computations (50% saved)

sample1.4s (21.9%)

Algorithm

1×

intervals

Results

944.0ms

8000×

body

128

valid

Compiler

Compiled 72 to 52 computations (27.8% saved)

Details

analyze243.0ms (3.7%)

sample39.0ms (0.6%)

simplify152.0ms (2.3%)

prune6.0ms (0.1%)

localize4.0ms (0.1%)

rewrite21.0ms (0.3%)

series54.0ms (0.8%)

simplify232.0ms (3.5%)

prune28.0ms (0.4%)

localize8.0ms (0.1%)

rewrite51.0ms (0.8%)

series48.0ms (0.7%)

simplify117.0ms (1.8%)

prune70.0ms (1.1%)

localize17.0ms (0.3%)

rewrite72.0ms (1.1%)

series2.1s (32.5%)

simplify239.0ms (3.7%)

prune143.0ms (2.2%)

localize21.0ms (0.3%)

rewrite27.0ms (0.4%)

series767.0ms (11.7%)

simplify151.0ms (2.3%)

prune158.0ms (2.4%)

regimes313.0ms (4.8%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.4s (21.9%)

Profiling