Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.3s (35.7%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify206.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	22	9
3	41	9
4	88	9
5	221	9
6	693	9
7	1098	9
8	1100	9
9	1248	9
10	1418	9
11	1600	9
12	1825	9
13	2110	9
14	2529	9
15	3094	9
16	3780	9
17	3998	9
18	4242	9
19	4324	9
20	4357	9
21	4378	9
22	4947	9

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

28.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	28.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series10.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

6.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
5.0ms	(*.f64 2 (pow.f64 x 2))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 41

Calls

2 calls:

7.0ms	(*.f64 2 (pow.f64 x 2))
4.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

simplify208.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

823×	`unswap-sqr_binary64`
448×	`hypot-def_binary64`
432×	`*-commutative_binary64`
402×	`sqr-pow_binary64`
358×	`times-frac_binary64`

Counts

53 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	490
1	110	449
2	247	437
3	826	431
4	1358	371
5	3482	371
6	4011	371
7	4935	371
8	4869	371

prune426.0ms (11.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	9	67

Error

0.0b

Counts

67 → 9

Alt Table

Status	Error	Program
	29.3b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))
✓	28.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	48.1b	(sqrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 6)))
▶	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	27.1b	(log1p.f64 (expm1.f64 (hypot.f64 x x)))
	29.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(*.f64 (sqrt.f64 2) x)
	29.3b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))

Compiler

Compiled 849 to 621 computations (26.9% saved)

localize8.0ms (0.2%)

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))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series24.0ms (0.6%)

Counts

3 → 24

Calls

3 calls:

13.0ms	(sqrt.f64 (hypot.f64 x x))
7.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
4.0ms	(hypot.f64 x x)

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

8.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(sqrt.f64 (hypot.f64 x x))
0.0ms	(hypot.f64 x x)

simplify182.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
446×	`unswap-sqr_binary64`
308×	`sqr-pow_binary64`
263×	`associate-+l+_binary64`
259×	`associate-/l*_binary64`

Counts

102 → 83

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	61	802
1	85	752
2	199	739
3	402	701
4	728	701
5	1353	701
6	2551	685
7	4580	685
8	5171	685

prune94.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	5	2	7
Picked	0	1	1
Done	1	0	1
Total	106	7	113

Error

0.0b

Counts

113 → 7

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	29.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(*.f64 (sqrt.f64 2) x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))

Compiler

Compiled 1486 to 368 computations (75.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune13.0ms (0.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	4	7	11

Error

0.0b

Counts

11 → 7

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	29.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(*.f64 (sqrt.f64 2) x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
▶	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))

Compiler

Compiled 163 to 82 computations (49.7% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(sqrt.f64 (hypot.f64 x x))
✓	0.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.5b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))

series395.0ms (10.6%)

Counts

3 → 24

Calls

3 calls:

365.0ms

(cbrt.f64 (hypot.f64 x x))

19.0ms

(*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

10.0ms

(*.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))

rewrite39.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
14×	`cbrt-prod_binary64`
14×	`pow1_binary64`
13×	`sqrt-prod_binary64`
12×	`associate-l_binary64`

Counts

3 → 76

Calls

3 calls:

15.0ms

(*.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))

12.0ms

(*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

1.0ms

(cbrt.f64 (hypot.f64 x x))

simplify222.0ms (6%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-def_binary64`
358×	`fma-neg_binary64`
324×	`*-commutative_binary64`
304×	`unswap-sqr_binary64`
234×	`sqr-pow_binary64`

Counts

100 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	103	1664
1	183	1476
2	472	1442
3	722	1019
4	998	993
5	1919	993
6	3922	993
7	4995	993
8	4845	993

prune103.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	144	7	151

Error

0.0b

Counts

151 → 7

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	29.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(*.f64 (sqrt.f64 2) x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
✓	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))

Compiler

Compiled 2811 to 573 computations (79.6% saved)

regimes253.0ms (6.8%)

Accuracy

Total 0.1b remaining (78.8%)

Threshold costs 0.1b (78.8%)

Counts

33 → 1

Compiler

Compiled 1727 to 1063 computations (38.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end141.0ms (3.8%)

Compiler: Compiled 76 to 41 computations (46.1% saved)

Details

analyze2.0ms (0.1%)

sample1.3s (35.7%)

simplify206.0ms (5.5%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series10.0ms (0.3%)

rewrite14.0ms (0.4%)

simplify208.0ms (5.6%)

prune426.0ms (11.5%)

localize8.0ms (0.2%)

series24.0ms (0.6%)

rewrite15.0ms (0.4%)

simplify182.0ms (4.9%)

prune94.0ms (2.5%)

localize4.0ms (0.1%)

prune13.0ms (0.4%)

localize15.0ms (0.4%)

series395.0ms (10.6%)

rewrite39.0ms (1.1%)

simplify222.0ms (6%)

prune103.0ms (2.8%)

regimes253.0ms (6.8%)

simplify3.0ms (0.1%)

end141.0ms (3.8%)

Profiling