Details

analyze6.0ms (0.3%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample799.0ms (33.6%)

Infinites

0% of outputs are infinite.

Results

614.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify142.0ms (6%)

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

prune2.0ms (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

28.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.6b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	28.6b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series5.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
2.0ms	(*.f64 2 (pow.f64 x 2))

rewrite7.0ms (0.3%)

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:

4.0ms	(*.f64 2 (pow.f64 x 2))
2.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

simplify89.0ms (3.7%)

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

prune39.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	7	67

Error

0.0b

Counts

67 → 7

Alt Table

Status	Error	Program
	30.3b	(log1p.f64 (expm1.f64 (hypot.f64 x x)))
	31.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.0b	(*.f64 (sqrt.f64 2) x)
✓	28.6b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
▶	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.3b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	29.0b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))

Compiler

Compiled 797 to 579 computations (27.4% saved)

localize3.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 x x)
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series16.0ms (0.7%)

Counts

3 → 24

Calls

3 calls:

9.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
3.0ms	(hypot.f64 x x)

rewrite10.0ms (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:

5.0ms	(*.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)

simplify218.0ms (9.2%)

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

prune184.0ms (7.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	2	3	5
Picked	1	0	1
Done	1	0	1
Total	104	7	111

Error

0.0b

Counts

111 → 7

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
▶	0.1b	(hypot.f64 x x)
	31.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.0b	(*.f64 (sqrt.f64 2) x)
	0.8b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.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))
	29.0b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))

Compiler

Compiled 1508 to 380 computations (74.8% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune7.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	4	7	11

Error

0.0b

Counts

11 → 7

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	0.1b	(hypot.f64 x x)
	31.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.0b	(*.f64 (sqrt.f64 2) x)
▶	0.8b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.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))
	29.0b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))

Compiler

Compiled 185 to 94 computations (49.2% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(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)))))
✓	0.5b	(cbrt.f64 (hypot.f64 x x))

series251.0ms (10.6%)

Counts

3 → 24

Calls

3 calls:

238.0ms

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

9.0ms

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

4.0ms

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

rewrite18.0ms (0.8%)

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:

7.0ms

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

7.0ms

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

1.0ms

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

simplify104.0ms (4.4%)

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

prune56.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	144	7	151

Error

0.0b

Counts

151 → 7

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	0.1b	(hypot.f64 x x)
	31.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.0b	(*.f64 (sqrt.f64 2) x)
✓	0.8b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.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))
	29.0b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))

Compiler

Compiled 2817 to 577 computations (79.5% saved)

regimes248.0ms (10.4%)

Accuracy

Total 0.1b remaining (76.9%)

Threshold costs 0.1b (76.9%)

Counts

59 → 1

Compiler

Compiled 3339 to 2004 computations (40% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end160.0ms (6.7%)

Compiler: Compiled 82 to 45 computations (45.1% saved)

Details

analyze6.0ms (0.3%)

sample799.0ms (33.6%)

simplify142.0ms (6%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite7.0ms (0.3%)

simplify89.0ms (3.7%)

prune39.0ms (1.6%)

localize3.0ms (0.1%)

series16.0ms (0.7%)

rewrite10.0ms (0.4%)

simplify218.0ms (9.2%)

prune184.0ms (7.7%)

localize2.0ms (0.1%)

prune7.0ms (0.3%)

localize8.0ms (0.3%)

series251.0ms (10.6%)

rewrite18.0ms (0.8%)

simplify104.0ms (4.4%)

prune56.0ms (2.4%)

regimes248.0ms (10.4%)

simplify2.0ms (0.1%)

end160.0ms (6.7%)

Profiling