Details

analyze5.0ms (0.2%)

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 8 to 7 computations (12.5% saved)

sample182.0ms (7.4%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify146.0ms (5.9%)

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

31.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.3b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	30.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series6.0ms (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))

rewrite8.0ms (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)))

simplify218.0ms (8.8%)

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

prune109.0ms (4.4%)

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
	31.7b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))
✓	31.3b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	3.0b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.3b	(*.f64 (sqrt.f64 2) x)
▶	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)))

Compiler

Compiled 807 to 591 computations (26.8% saved)

localize4.0ms (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))
✓	0.4b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series18.0ms (0.7%)

Counts

3 → 24

Calls

3 calls:

11.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
4.0ms	(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)

simplify83.0ms (3.4%)

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

prune56.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	2	3	5
Picked	1	0	1
Done	1	0	1
Total	103	8	111

Error

0.0b

Counts

111 → 8

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)
	32.3b	(*.f64 (sqrt.f64 2) x)
	0.6b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.7b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))
	21.1b	(.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.4b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))

Compiler

Compiled 1580 to 404 computations (74.4% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune8.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	4	8	12

Error

0.0b

Counts

12 → 8

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)
	32.3b	(*.f64 (sqrt.f64 2) x)
▶	0.6b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.7b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))
	21.1b	(.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.4b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))

Compiler

Compiled 257 to 118 computations (54.1% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.1b	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
✓	0.4b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	0.4b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))

series239.0ms (9.7%)

Counts

3 → 24

Calls

3 calls:

221.0ms

(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

13.0ms

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

4.0ms

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

rewrite38.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`sqrt-prod_binary64`
87×	`sqrt-pow1_binary64`
83×	`add-sqr-sqrt_binary64`
66×	`pow1_binary64`
45×	`pow1/2_binary64`

Counts

3 → 158

Calls

3 calls:

13.0ms

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

8.0ms

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

1.0ms

(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

simplify130.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
529×	`unswap-sqr_binary64`
376×	`associate-l_binary64`
373×	`*-commutative_binary64`
342×	`exp-prod_binary64`

Counts

182 → 170

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	1633
1	165	1558
2	417	1515
3	1207	1423
4	2575	1414
5	4265	1414
6	4971	1414
7	4949	1414

prune122.0ms (4.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	247	2	249
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	249	8	257

Error

Counts

257 → 8

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)
	32.3b	(*.f64 (sqrt.f64 2) x)
✓	0.6b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.6b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 4) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.7b	(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 4950 to 1155 computations (76.7% saved)

regimes296.0ms (12%)

Accuracy

Total 0.1b remaining (80%)

Threshold costs 0.1b (80%)

Counts

81 → 1

Compiler

Compiled 4929 to 2907 computations (41% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end0.0ms (0%)

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

sample779.0ms (31.5%)

Algorithm

1×

intervals

Results

485.0ms

8000×

body

128

valid

Compiler

Compiled 123 to 68 computations (44.7% saved)

Details

analyze5.0ms (0.2%)

sample182.0ms (7.4%)

simplify146.0ms (5.9%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite8.0ms (0.3%)

simplify218.0ms (8.8%)

prune109.0ms (4.4%)

localize4.0ms (0.1%)

series18.0ms (0.7%)

rewrite10.0ms (0.4%)

simplify83.0ms (3.4%)

prune56.0ms (2.2%)

localize2.0ms (0.1%)

prune8.0ms (0.3%)

localize6.0ms (0.2%)

series239.0ms (9.7%)

rewrite38.0ms (1.5%)

simplify130.0ms (5.2%)

prune122.0ms (4.9%)

regimes296.0ms (12%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample779.0ms (31.5%)

Profiling