Details

analyze1.2s (26.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample813.0ms (18.5%)

Results

782.0ms	8256×	body	128	valid
1.0ms	2×	body	8192	exit

Compiler

Compiled 19 to 9 computations (52.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	15	4
4	15	4

prune3.0ms (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 9 computations (55% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(hypot.f64 x x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(hypot.f64 x x)

simplify163.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1032×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
575×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

22 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	159
1	29	150
2	46	150
3	52	150
4	61	150
5	88	150
6	119	150
7	178	150
8	376	150
9	696	150
10	701	150
11	875	150
12	1086	150
13	1314	150
14	1571	150
15	1876	150
16	2224	150
17	2699	150
18	3317	150
19	3513	150
20	3687	150
21	3801	150
22	3848	150
23	3900	150
24	4778	150
25	4863	150
26	4688	150

prune12.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	10	5	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	6	16

Error

0.0b

Counts

16 → 6

Alt Table

Status	Error	Program
	34.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	28.7b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
▶	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)))
	41.2b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))

Compiler

Compiled 191 to 91 computations (52.4% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series13.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

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

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

7.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(sqrt.f64 (hypot.f64 x x))

simplify77.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

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

Counts

80 → 79

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	54	643
1	79	602
2	190	589
3	392	554
4	718	554
5	1343	554
6	2541	540
7	4570	540
8	5161	540

prune106.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	124	8	132

Error

0.0b

Counts

132 → 8

Alt Table

Status	Error	Program
	28.7b	(*.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))))
✓	0.1b	(hypot.f64 x x)
	1.4b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	34.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x 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)))))

Compiler

Compiled 1828 to 456 computations (75.1% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series371.0ms (8.5%)

Counts

2 → 24

Calls

2 calls:

367.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
4.0ms	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`sqrt-pow1_binary64`
48×	`pow1_binary64`
42×	`add-sqr-sqrt_binary64`
37×	`sqrt-prod_binary64`
36×	`pow-prod-up_binary64`

Counts

2 → 100

Calls

2 calls:

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

simplify111.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
338×	`fma-neg_binary64`
322×	`unswap-sqr_binary64`
245×	`exp-prod_binary64`
220×	`exp-sum_binary64`

Counts

124 → 126

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	100	1686
1	192	1428
2	410	1242
3	724	1206
4	1739	1160
5	4430	1156
6	4990	1156
7	4843	1156

prune108.0ms (2.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	221	9	230

Error

0.0b

Counts

230 → 9

Alt Table

Status	Error	Program
	28.7b	(*.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))))
✓	0.1b	(hypot.f64 x x)
	1.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))) (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.4b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	34.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x 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)))))

Compiler

Compiled 4532 to 1046 computations (76.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(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))

series240.0ms (5.5%)

Counts

3 → 24

Calls

3 calls:

226.0ms

(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)))))

rewrite19.0ms (0.4%)

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)))))

6.0ms

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

1.0ms

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

simplify722.0ms (16.5%)

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

prune93.0ms (2.1%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	2	3	5
Picked	0	1	1
Done	0	3	3
Total	172	9	181

Error

0.0b

Counts

181 → 9

Alt Table

Status	Error	Program
	1.1b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (fabs.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))
	28.7b	(*.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))))
✓	0.1b	(hypot.f64 x x)
	1.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))) (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.0b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
✓	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x 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)))))

Compiler

Compiled 3394 to 749 computations (77.9% saved)

regimes203.0ms (4.6%)

Accuracy

Total 0.1b remaining (76.7%)

Threshold costs 0.1b (76.7%)

Counts

62 → 1

Compiler

Compiled 4522 to 1960 computations (56.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end90.0ms (2.1%)

Compiler: Compiled 152 to 61 computations (59.9% saved)

Details

analyze1.2s (26.6%)

sample813.0ms (18.5%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize2.0ms (0%)

series5.0ms (0.1%)

rewrite1.0ms (0%)

simplify163.0ms (3.7%)

prune12.0ms (0.3%)

localize4.0ms (0.1%)

series13.0ms (0.3%)

rewrite12.0ms (0.3%)

simplify77.0ms (1.8%)

prune106.0ms (2.4%)

localize6.0ms (0.1%)

series371.0ms (8.5%)

rewrite29.0ms (0.7%)

simplify111.0ms (2.5%)

prune108.0ms (2.5%)

localize7.0ms (0.2%)

series240.0ms (5.5%)

rewrite19.0ms (0.4%)

simplify722.0ms (16.5%)

prune93.0ms (2.1%)

regimes203.0ms (4.6%)

simplify2.0ms (0%)

end90.0ms (2.1%)

Profiling