Details

analyze4.0ms (0.1%)

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 5 computations (50% saved)

sample29.0ms (0.9%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 20 to 10 computations (50% saved)

simplify6.0ms (0.2%)

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(hypot.f64 x x)

Compiler

Compiled 20 to 9 computations (55% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(hypot.f64 x x)

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(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)

simplify161.0ms (5.2%)

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

prune18.0ms (0.6%)

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

0.1b

Counts

16 → 6

Alt Table

Status	Error	Program
	28.8b	(*.f64 (sqrt.f64 2) x)
✓	0.2b	(hypot.f64 x x)
▶	0.6b	(*.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)))
	39.7b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	34.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))

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))
	0.2b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series15.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

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

rewrite10.0ms (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:

5.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(sqrt.f64 (hypot.f64 x x))

simplify76.0ms (2.5%)

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

prune73.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	119	7	126
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	122	10	132

Error

0.0b

Counts

132 → 10

Alt Table

Status	Error	Program
	39.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (pow.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)))))
	1.3b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (*.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)))))
	0.9b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	34.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	20.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	28.8b	(*.f64 (sqrt.f64 2) x)
✓	0.2b	(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))))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))

Compiler

Compiled 1878 to 496 computations (73.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (hypot.f64 x x))
	0.2b	(hypot.f64 x x)
✓	0.3b	(.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)))

series350.0ms (11.4%)

Counts

2 → 24

Calls

2 calls:

346.0ms	(*.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 (0.9%)

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)))

simplify106.0ms (3.4%)

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

prune107.0ms (3.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	222	10	232

Error

0.0b

Counts

232 → 10

Alt Table

Status	Error	Program
▶	0.8b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	39.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (pow.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)))))
	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)))))
	34.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	28.8b	(*.f64 (sqrt.f64 2) x)
✓	0.2b	(hypot.f64 x x)
	1.3b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (*.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)))))
✓	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))

Compiler

Compiled 4562 to 1070 computations (76.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series332.0ms (10.8%)

Counts

2 → 24

Calls

2 calls:

328.0ms

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

4.0ms

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

rewrite80.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

237×	`sqrt-pow1_binary64`
136×	`pow-prod-up_binary64`
121×	`pow1_binary64`
112×	`add-sqr-sqrt_binary64`
96×	`sqrt-prod_binary64`

Counts

2 → 151

Calls

2 calls:

27.0ms

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

16.0ms

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

simplify112.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-neg_binary64`
388×	`exp-sum_binary64`
359×	`*-commutative_binary64`
346×	`fma-def_binary64`
308×	`times-frac_binary64`

Counts

175 → 155

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	123	3122
1	247	1731
2	615	1704
3	999	1378
4	1910	1342
5	3720	1338
6	4918	1338

prune183.0ms (6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	275	3	278
Fresh	2	5	7
Picked	1	0	1
Done	1	1	2
Total	279	9	288

Error

Counts

288 → 9

Alt Table

Status	Error	Program
	28.8b	(*.f64 (sqrt.f64 2) x)
✓	0.2b	(hypot.f64 x x)
	1.4b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))) (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))))
	39.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 3))))
	1.3b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (*.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)))))
	34.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	0.8b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (hypot.f64 x x) 3/4)))

Compiler

Compiled 7465 to 1891 computations (74.7% saved)

regimes794.0ms (25.8%)

Accuracy

Total 0.1b remaining (82.6%)

Threshold costs 0.1b (82.6%)

Counts

212 → 1

Compiler

Compiled 18226 to 8680 computations (52.4% 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)

sample559.0ms (18.2%)

Algorithm

1×

intervals

Results

251.0ms

8000×

body

128

valid

Compiler

Compiled 183 to 78 computations (57.4% saved)

Details

analyze4.0ms (0.1%)

sample29.0ms (0.9%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify161.0ms (5.2%)

prune18.0ms (0.6%)

localize4.0ms (0.1%)

series15.0ms (0.5%)

rewrite10.0ms (0.3%)

simplify76.0ms (2.5%)

prune73.0ms (2.4%)

localize6.0ms (0.2%)

series350.0ms (11.4%)

rewrite29.0ms (0.9%)

simplify106.0ms (3.4%)

prune107.0ms (3.5%)

localize10.0ms (0.3%)

series332.0ms (10.8%)

rewrite80.0ms (2.6%)

simplify112.0ms (3.6%)

prune183.0ms (6%)

regimes794.0ms (25.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample559.0ms (18.2%)

Profiling