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)

sample733.0ms (25.5%)

Results

704.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 14 computations (51.7% 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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 20 to 9 computations (55% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(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)

simplify157.0ms (5.5%)

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

prune10.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	11	4	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	5	16

Error

0.0b

Counts

16 → 5

Alt Table

Status	Error	Program
▶	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)))
	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	29.8b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 177 to 81 computations (54.2% saved)

localize5.0ms (0.2%)

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)))

series13.0ms (0.4%)

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)))

rewrite9.0ms (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))

simplify84.0ms (2.9%)

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

prune53.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	123	8	131

Error

0.0b

Counts

131 → 8

Alt Table

Status	Error	Program
	19.2b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	33.2b	(neg.f64 (*.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))))
	29.8b	(*.f64 (sqrt.f64 2) x)
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (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))
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 1752 to 454 computations (74.1% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
✓	0.7b	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)

series222.0ms (7.7%)

Counts

2 → 24

Calls

2 calls:

217.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)
5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`sqrt-prod_binary64`
64×	`add-sqr-sqrt_binary64`
27×	`cube-prod_binary64`
27×	`unpow-prod-down_binary64`
24×	`associate-r_binary64`

Counts

2 → 114

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
3.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)

simplify109.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

569×	`unswap-sqr_binary64`
453×	`exp-prod_binary64`
451×	`sqr-pow_binary64`
387×	`log-prod_binary64`
386×	`*-commutative_binary64`

Counts

138 → 105

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	1997
1	236	1755
2	795	1526
3	1494	1445
4	3364	1372
5	4590	1372
6	4855	1372

prune80.0ms (2.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	169	8	177

Error

0.0b

Counts

177 → 8

Alt Table

Status	Error	Program
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	29.8b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
▶	1.3b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3)))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

Compiler

Compiled 3151 to 1045 computations (66.8% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3)))
✓	0.5b	(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3))
✓	0.8b	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3)

series515.0ms (17.9%)

Counts

3 → 36

Calls

3 calls:

295.0ms

(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3))

215.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3)

4.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3)))

rewrite103.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

648×	`sqrt-prod_binary64`
346×	`add-sqr-sqrt_binary64`
212×	`cube-prod_binary64`
212×	`unpow-prod-down_binary64`
103×	`unswap-sqr_binary64`

Counts

3 → 372

Calls

3 calls:

21.0ms

(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3))

14.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3)))

3.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3)

simplify326.0ms (11.4%)

Algorithm

1×	egg-herbie

Rules

1049×	`fma-def_binary64`
542×	`exp-prod_binary64`
487×	`log-prod_binary64`
412×	`cube-prod_binary64`
307×	`sqr-pow_binary64`

Counts

408 → 201

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	194	9490
1	388	8589
2	1507	7439
3	2416	7376
4	3850	7318
5	4936	7318
6	5050	7318

prune152.0ms (5.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	299	1	300
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	299	9	308

Error

Counts

308 → 9

Alt Table

Status	Error	Program
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	29.8b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
✓	1.3b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3)))
	2.0b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (pow.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)))))) 3) (sqrt.f64 (hypot.f64 x x))))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

Compiler

Compiled 8798 to 2749 computations (68.8% saved)

regimes151.0ms (5.3%)

Accuracy

Total 0.1b remaining (81.2%)

Threshold costs 0.1b (81.2%)

Counts

45 → 1

Compiler

Compiled 2926 to 1444 computations (50.6% saved)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end95.0ms (3.3%)

Compiler: Compiled 125 to 62 computations (50.4% saved)

Details

analyze4.0ms (0.1%)

sample733.0ms (25.5%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify157.0ms (5.5%)

prune10.0ms (0.3%)

localize5.0ms (0.2%)

series13.0ms (0.4%)

rewrite9.0ms (0.3%)

simplify84.0ms (2.9%)

prune53.0ms (1.9%)

localize6.0ms (0.2%)

series222.0ms (7.7%)

rewrite22.0ms (0.7%)

simplify109.0ms (3.8%)

prune80.0ms (2.8%)

localize8.0ms (0.3%)

series515.0ms (17.9%)

rewrite103.0ms (3.6%)

simplify326.0ms (11.4%)

prune152.0ms (5.3%)

regimes151.0ms (5.3%)

simplify1.0ms (0.1%)

end95.0ms (3.3%)

Profiling