Details

analyze6.0ms (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 8 computations (20% saved)

sample1.3s (29%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify123.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1333×	`fma-def_binary64`
773×	`distribute-rgt-out_binary64`
559×	`hypot-def_binary64`
453×	`associate-l_binary64`
451×	`count-2_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	4
2	25	4
3	46	4
4	98	4
5	245	4
6	763	4
7	1382	4
8	2673	4
9	3450	4
10	4144	4
11	4482	4
12	4395	4
13	4766	4
14	4993	4
15	4742	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 12 computations (40% saved)

localize2.0ms (0%)

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:

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)

simplify162.0ms (3.6%)

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

prune9.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Error

0.0b

Counts

16 → 4

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	32.2b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 147 to 71 computations (51.7% 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))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series14.0ms (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)))

rewrite9.0ms (0.2%)

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))

simplify85.0ms (1.9%)

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

prune54.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	124	6	130

Error

0.0b

Counts

130 → 6

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	1.5b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	32.2b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 1720 to 426 computations (75.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
✓	0.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))
✓	0.6b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)

series1.2s (27.1%)

Counts

4 → 48

Calls

4 calls:

708.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
295.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
213.0ms	(cbrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
20×	`sqrt-prod_binary64`
18×	`unpow-prod-down_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

8.0ms	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
2.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
1.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify113.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-def_binary64`
542×	`unswap-sqr_binary64`
388×	`associate-l_binary64`
354×	`log-prod_binary64`
328×	`sqr-pow_binary64`

Counts

151 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	134	2505
1	264	2445
2	586	2357
3	1596	1776
4	3150	1734
5	4609	1734
6	4856	1734

prune76.0ms (1.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	167	7	174

Error

0.0b

Counts

174 → 7

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
▶	1.5b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.7b	(.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 5/2) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 5/2)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	32.2b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 3077 to 1120 computations (63.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.4b	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
✓	0.5b	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓	0.6b	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))

series771.0ms (17.1%)

Counts

4 → 48

Calls

4 calls:

320.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
232.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
212.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
6.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
56×	`cbrt-prod_binary64`
34×	`sqrt-prod_binary64`
28×	`pow1_binary64`
23×	`*-un-lft-identity_binary64`

Counts

4 → 138

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
6.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
5.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))

simplify138.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-def_binary64`
451×	`prod-exp_binary64`
361×	`exp-prod_binary64`
359×	`sqr-pow_binary64`
250×	`*-commutative_binary64`

Counts

186 → 174

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	146	2880
1	277	2681
2	659	2046
3	1275	1900
4	2610	1637
5	4425	1635
6	4273	1629
7	5131	1629

prune76.0ms (1.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	215	8	223

Error

Counts

223 → 8

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	1.5b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	2.2b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) 5) (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	1.7b	(.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 5/2) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 5/2)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	32.2b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 5866 to 905 computations (84.6% saved)

regimes179.0ms (4%)

Accuracy

Total 0.1b remaining (75.8%)

Threshold costs 0.1b (75.8%)

Counts

51 → 1

Compiler

Compiled 3358 to 1618 computations (51.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end82.0ms (1.8%)

Compiler: Compiled 118 to 53 computations (55.1% saved)

Details

analyze6.0ms (0.1%)

sample1.3s (29%)

simplify123.0ms (2.7%)

prune3.0ms (0.1%)

localize2.0ms (0%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify162.0ms (3.6%)

prune9.0ms (0.2%)

localize4.0ms (0.1%)

series14.0ms (0.3%)

rewrite9.0ms (0.2%)

simplify85.0ms (1.9%)

prune54.0ms (1.2%)

localize8.0ms (0.2%)

series1.2s (27.1%)

rewrite17.0ms (0.4%)

simplify113.0ms (2.5%)

prune76.0ms (1.7%)

localize7.0ms (0.2%)

series771.0ms (17.1%)

rewrite35.0ms (0.8%)

simplify138.0ms (3.1%)

prune76.0ms (1.7%)

regimes179.0ms (4%)

simplify2.0ms (0%)

end82.0ms (1.8%)

Profiling