Details

analyze12.0ms (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 10 to 8 computations (20% saved)

sample2.3s (42.1%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify147.0ms (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

prune6.0ms (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)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

7.0ms

(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:

1.0ms

(hypot.f64 x x)

simplify194.0ms (3.5%)

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

prune21.0ms (0.4%)

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
▶	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)))
	42.7b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	31.5b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.6b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 191 to 91 computations (52.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.2b	(sqrt.f64 (hypot.f64 x x))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series25.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

18.0ms	(sqrt.f64 (hypot.f64 x x))
7.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite22.0ms (0.4%)

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:

10.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
2.0ms	(sqrt.f64 (hypot.f64 x x))

simplify234.0ms (4.3%)

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

prune110.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	125	7	132

Error

0.0b

Counts

132 → 7

Alt Table

Status	Error	Program
	0.8b	(.f64 (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 (hypot.f64 x x))))
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
✓	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)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.5b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.6b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 1752 to 444 computations (74.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series919.0ms (16.7%)

Counts

4 → 36

Calls

4 calls:

460.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
433.0ms	(cbrt.f64 (hypot.f64 x x))
18.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
7.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
27×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
12×	`associate-l_binary64`

Counts

4 → 89

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
12.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
2.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify145.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

459×	`unswap-sqr_binary64`
433×	`fma-def_binary64`
360×	`fma-neg_binary64`
347×	`*-commutative_binary64`
313×	`sqr-pow_binary64`

Counts

125 → 129

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	107	2085
1	208	1926
2	536	1787
3	923	1329
4	1175	1298
5	2456	1298
6	4266	1298
7	4938	1298

prune54.0ms (1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	127	9	136

Error

0.0b

Counts

136 → 9

Alt Table

Status	Error	Program
▶	0.8b	(.f64 (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 (hypot.f64 x x))))
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	1.2b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))))
	1.2b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (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)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.5b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.6b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 2735 to 574 computations (79% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series657.0ms (12%)

Counts

3 → 36

Calls

3 calls:

331.0ms

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

320.0ms

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

6.0ms

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

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
29×	`pow1_binary64`
23×	`cbrt-prod_binary64`
21×	`sqrt-pow1_binary64`
20×	`pow1/3_binary64`

Counts

3 → 114

Calls

3 calls:

12.0ms

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

6.0ms

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

5.0ms

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

simplify131.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
420×	`*-commutative_binary64`
384×	`exp-prod_binary64`
373×	`fma-def_binary64`
362×	`exp-sum_binary64`

Counts

150 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	2589
1	269	2174
2	614	1948
3	965	1683
4	1687	1419
5	3511	1419
6	4218	1419
7	4898	1419

prune94.0ms (1.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	211	9	220

Error

0.0b

Counts

220 → 9

Alt Table

Status	Error	Program
✓	0.8b	(.f64 (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 (hypot.f64 x x))))
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	1.2b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))))
	1.2b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (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)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.5b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.6b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 5525 to 1046 computations (81.1% saved)

regimes194.0ms (3.5%)

Accuracy

Total 0.1b remaining (83.6%)

Threshold costs 0.1b (83.6%)

Counts

55 → 1

Compiler

Compiled 3730 to 1754 computations (53% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end95.0ms (1.7%)

Compiler: Compiled 137 to 62 computations (54.7% saved)

Details

analyze12.0ms (0.2%)

sample2.3s (42.1%)

simplify147.0ms (2.7%)

prune6.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite1.0ms (0%)

simplify194.0ms (3.5%)

prune21.0ms (0.4%)

localize7.0ms (0.1%)

series25.0ms (0.5%)

rewrite22.0ms (0.4%)

simplify234.0ms (4.3%)

prune110.0ms (2%)

localize15.0ms (0.3%)

series919.0ms (16.7%)

rewrite37.0ms (0.7%)

simplify145.0ms (2.7%)

prune54.0ms (1%)

localize9.0ms (0.2%)

series657.0ms (12%)

rewrite36.0ms (0.7%)

simplify131.0ms (2.4%)

prune94.0ms (1.7%)

regimes194.0ms (3.5%)

simplify2.0ms (0%)

end95.0ms (1.7%)

Profiling