Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 10 to 8 computations (20% saved)

sample1.8s (34.8%)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify188.0ms (3.6%)

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

prune5.0ms (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)

localize3.0ms (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)

simplify229.0ms (4.4%)

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

prune20.0ms (0.4%)

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
	29.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	33.1b	(*.f64 (sqrt.f64 2) x)
▶	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 177 to 81 computations (54.2% saved)

localize8.0ms (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)))

series28.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

21.0ms	(sqrt.f64 (hypot.f64 x x))
8.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite19.0ms (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)))
1.0ms	(sqrt.f64 (hypot.f64 x x))

simplify154.0ms (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

prune91.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	124	7	131

Error

0.0b

Counts

131 → 7

Alt Table

Status	Error	Program
	33.1b	(*.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))))
✓	0.5b	(*.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))
▶	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	29.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 1734 to 442 computations (74.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(sqrt.f64 (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))

series435.0ms (8.3%)

Counts

3 → 24

Calls

3 calls:

405.0ms

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

20.0ms

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

10.0ms

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

rewrite39.0ms (0.8%)

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:

15.0ms

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

12.0ms

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

1.0ms

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

simplify224.0ms (4.3%)

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

prune106.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	144	7	151

Error

0.0b

Counts

151 → 7

Alt Table

Status	Error	Program
	33.1b	(*.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))))
✓	0.5b	(*.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))
✓	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	29.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 2849 to 597 computations (79% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series929.0ms (17.8%)

Counts

3 → 36

Calls

3 calls:

522.0ms	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
398.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)
8.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

rewrite61.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 135

Calls

3 calls:

23.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
6.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)
3.0ms	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

simplify260.0ms (5%)

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

171 → 131

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	117	2417
1	238	2133
2	797	1880
3	1496	1751
4	3366	1674
5	4592	1674
6	4857	1674

prune206.0ms (3.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	190	8	198

Error

Counts

198 → 8

Alt Table

Status	Error	Program
	29.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.4b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))) 3))
	33.1b	(*.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))))
✓	0.5b	(*.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))
✓	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 3513 to 1135 computations (67.7% saved)

regimes218.0ms (4.2%)

Accuracy

Total 0.1b remaining (80.5%)

Threshold costs 0.1b (80.5%)

Counts

32 → 1

Compiler

Compiled 1770 to 906 computations (48.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end149.0ms (2.9%)

Compiler: Compiled 98 to 50 computations (49% saved)

Details

analyze3.0ms (0.1%)

sample1.8s (34.8%)

simplify188.0ms (3.6%)

prune5.0ms (0.1%)

localize3.0ms (0.1%)

series7.0ms (0.1%)

rewrite1.0ms (0%)

simplify229.0ms (4.4%)

prune20.0ms (0.4%)

localize8.0ms (0.1%)

series28.0ms (0.5%)

rewrite19.0ms (0.4%)

simplify154.0ms (3%)

prune91.0ms (1.7%)

localize11.0ms (0.2%)

series435.0ms (8.3%)

rewrite39.0ms (0.8%)

simplify224.0ms (4.3%)

prune106.0ms (2%)

localize6.0ms (0.1%)

series929.0ms (17.8%)

rewrite61.0ms (1.2%)

simplify260.0ms (5%)

prune206.0ms (3.9%)

regimes218.0ms (4.2%)

simplify3.0ms (0.1%)

end149.0ms (2.9%)

Profiling