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)

sample1.4s (32.3%)

Results

1.2s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify120.0ms (2.8%)

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(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
✓	0.2b	(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 (3.8%)

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

prune12.0ms (0.3%)

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
✓	0.2b	(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)))
	41.9b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	31.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.1b	(*.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)))

series17.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

13.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite10.0ms (0.2%)

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))

simplify77.0ms (1.8%)

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

prune62.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	122	10	132

Error

0.0b

Counts

132 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
✓	0.2b	(hypot.f64 x x)
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (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))))
	31.1b	(*.f64 (sqrt.f64 2) x)
	23.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	31.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	1.4b	(.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))))

Compiler

Compiled 1848 to 484 computations (73.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series989.0ms (23.2%)

Counts

4 → 48

Calls

4 calls:

396.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
370.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))))
218.0ms	(cbrt.f64 (hypot.f64 x x))
4.0ms	(.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))))

rewrite85.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
34×	`pow1_binary64`
27×	`pow1/3_binary64`
26×	`sqrt-pow1_binary64`
23×	`cbrt-prod_binary64`

Counts

4 → 127

Calls

4 calls:

62.0ms	(.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))))
8.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))))
4.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify207.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-def_binary64`
383×	`exp-prod_binary64`
363×	`exp-sum_binary64`
338×	`fma-neg_binary64`
331×	`sqr-pow_binary64`

Counts

175 → 185

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	171	2842
1	358	2516
2	824	2304
3	1408	1940
4	2751	1553
5	4541	1553
6	4106	1553
7	4795	1553
8	5128	1553

prune129.0ms (3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	219	4	223
Fresh	3	4	7
Picked	1	0	1
Done	0	2	2
Total	223	10	233

Error

Counts

233 → 10

Alt Table

Status	Error	Program
✓	0.2b	(hypot.f64 x x)
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.0b	(.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 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))
	1.2b	(.f64 (.f64 (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	23.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	31.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	1.0b	(.f64 (.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 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	31.1b	(*.f64 (sqrt.f64 2) x)
	1.3b	(*.f64 (fabs.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	1.4b	(.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))))

Compiler

Compiled 5761 to 1297 computations (77.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series5.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`rem-sqrt-square_binary64`
32×	`add-sqr-sqrt_binary64`
30×	`sqrt-pow1_binary64`
27×	`sqrt-prod_binary64`
27×	`mul-fabs_binary64`

Counts

1 → 49

Calls

1 calls:

23.0ms

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

simplify100.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

527×	`log-div_binary64`
470×	`fma-def_binary64`
454×	`*-commutative_binary64`
354×	`sqr-pow_binary64`
320×	`associate-/l*_binary64`

Counts

61 → 61

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	105	1644
1	229	1440
2	788	1148
3	1040	1081
4	1426	658
5	1674	558
6	3241	558
7	4730	558
8	5232	558

prune130.0ms (3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	252	10	262

Error

Counts

262 → 10

Alt Table

Status	Error	Program
✓	0.2b	(hypot.f64 x x)
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.0b	(.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 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))
	1.2b	(.f64 (.f64 (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	23.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	31.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	1.0b	(.f64 (.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 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	31.1b	(*.f64 (sqrt.f64 2) x)
	1.3b	(*.f64 (fabs.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	1.4b	(.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))))

Compiler

Compiled 8313 to 1586 computations (80.9% saved)

regimes537.0ms (12.6%)

Accuracy

Total 0.1b remaining (83.2%)

Threshold costs 0.1b (83.2%)

Counts

137 → 1

Compiler

Compiled 12070 to 5558 computations (54% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end173.0ms (4.1%)

Compiler: Compiled 170 to 73 computations (57.1% saved)

Details

analyze6.0ms (0.1%)

sample1.4s (32.3%)

simplify120.0ms (2.8%)

prune3.0ms (0.1%)

localize2.0ms (0%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify161.0ms (3.8%)

prune12.0ms (0.3%)

localize4.0ms (0.1%)

series17.0ms (0.4%)

rewrite10.0ms (0.2%)

simplify77.0ms (1.8%)

prune62.0ms (1.5%)

localize9.0ms (0.2%)

series989.0ms (23.2%)

rewrite85.0ms (2%)

simplify207.0ms (4.8%)

prune129.0ms (3%)

localize12.0ms (0.3%)

series5.0ms (0.1%)

rewrite35.0ms (0.8%)

simplify100.0ms (2.3%)

prune130.0ms (3%)

regimes537.0ms (12.6%)

simplify2.0ms (0%)

end173.0ms (4.1%)

Profiling