Details

analyze6.0ms (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 5 computations (50% saved)

sample28.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 20 to 10 computations (50% saved)

simplify7.0ms (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:

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 (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

prune11.0ms (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
▶	0.5b	(*.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)))
	33.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	29.2b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 177 to 81 computations (54.2% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
	0.1b	(hypot.f64 x x)
✓	0.4b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series14.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

10.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite11.0ms (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:

6.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(sqrt.f64 (hypot.f64 x x))

simplify78.0ms (2.2%)

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

prune101.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	123	8	131

Error

0.0b

Counts

131 → 8

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (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))))
	41.0b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.3b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	0.9b	(.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))))
	33.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	29.2b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 1882 to 470 computations (75% saved)

localize10.0ms (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)))))
✓	0.3b	(.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))

series960.0ms (26.5%)

Counts

4 → 48

Calls

4 calls:

390.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))))
323.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
240.0ms	(cbrt.f64 (hypot.f64 x x))
5.0ms	(.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))))

rewrite38.0ms (1%)

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:

13.0ms	(.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)))))
5.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify172.0ms (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

prune107.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	223	8	231

Error

0.0b

Counts

231 → 8

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	1.7b	(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (*.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	41.0b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.3b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
▶	0.9b	(.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))))
	33.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	29.2b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 5733 to 1263 computations (78% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series338.0ms (9.3%)

Counts

2 → 24

Calls

2 calls:

332.0ms

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

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-pow1_binary64`
21×	`pow1_binary64`
17×	`sqrt-prod_binary64`
14×	`pow1/3_binary64`

Counts

2 → 72

Calls

2 calls:

13.0ms

(*.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))))

7.0ms

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

simplify130.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

860×	`fma-neg_binary64`
417×	`exp-sum_binary64`
377×	`unswap-sqr_binary64`
319×	`*-commutative_binary64`
304×	`exp-prod_binary64`

Counts

96 → 106

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	109	1948
1	227	1589
2	518	1532
3	844	1128
4	1379	968
5	3166	968
6	3947	968
7	4916	968
8	4942	968

prune115.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	221	9	230

Error

Counts

230 → 9

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	1.7b	(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (*.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	41.0b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.3b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	1.5b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))))
✓	0.9b	(.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))))
	33.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	29.2b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 5736 to 1112 computations (80.6% saved)

regimes757.0ms (20.9%)

Accuracy

Total 0.1b remaining (80.4%)

Threshold costs 0.1b (80.4%)

Counts

185 → 1

Compiler

Compiled 13430 to 6276 computations (53.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end0.0ms (0%)

Compiler: Compiled 4 to 2 computations (50% saved)

sample528.0ms (14.6%)

Algorithm

1×

intervals

Results

255.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 205 to 70 computations (65.9% saved)

Details

analyze6.0ms (0.2%)

sample28.0ms (0.8%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify161.0ms (4.4%)

prune11.0ms (0.3%)

localize4.0ms (0.1%)

series14.0ms (0.4%)

rewrite11.0ms (0.3%)

simplify78.0ms (2.2%)

prune101.0ms (2.8%)

localize10.0ms (0.3%)

series960.0ms (26.5%)

rewrite38.0ms (1%)

simplify172.0ms (4.8%)

prune107.0ms (3%)

localize11.0ms (0.3%)

series338.0ms (9.3%)

rewrite26.0ms (0.7%)

simplify130.0ms (3.6%)

prune115.0ms (3.2%)

regimes757.0ms (20.9%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample528.0ms (14.6%)

Profiling