Details

analyze1.5s (33.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.1s (22.9%)

Results

1.0s	8256×	body	128	valid
1.0ms	3×	body	8192	exit

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	11	9
3	11	9

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

29.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	28.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
3.0ms	(.f64 2 (.f64 x x))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`pow-prod-down_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

2 → 35

Calls

2 calls:

6.0ms	(.f64 2 (.f64 x x))
3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

597×	`distribute-rgt-out_binary64`
429×	`fma-def_binary64`
339×	`*-commutative_binary64`
318×	`times-frac_binary64`
249×	`fma-neg_binary64`

Counts

59 → 47

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	514
1	97	472
2	229	461
3	599	461
4	904	401
5	1456	401
6	3025	401
7	4826	401
8	4904	401

prune29.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	40	7	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	8	48

Error

0.1b

Counts

48 → 8

Alt Table

Status	Error	Program
▶	0.6b	(*.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)))
	38.3b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	3.1b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	34.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	28.4b	(*.f64 (sqrt.f64 2) x)
✓	29.2b	(sqrt.f64 (.f64 2 (.f64 x x)))
	51.3b	(sqrt.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 2) 2) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))))

Compiler

Compiled 598 to 349 computations (41.6% 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)))

series19.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

11.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(hypot.f64 x x)
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

5.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(sqrt.f64 (hypot.f64 x x))
0.0ms	(hypot.f64 x x)

simplify87.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
446×	`unswap-sqr_binary64`
308×	`sqr-pow_binary64`
263×	`associate-+l+_binary64`
259×	`associate-/l*_binary64`

Counts

102 → 83

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	61	802
1	85	752
2	199	739
3	402	701
4	728	701
5	1353	701
6	2551	685
7	4580	685
8	5171	685

prune109.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	3	3	6
Picked	0	1	1
Done	1	0	1
Total	104	8	112

Error

0.0b

Counts

112 → 8

Alt Table

Status	Error	Program
	2.0b	(.f64 (.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))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	38.3b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
▶	0.1b	(hypot.f64 x x)
	34.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.6b	(*.f64 (sqrt.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))
	28.4b	(*.f64 (sqrt.f64 2) x)
	0.8b	(.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))))

Compiler

Compiled 1558 to 380 computations (75.6% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

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

prune8.0ms (0.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	4	8	12

Error

0.0b

Counts

12 → 8

Alt Table

Status	Error	Program
	2.0b	(.f64 (.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))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	38.3b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
✓	0.1b	(hypot.f64 x x)
	34.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.6b	(*.f64 (sqrt.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))
	28.4b	(*.f64 (sqrt.f64 2) x)
▶	0.8b	(.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))))

Compiler

Compiled 235 to 94 computations (60% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series959.0ms (20.9%)

Counts

4 → 48

Calls

4 calls:

350.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))))
327.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
278.0ms	(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))))

rewrite41.0ms (0.9%)

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:

16.0ms	(.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))))
9.0ms	(.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))

simplify165.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-def_binary64`
375×	`fma-neg_binary64`
370×	`exp-prod_binary64`
363×	`exp-sum_binary64`
333×	`sqr-pow_binary64`

Counts

175 → 186

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	171	2868
1	358	2506
2	824	2279
3	1408	1915
4	2751	1553
5	4544	1553
6	4109	1553
7	4971	1553
8	4900	1553

prune104.0ms (2.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	225	9	234

Error

0.0b

Counts

234 → 9

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	34.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.5b	(.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))))
	28.4b	(*.f64 (sqrt.f64 2) x)
✓	0.6b	(*.f64 (sqrt.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))
	38.3b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	1.1b	(.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.8b	(.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))))

Compiler

Compiled 5644 to 1247 computations (77.9% saved)

regimes249.0ms (5.4%)

Accuracy

Total 0.1b remaining (81.2%)

Threshold costs 0.1b (81.2%)

Counts

62 → 1

Compiler

Compiled 5407 to 2452 computations (54.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end100.0ms (2.2%)

Compiler: Compiled 129 to 64 computations (50.4% saved)

Details

analyze1.5s (33.5%)

sample1.1s (22.9%)

simplify8.0ms (0.2%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite10.0ms (0.2%)

simplify76.0ms (1.7%)

prune29.0ms (0.6%)

localize4.0ms (0.1%)

series19.0ms (0.4%)

rewrite11.0ms (0.2%)

simplify87.0ms (1.9%)

prune109.0ms (2.4%)

localize2.0ms (0%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

series959.0ms (20.9%)

rewrite41.0ms (0.9%)

simplify165.0ms (3.6%)

prune104.0ms (2.3%)

regimes249.0ms (5.4%)

simplify2.0ms (0%)

end100.0ms (2.2%)

Profiling