Details

analyze1.6s (33.2%)

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
2.0ms	4×	body	8192	exit

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.1%)

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

prune2.0ms (0.1%)

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

31.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.0b	(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))
✓	30.0b	(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)))
2.0ms	(.f64 2 (.f64 x x))

rewrite9.0ms (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:

4.0ms	(.f64 2 (.f64 x x))
3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

simplify78.0ms (1.6%)

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

prune27.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	41	6	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	7	48

Error

0.1b

Counts

48 → 7

Alt Table

Status	Error	Program
✓	31.0b	(sqrt.f64 (.f64 2 (.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)))
	2.5b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(*.f64 (sqrt.f64 2) x)
	45.7b	(sqrt.f64 (log1p.f64 (expm1.f64 (.f64 2 (.f64 x x)))))
▶	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

Compiler

Compiled 562 to 329 computations (41.5% 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))
✓	0.4b	(*.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	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
4.0ms	(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:

6.0ms	(*.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)

simplify119.0ms (2.5%)

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

prune51.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	3	2	5
Picked	1	0	1
Done	1	0	1
Total	104	7	111

Error

0.0b

Counts

111 → 7

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)
	30.4b	(*.f64 (sqrt.f64 2) x)
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	0.9b	(.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 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	22.2b	(.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))

Compiler

Compiled 1538 to 376 computations (75.6% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

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

prune7.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	4	7	11

Error

0.0b

Counts

11 → 7

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	30.4b	(*.f64 (sqrt.f64 2) x)
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	0.9b	(.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 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	22.2b	(.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))

Compiler

Compiled 215 to 90 computations (58.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.4b	(.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)))))
✓	0.5b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))

series251.0ms (5.3%)

Counts

3 → 24

Calls

3 calls:

236.0ms

(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

10.0ms

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

4.0ms

(*.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)))))

rewrite122.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

484×	`sqrt-pow1_binary64`
363×	`pow1_binary64`
253×	`pow-prod-up_binary64`
242×	`pow1/2_binary64`
193×	`add-sqr-sqrt_binary64`

Counts

3 → 317

Calls

3 calls:

45.0ms

(*.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)))))

9.0ms

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

1.0ms

(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

simplify136.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

924×	`fma-def_binary64`
461×	`associate-l_binary64`
373×	`*-commutative_binary64`
260×	`associate-/l*_binary64`
250×	`associate-r_binary64`

Counts

341 → 280

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	1932
1	169	1821
2	420	1760
3	1253	1668
4	2128	1642
5	4303	1642
6	4929	1642

prune361.0ms (7.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	508	2	510
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	511	6	517

Error

0.0b

Counts

517 → 6

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	30.4b	(*.f64 (sqrt.f64 2) x)
	1.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3)))
	0.6b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 1) (sqrt.f64 (hypot.f64 x x))))
	22.2b	(.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))

Compiler

Compiled 12435 to 2985 computations (76% saved)

regimes771.0ms (16.4%)

Accuracy

Total 0.1b remaining (64.4%)

Threshold costs 0.1b (64.4%)

Counts

208 → 1

Compiler

Compiled 17182 to 8308 computations (51.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end70.0ms (1.5%)

Compiler: Compiled 99 to 44 computations (55.6% saved)

Details

analyze1.6s (33.2%)

sample1.1s (22.9%)

simplify6.0ms (0.1%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite9.0ms (0.2%)

simplify78.0ms (1.6%)

prune27.0ms (0.6%)

localize4.0ms (0.1%)

series19.0ms (0.4%)

rewrite11.0ms (0.2%)

simplify119.0ms (2.5%)

prune51.0ms (1.1%)

localize2.0ms (0%)

prune7.0ms (0.1%)

localize7.0ms (0.2%)

series251.0ms (5.3%)

rewrite122.0ms (2.6%)

simplify136.0ms (2.9%)

prune361.0ms (7.7%)

regimes771.0ms (16.4%)

simplify2.0ms (0%)

end70.0ms (1.5%)

Profiling