Details

analyze4.0ms (0.3%)

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 8 to 6 computations (25% saved)

sample817.0ms (50.4%)

Results

788.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.3%)

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 (0.1%)

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

28.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	27.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
2.0ms	(.f64 2 (.f64 x x))

rewrite52.0ms (3.2%)

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:

46.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
4.0ms	(.f64 2 (.f64 x x))

simplify73.0ms (4.5%)

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

prune37.0ms (2.3%)

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
	31.8b	(*.f64 (sqrt.f64 2) x)
✓	28.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
	28.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (.f64 2 (.f64 x x)))))
▶	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)))
	2.8b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) 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 628 to 367 computations (41.6% saved)

localize4.0ms (0.2%)

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)))

series19.0ms (1.2%)

Counts

3 → 24

Calls

3 calls:

12.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
3.0ms	(hypot.f64 x x)

rewrite10.0ms (0.6%)

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)

simplify83.0ms (5.2%)

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

prune62.0ms (3.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	9	104
Fresh	4	2	6
Picked	1	0	1
Done	1	0	1
Total	101	11	112

Error

Counts

112 → 11

Alt Table

Status	Error	Program
	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	1.0b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.4b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (*.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)))))
	31.8b	(*.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))))
	18.9b	(.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)))))
	4.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (exp.f64 (log.f64 (sqrt.f64 (hypot.f64 x x)))))
	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (fabs.f64 (sqrt.f64 (hypot.f64 x x))))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
▶	0.2b	(hypot.f64 x x)

Compiler

Compiled 1642 to 426 computations (74.1% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.2b	(hypot.f64 x x)

prune11.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	4	11	15

Error

Counts

15 → 11

Alt Table

Status	Error	Program
	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	1.0b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.4b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (*.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)))))
	31.8b	(*.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))))
	18.9b	(.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)))))
	4.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (exp.f64 (log.f64 (sqrt.f64 (hypot.f64 x x)))))
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (fabs.f64 (sqrt.f64 (hypot.f64 x x))))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.2b	(hypot.f64 x x)

Compiler

Compiled 319 to 140 computations (56.1% saved)

localize4.0ms (0.3%)

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

series16.0ms (1%)

Counts

1 → 0

Calls

1 calls:

16.0ms

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

rewrite11.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
20×	`sqrt-prod_binary64`
11×	`associate-r_binary64`
10×	`fabs-sqr_binary64`
10×	`fabs-mul_binary64`

Counts

1 → 46

Calls

1 calls:

6.0ms

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

simplify68.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-/r/_binary64`
421×	`associate-/l/_binary64`
396×	`cube-div_binary64`
396×	`log-div_binary64`
357×	`times-frac_binary64`

Counts

46 → 50

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	52	1100
1	90	455
2	148	455
3	295	455
4	470	455
5	778	455
6	1622	455
7	3705	441
8	5014	441

prune44.0ms (2.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	92	11	103

Error

Counts

103 → 11

Alt Table

Status	Error	Program
	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	1.0b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.4b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (*.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)))))
	31.8b	(*.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))))
	18.9b	(.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)))))
	4.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (exp.f64 (log.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (fabs.f64 (sqrt.f64 (hypot.f64 x x))))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.2b	(hypot.f64 x x)

Compiler

Compiled 1549 to 320 computations (79.3% saved)

regimes175.0ms (10.8%)

Accuracy

Total 0.1b remaining (83.2%)

Threshold costs 0.1b (83.2%)

Counts

51 → 1

Compiler

Compiled 3019 to 1567 computations (48.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	4	6

end111.0ms (6.9%)

Compiler: Compiled 151 to 70 computations (53.6% saved)

Details

analyze4.0ms (0.3%)

sample817.0ms (50.4%)

simplify6.0ms (0.3%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite52.0ms (3.2%)

simplify73.0ms (4.5%)

prune37.0ms (2.3%)

localize4.0ms (0.2%)

series19.0ms (1.2%)

rewrite10.0ms (0.6%)

simplify83.0ms (5.2%)

prune62.0ms (3.8%)

localize2.0ms (0.1%)

prune11.0ms (0.7%)

localize4.0ms (0.3%)

series16.0ms (1%)

rewrite11.0ms (0.7%)

simplify68.0ms (4.2%)

prune44.0ms (2.7%)

regimes175.0ms (10.8%)

simplify2.0ms (0.1%)

end111.0ms (6.9%)

Profiling