Details

analyze38.0ms (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 8 to 6 computations (25% saved)

sample27.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% saved)

simplify12.0ms (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

prune3.0ms (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

29.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.7b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	28.5b	(sqrt.f64 (.f64 2 (.f64 x x)))

series11.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
5.0ms	(.f64 2 (.f64 x x))

rewrite25.0ms (0.7%)

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:

16.0ms	(.f64 2 (.f64 x x))
6.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

simplify104.0ms (2.8%)

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

prune62.0ms (1.7%)

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
	32.8b	(*.f64 (sqrt.f64 2) x)
	30.1b	(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)))))
	50.3b	(sqrt.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) (.f64 2 (.f64 x x))) (.f64 2 (.f64 x x)))))
▶	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)))
✓	29.7b	(sqrt.f64 (.f64 2 (.f64 x x)))
	2.6b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	30.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 628 to 367 computations (41.6% saved)

localize7.0ms (0.2%)

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)))

series37.0ms (1%)

Counts

3 → 24

Calls

3 calls:

18.0ms	(sqrt.f64 (hypot.f64 x x))
11.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
7.0ms	(hypot.f64 x x)

rewrite25.0ms (0.7%)

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:

10.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
2.0ms	(sqrt.f64 (hypot.f64 x x))
1.0ms	(hypot.f64 x x)

simplify143.0ms (3.9%)

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

prune104.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	3	3	6
Picked	0	1	1
Done	1	0	1
Total	103	9	112

Error

Counts

112 → 9

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (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 (cbrt.f64 (hypot.f64 x x)))))
	30.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
▶	0.1b	(hypot.f64 x x)
	50.3b	(sqrt.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) (.f64 2 (.f64 x x))) (.f64 2 (.f64 x x)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

Compiler

Compiled 1592 to 406 computations (74.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune16.0ms (0.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	4	9	13

Error

Counts

13 → 9

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (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 (cbrt.f64 (hypot.f64 x x)))))
	30.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
	50.3b	(sqrt.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) (.f64 2 (.f64 x x))) (.f64 2 (.f64 x x)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
▶	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

Compiler

Compiled 269 to 120 computations (55.4% saved)

localize12.0ms (0.3%)

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))
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
✓	0.7b	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)

series938.0ms (25.4%)

Counts

3 → 36

Calls

3 calls:

486.0ms	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
437.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)
15.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

rewrite57.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`sqrt-prod_binary64`
69×	`add-sqr-sqrt_binary64`
27×	`cube-prod_binary64`
27×	`unpow-prod-down_binary64`
24×	`associate-r_binary64`

Counts

3 → 135

Calls

3 calls:

26.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
6.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)
3.0ms	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

simplify396.0ms (10.7%)

Algorithm

1×	egg-herbie

Rules

569×	`unswap-sqr_binary64`
453×	`exp-prod_binary64`
451×	`sqr-pow_binary64`
387×	`log-prod_binary64`
386×	`*-commutative_binary64`

Counts

171 → 131

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	117	2417
1	238	2133
2	797	1880
3	1496	1751
4	3366	1674
5	4592	1674
6	4857	1674

prune182.0ms (4.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	192	8	200

Error

Counts

200 → 8

Alt Table

Status	Error	Program
	32.8b	(*.f64 (sqrt.f64 2) x)
	0.9b	(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 5/2) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)))
✓	0.1b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	1.0b	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	30.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 3510 to 1137 computations (67.6% saved)

regimes492.0ms (13.3%)

Accuracy

Total 0.1b remaining (82.8%)

Threshold costs 0.1b (82.8%)

Counts

61 → 1

Compiler

Compiled 3803 to 2192 computations (42.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end1.0ms (0%)

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

sample987.0ms (26.7%)

Algorithm

1×

intervals

Results

464.0ms

8000×

body

128

valid

Compiler

Compiled 100 to 57 computations (43% saved)

Details

analyze38.0ms (1%)

sample27.0ms (0.7%)

simplify12.0ms (0.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series11.0ms (0.3%)

rewrite25.0ms (0.7%)

simplify104.0ms (2.8%)

prune62.0ms (1.7%)

localize7.0ms (0.2%)

series37.0ms (1%)

rewrite25.0ms (0.7%)

simplify143.0ms (3.9%)

prune104.0ms (2.8%)

localize5.0ms (0.1%)

prune16.0ms (0.4%)

localize12.0ms (0.3%)

series938.0ms (25.4%)

rewrite57.0ms (1.5%)

simplify396.0ms (10.7%)

prune182.0ms (4.9%)

regimes492.0ms (13.3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample987.0ms (26.7%)

Profiling