Details

analyze1.5s (38.6%)

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)

sample1.2s (29.8%)

Results

1.2s	8256×	body	128	valid
1.0ms	2×	body	8192	exit

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify7.0ms (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

prune2.0ms (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

30.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.2b	(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))
✓	29.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

series5.0ms (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))
4.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

simplify77.0ms (1.9%)

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

prune28.0ms (0.7%)

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
	41.2b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	28.7b	(*.f64 (sqrt.f64 2) x)
	30.6b	(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)))))
▶	0.5b	(*.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)))
✓	30.2b	(sqrt.f64 (.f64 2 (.f64 x x)))
	33.1b	(log1p.f64 (expm1.f64 (hypot.f64 x x)))
	34.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 602 to 353 computations (41.4% saved)

localize5.0ms (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)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series18.0ms (0.5%)

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 (0.3%)

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 (2.1%)

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

prune52.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	4	2	6
Picked	0	1	1
Done	1	0	1
Total	104	8	112

Error

0.0b

Counts

112 → 8

Alt Table

Status	Error	Program
	34.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	0.1b	(hypot.f64 x x)
	0.8b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.4b	(.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))))
	28.7b	(*.f64 (sqrt.f64 2) x)
	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))))
	1.4b	(.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)))))

Compiler

Compiled 1580 to 382 computations (75.8% 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
	34.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	0.8b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.4b	(.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))))
	28.7b	(*.f64 (sqrt.f64 2) x)
▶	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))))
	1.4b	(.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)))))

Compiler

Compiled 257 to 96 computations (62.6% saved)

localize6.0ms (0.1%)

Local error

Found 4 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 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.4b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))

series405.0ms (10.1%)

Counts

2 → 24

Calls

2 calls:

401.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
4.0ms	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`sqrt-pow1_binary64`
48×	`pow1_binary64`
42×	`add-sqr-sqrt_binary64`
37×	`sqrt-prod_binary64`
36×	`pow-prod-up_binary64`

Counts

2 → 100

Calls

2 calls:

13.0ms	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
7.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))

simplify114.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
338×	`fma-neg_binary64`
322×	`unswap-sqr_binary64`
245×	`exp-prod_binary64`
220×	`exp-sum_binary64`

Counts

124 → 126

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	100	1686
1	192	1428
2	410	1242
3	724	1206
4	1739	1160
5	4430	1156
6	4990	1156
7	4843	1156

prune93.0ms (2.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	188	9	197

Error

0.0b

Counts

197 → 9

Alt Table

Status	Error	Program
	34.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	0.8b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))) (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.4b	(.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))))
	28.7b	(*.f64 (sqrt.f64 2) x)
✓	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))))
	1.4b	(.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)))))

Compiler

Compiled 3807 to 853 computations (77.6% saved)

regimes216.0ms (5.4%)

Accuracy

Total 0.1b remaining (84.5%)

Threshold costs 0.1b (84.5%)

Counts

52 → 1

Compiler

Compiled 3611 to 1752 computations (51.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	7	4
2	6	4

end91.0ms (2.3%)

Compiler: Compiled 155 to 57 computations (63.2% saved)

Details

analyze1.5s (38.6%)

sample1.2s (29.8%)

simplify7.0ms (0.2%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite9.0ms (0.2%)

simplify77.0ms (1.9%)

prune28.0ms (0.7%)

localize5.0ms (0.1%)

series18.0ms (0.5%)

rewrite11.0ms (0.3%)

simplify83.0ms (2.1%)

prune52.0ms (1.3%)

localize2.0ms (0%)

prune8.0ms (0.2%)

localize6.0ms (0.1%)

series405.0ms (10.1%)

rewrite29.0ms (0.7%)

simplify114.0ms (2.8%)

prune93.0ms (2.3%)

regimes216.0ms (5.4%)

simplify2.0ms (0.1%)

end91.0ms (2.3%)

Profiling