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)

sample804.0ms (49.8%)

Results

778.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify7.0ms (0.5%)

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

31.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.4b	(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))
✓	30.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

series5.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite11.0ms (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:

7.0ms	(.f64 2 (.f64 x x))
3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

simplify77.0ms (4.8%)

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

prune31.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	39	8	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	9	48

Error

0.1b

Counts

48 → 9

Alt Table

Status	Error	Program
	40.7b	(cbrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 x x))) (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (.f64 2 (.f64 x x)))))
	3.2b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.9b	(*.f64 (sqrt.f64 2) x)
✓	31.4b	(sqrt.f64 (.f64 2 (.f64 x x)))
	50.4b	(sqrt.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 2) 2) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))))
	31.8b	(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)))
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 672 to 395 computations (41.2% saved)

localize4.0ms (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)))

series14.0ms (0.9%)

Counts

3 → 24

Calls

3 calls:

6.0ms	(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)))

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)

simplify84.0ms (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

prune52.0ms (3.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	4	3	7
Picked	0	1	1
Done	1	0	1
Total	104	9	113

Error

0.0b

Counts

113 → 9

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	40.7b	(cbrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 x x))) (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (.f64 2 (.f64 x x)))))
	0.7b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	50.4b	(sqrt.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 2) 2) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.0b	(.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)))))
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 1614 to 422 computations (73.9% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

prune8.0ms (0.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	4	9	13

Error

0.0b

Counts

13 → 9

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	40.7b	(cbrt.f64 (.f64 (.f64 (hypot.f64 x x) (hypot.f64 x x)) (hypot.f64 x x)))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
▶	0.7b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	50.4b	(sqrt.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 2) 2) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.0b	(.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)))))
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 273 to 118 computations (56.8% saved)

localize6.0ms (0.3%)

Local error

Found 4 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)) (.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))))

series11.0ms (0.7%)

Counts

2 → 12

Calls

2 calls:

8.0ms

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

4.0ms

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

rewrite35.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`sqrt-prod_binary64`
83×	`sqrt-pow1_binary64`
78×	`add-sqr-sqrt_binary64`
63×	`pow1_binary64`
43×	`pow1/2_binary64`

Counts

2 → 137

Calls

2 calls:

13.0ms

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

8.0ms

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

simplify110.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-def_binary64`
529×	`unswap-sqr_binary64`
412×	`log-prod_binary64`
373×	`associate-l_binary64`
353×	`*-commutative_binary64`

Counts

149 → 141

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	88	1283
1	125	1208
2	352	1182
3	1036	1116
4	2170	1116
5	3751	1065
6	4436	1065
7	4906	1065

prune94.0ms (5.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	204	9	213

Error

0.0b

Counts

213 → 9

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	40.7b	(cbrt.f64 (.f64 (.f64 (hypot.f64 x x) (hypot.f64 x x)) (hypot.f64 x x)))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓	0.7b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	50.4b	(sqrt.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 2) 2) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.0b	(.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)))))
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 4036 to 924 computations (77.1% saved)

regimes152.0ms (9.4%)

Accuracy

Total 0.1b remaining (72.6%)

Threshold costs 0.1b (72.6%)

Counts

41 → 1

Compiler

Compiled 2359 to 1280 computations (45.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end86.0ms (5.3%)

Compiler: Compiled 131 to 59 computations (55% saved)

Details

analyze4.0ms (0.3%)

sample804.0ms (49.8%)

simplify7.0ms (0.5%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series5.0ms (0.3%)

rewrite11.0ms (0.7%)

simplify77.0ms (4.8%)

prune31.0ms (1.9%)

localize4.0ms (0.2%)

series14.0ms (0.9%)

rewrite10.0ms (0.6%)

simplify84.0ms (5.2%)

prune52.0ms (3.2%)

localize3.0ms (0.2%)

prune8.0ms (0.5%)

localize6.0ms (0.3%)

series11.0ms (0.7%)

rewrite35.0ms (2.1%)

simplify110.0ms (6.8%)

prune94.0ms (5.8%)

regimes152.0ms (9.4%)

simplify2.0ms (0.1%)

end86.0ms (5.3%)

Profiling