Details

analyze4.0ms (0.2%)

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)

sample779.0ms (27.5%)

Results

751.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify7.0ms (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

32.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.7b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	31.5b	(sqrt.f64 (.f64 2 (.f64 x x)))

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite9.0ms (0.3%)

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)))

simplify74.0ms (2.6%)

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 (1%)

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
	33.1b	(*.f64 (sqrt.f64 2) x)
✓	32.7b	(sqrt.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)))
	44.0b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	2.9b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 558 to 325 computations (41.8% 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))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series53.0ms (1.9%)

Counts

3 → 24

Calls

3 calls:

39.0ms	(hypot.f64 x x)
10.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite10.0ms (0.4%)

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)

simplify80.0ms (2.8%)

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

prune85.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	2	3	5
Picked	0	1	1
Done	1	0	1
Total	104	7	111

Error

0.0b

Counts

111 → 7

Alt Table

Status	Error	Program
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	33.1b	(*.f64 (sqrt.f64 2) x)
▶	0.1b	(hypot.f64 x x)
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	44.0b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 1464 to 360 computations (75.4% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune7.0ms (0.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	4	7	11

Error

0.0b

Counts

11 → 7

Alt Table

Status	Error	Program
▶	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	33.1b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	44.0b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 141 to 74 computations (47.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
✓	0.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.5b	(cbrt.f64 (hypot.f64 x x))
✓	0.6b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)

series1.2s (40.9%)

Counts

4 → 48

Calls

4 calls:

675.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
240.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
240.0ms	(cbrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
20×	`sqrt-prod_binary64`
18×	`unpow-prod-down_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

8.0ms	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
2.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
1.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify116.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-def_binary64`
542×	`unswap-sqr_binary64`
388×	`associate-l_binary64`
354×	`log-prod_binary64`
328×	`sqr-pow_binary64`

Counts

151 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	134	2505
1	264	2445
2	586	2357
3	1596	1776
4	3150	1734
5	4609	1734
6	4856	1734

prune78.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	166	9	175

Error

0.0b

Counts

175 → 9

Alt Table

Status	Error	Program
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	2.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x))))))
	2.2b	(.f64 (.f64 (pow.f64 (*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5/2)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	33.1b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
	1.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/4) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/4)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	44.0b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 3045 to 1112 computations (63.5% saved)

regimes195.0ms (6.9%)

Accuracy

Total 0.1b remaining (77.5%)

Threshold costs 0.1b (77.5%)

Counts

52 → 1

Compiler

Compiled 3007 to 1835 computations (39% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end104.0ms (3.7%)

Compiler: Compiled 115 to 61 computations (47% saved)

Details

analyze4.0ms (0.2%)

sample779.0ms (27.5%)

simplify7.0ms (0.3%)

prune1.0ms (0.1%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite9.0ms (0.3%)

simplify74.0ms (2.6%)

prune27.0ms (1%)

localize4.0ms (0.1%)

series53.0ms (1.9%)

rewrite10.0ms (0.4%)

simplify80.0ms (2.8%)

prune85.0ms (3%)

localize2.0ms (0.1%)

prune7.0ms (0.3%)

localize8.0ms (0.3%)

series1.2s (40.9%)

rewrite23.0ms (0.8%)

simplify116.0ms (4.1%)

prune78.0ms (2.7%)

regimes195.0ms (6.9%)

simplify2.0ms (0.1%)

end104.0ms (3.7%)

Profiling