Details

analyze5.0ms (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 7 computations (12.5% saved)

sample1.0s (28.4%)

Results

836.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify141.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	22	9
3	41	9
4	88	9
5	221	9
6	693	9
7	1098	9
8	1100	9
9	1248	9
10	1418	9
11	1600	9
12	1825	9
13	2110	9
14	2529	9
15	3094	9
16	3780	9
17	3998	9
18	4242	9
19	4324	9
20	4357	9
21	4378	9
22	4947	9

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

32.7b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series5.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

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

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 41

Calls

2 calls:

5.0ms	(*.f64 2 (pow.f64 x 2))
2.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

simplify154.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

823×	`unswap-sqr_binary64`
448×	`hypot-def_binary64`
432×	`*-commutative_binary64`
402×	`sqr-pow_binary64`
358×	`times-frac_binary64`

Counts

53 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	490
1	110	449
2	247	437
3	826	431
4	1358	371
5	3482	371
6	4011	371
7	4935	371
8	4869	371

prune116.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	7	67

Error

0.1b

Counts

67 → 7

Alt Table

Status	Error	Program
	33.1b	(*.f64 (sqrt.f64 2) x)
✓	32.7b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
▶	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 785 to 571 computations (27.3% saved)

localize3.0ms (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)))

series142.0ms (4%)

Counts

3 → 24

Calls

3 calls:

135.0ms	(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 (0.3%)

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)

simplify122.0ms (3.4%)

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

prune46.0ms (1.3%)

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
▶	0.1b	(hypot.f64 x x)
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(*.f64 (sqrt.f64 2) 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))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

Compiler

Compiled 1464 to 360 computations (75.4% 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

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
✓	0.1b	(hypot.f64 x x)
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(*.f64 (sqrt.f64 2) 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))
▶	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

Compiler

Compiled 141 to 74 computations (47.5% saved)

localize8.0ms (0.2%)

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 (34.3%)

Counts

4 → 48

Calls

4 calls:

675.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
329.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
216.0ms	(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))))

rewrite18.0ms (0.5%)

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:

7.0ms	(*.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))

simplify118.0ms (3.3%)

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

prune81.0ms (2.3%)

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
	33.1b	(*.f64 (sqrt.f64 2) 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))))
✓	0.1b	(hypot.f64 x x)
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) 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))))))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (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)))
	44.0b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))

Compiler

Compiled 3045 to 1112 computations (63.5% saved)

regimes232.0ms (6.5%)

Accuracy

Total 0.1b remaining (77.5%)

Threshold costs 0.1b (77.5%)

Counts

52 → 1

Compiler

Compiled 3007 to 1924 computations (36% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	4	6

end102.0ms (2.9%)

Compiler: Compiled 117 to 63 computations (46.2% saved)

Details

analyze5.0ms (0.2%)

sample1.0s (28.4%)

simplify141.0ms (4%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify154.0ms (4.3%)

prune116.0ms (3.3%)

localize3.0ms (0.1%)

series142.0ms (4%)

rewrite10.0ms (0.3%)

simplify122.0ms (3.4%)

prune46.0ms (1.3%)

localize2.0ms (0%)

prune8.0ms (0.2%)

localize8.0ms (0.2%)

series1.2s (34.3%)

rewrite18.0ms (0.5%)

simplify118.0ms (3.3%)

prune81.0ms (2.3%)

regimes232.0ms (6.5%)

simplify2.0ms (0%)

end102.0ms (2.9%)

Profiling