Details

analyze6.0ms (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 (38.2%)

Results

877.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify139.0ms (5.1%)

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

32.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.8b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (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 (0.3%)

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:

4.0ms	(*.f64 2 (pow.f64 x 2))
2.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

simplify136.0ms (4.9%)

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

prune131.0ms (4.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	9	67

Error

0.0b

Counts

67 → 9

Alt Table

Status	Error	Program
	33.6b	(*.f64 (sqrt.f64 2) x)
✓	32.8b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	29.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))
	33.1b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))
	33.1b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (cbrt.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)))
	2.9b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))

Compiler

Compiled 877 to 647 computations (26.2% saved)

localize4.0ms (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)
✓	0.4b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series132.0ms (4.8%)

Counts

3 → 24

Calls

3 calls:

125.0ms	(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 (0.4%)

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)

simplify82.0ms (3%)

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

prune80.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	4	3	7
Picked	0	1	1
Done	1	0	1
Total	106	7	113

Error

0.0b

Counts

113 → 7

Alt Table

Status	Error	Program
	33.1b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))
▶	0.1b	(hypot.f64 x x)
	29.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	0.9b	(.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)))))
	33.6b	(*.f64 (sqrt.f64 2) x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.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 1512 to 380 computations (74.9% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune6.0ms (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
	33.1b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))
✓	0.1b	(hypot.f64 x x)
	29.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	0.9b	(.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)))))
	33.6b	(*.f64 (sqrt.f64 2) x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.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 189 to 94 computations (50.3% saved)

localize10.0ms (0.4%)

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

series196.0ms (7.1%)

Counts

2 → 24

Calls

2 calls:

192.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)
4.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 114

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
3.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)

simplify138.0ms (5%)

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

138 → 105

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	1997
1	236	1755
2	795	1526
3	1494	1445
4	3364	1372
5	4590	1372
6	4855	1372

prune176.0ms (6.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	147	7	154

Error

Counts

154 → 7

Alt Table

Status	Error	Program
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 7/2))
	0.9b	(.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)))))
	29.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.6b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	0.8b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

Compiler

Compiled 2747 to 866 computations (68.5% saved)

regimes336.0ms (12.2%)

Accuracy

Total 0.1b remaining (74.4%)

Threshold costs 0.1b (74.4%)

Counts

85 → 1

Compiler

Compiled 5426 to 3243 computations (40.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end72.0ms (2.6%)

Compiler: Compiled 92 to 44 computations (52.2% saved)

Details

analyze6.0ms (0.2%)

sample1.0s (38.2%)

simplify139.0ms (5.1%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series5.0ms (0.2%)

rewrite8.0ms (0.3%)

simplify136.0ms (4.9%)

prune131.0ms (4.8%)

localize4.0ms (0.1%)

series132.0ms (4.8%)

rewrite10.0ms (0.4%)

simplify82.0ms (3%)

prune80.0ms (2.9%)

localize2.0ms (0.1%)

prune6.0ms (0.2%)

localize10.0ms (0.4%)

series196.0ms (7.1%)

rewrite23.0ms (0.8%)

simplify138.0ms (5%)

prune176.0ms (6.4%)

regimes336.0ms (12.2%)

simplify2.0ms (0.1%)

end72.0ms (2.6%)

Profiling