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 (36.8%)

Results

860.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify140.0ms (4.9%)

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

32.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.3b	(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))
✓	31.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series6.0ms (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)))

simplify87.0ms (3.1%)

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

prune141.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	8	67

Error

0.0b

Counts

67 → 8

Alt Table

Status	Error	Program
	32.7b	(*.f64 (sqrt.f64 2) x)
	32.6b	(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)))
✓	32.3b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	2.7b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.5b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))

Compiler

Compiled 841 to 619 computations (26.4% 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)))

series17.0ms (0.6%)

Counts

3 → 24

Calls

3 calls:

9.0ms	(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)

rewrite102.0ms (3.6%)

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)

simplify191.0ms (6.8%)

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

prune96.0ms (3.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	104	8	112

Error

0.0b

Counts

112 → 8

Alt Table

Status	Error	Program
	32.7b	(*.f64 (sqrt.f64 2) x)
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	20.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	1.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	32.6b	(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)))))
▶	0.1b	(hypot.f64 x x)
	32.5b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))

Compiler

Compiled 1572 to 428 computations (72.8% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune10.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	4	8	12

Error

0.0b

Counts

12 → 8

Alt Table

Status	Error	Program
	32.7b	(*.f64 (sqrt.f64 2) x)
▶	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	20.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	1.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	32.6b	(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)))))
✓	0.1b	(hypot.f64 x x)
	32.5b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))

Compiler

Compiled 249 to 142 computations (43% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.5b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))

series236.0ms (8.3%)

Counts

3 → 24

Calls

3 calls:

221.0ms

(cbrt.f64 (hypot.f64 x x))

11.0ms

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

4.0ms

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

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
14×	`cbrt-prod_binary64`
14×	`pow1_binary64`
13×	`sqrt-prod_binary64`
12×	`associate-l_binary64`

Counts

3 → 76

Calls

3 calls:

7.0ms

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

6.0ms

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

1.0ms

(cbrt.f64 (hypot.f64 x x))

simplify109.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-def_binary64`
358×	`fma-neg_binary64`
324×	`*-commutative_binary64`
304×	`unswap-sqr_binary64`
234×	`sqr-pow_binary64`

Counts

100 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	103	1664
1	183	1476
2	472	1442
3	722	1019
4	998	993
5	1919	993
6	3922	993
7	4995	993
8	4845	993

prune66.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	145	7	152

Error

Counts

152 → 7

Alt Table

Status	Error	Program
	20.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	32.7b	(*.f64 (sqrt.f64 2) x)
	32.6b	(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)))))
	1.2b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.1b	(hypot.f64 x x)
	32.5b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))

Compiler

Compiled 2839 to 597 computations (79% saved)

regimes447.0ms (15.8%)

Accuracy

Total 0.1b remaining (65.1%)

Threshold costs 0.1b (65.1%)

Counts

101 → 1

Compiler

Compiled 6241 to 3452 computations (44.7% 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

end86.0ms (3%)

Compiler: Compiled 104 to 65 computations (37.5% saved)

Details

analyze6.0ms (0.2%)

sample1.0s (36.8%)

simplify140.0ms (4.9%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite8.0ms (0.3%)

simplify87.0ms (3.1%)

prune141.0ms (5%)

localize4.0ms (0.1%)

series17.0ms (0.6%)

rewrite102.0ms (3.6%)

simplify191.0ms (6.8%)

prune96.0ms (3.4%)

localize2.0ms (0.1%)

prune10.0ms (0.3%)

localize7.0ms (0.2%)

series236.0ms (8.3%)

rewrite19.0ms (0.7%)

simplify109.0ms (3.9%)

prune66.0ms (2.3%)

regimes447.0ms (15.8%)

simplify2.0ms (0.1%)

end86.0ms (3%)

Profiling