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 (31.2%)

Results

843.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify137.0ms (4.2%)

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

31.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.2b	(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))
✓	30.1b	(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 (0.2%)

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:

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

simplify95.0ms (2.9%)

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

prune123.0ms (3.8%)

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

0.1b

Counts

67 → 8

Alt Table

Status	Error	Program
	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	31.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
▶	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	33.5b	(*.f64 (sqrt.f64 2) x)
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	31.4b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))
	31.6b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))
	3.0b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))

Compiler

Compiled 833 to 611 computations (26.7% 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)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series103.0ms (3.2%)

Counts

3 → 24

Calls

3 calls:

90.0ms	(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 (0.3%)

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)

simplify164.0ms (5%)

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

prune100.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	103	9	112

Error

0.0b

Counts

112 → 9

Alt Table

Status	Error	Program
	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) 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)))))
	33.5b	(*.f64 (sqrt.f64 2) x)
▶	0.1b	(hypot.f64 x x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	1.3b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	31.6b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))

Compiler

Compiled 1594 to 416 computations (73.9% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

prune9.0ms (0.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	4	9	13

Error

0.0b

Counts

13 → 9

Alt Table

Status	Error	Program
	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) 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)))))
	33.5b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	1.3b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
▶	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	31.6b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))

Compiler

Compiled 271 to 130 computations (52% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
	0.1b	(hypot.f64 x x)
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

series618.0ms (18.9%)

Counts

3 → 36

Calls

3 calls:

316.0ms

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

295.0ms

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

7.0ms

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

rewrite32.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`sqrt-pow1_binary64`
51×	`pow1_binary64`
47×	`sqrt-prod_binary64`
47×	`add-sqr-sqrt_binary64`
36×	`pow-prod-up_binary64`

Counts

3 → 121

Calls

3 calls:

13.0ms

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

7.0ms

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

1.0ms

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

simplify102.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
340×	`unswap-sqr_binary64`
272×	`exp-sum_binary64`
265×	`distribute-rgt-in_binary64`
219×	`fma-neg_binary64`

Counts

157 → 153

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	1915
1	224	1702
2	445	1614
3	843	1530
4	2021	1476
5	4741	1476
6	4949	1476

prune128.0ms (3.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	193	9	202

Error

0.0b

Counts

202 → 9

Alt Table

Status	Error	Program
	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) 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)))))
	0.9b	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 4)
	33.5b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
✓	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	0.9b	(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	31.6b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))
	1.0b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (fabs.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))

Compiler

Compiled 3893 to 942 computations (75.8% saved)

regimes442.0ms (13.5%)

Accuracy

Total 0.1b remaining (82.7%)

Threshold costs 0.1b (82.7%)

Counts

95 → 1

Compiler

Compiled 5598 to 3142 computations (43.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end142.0ms (4.3%)

Compiler: Compiled 127 to 67 computations (47.2% saved)

Details

analyze6.0ms (0.2%)

sample1.0s (31.2%)

simplify137.0ms (4.2%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify95.0ms (2.9%)

prune123.0ms (3.8%)

localize4.0ms (0.1%)

series103.0ms (3.2%)

rewrite10.0ms (0.3%)

simplify164.0ms (5%)

prune100.0ms (3.1%)

localize6.0ms (0.2%)

prune9.0ms (0.3%)

localize6.0ms (0.2%)

series618.0ms (18.9%)

rewrite32.0ms (1%)

simplify102.0ms (3.1%)

prune128.0ms (3.9%)

regimes442.0ms (13.5%)

simplify2.0ms (0.1%)

end142.0ms (4.3%)

Profiling