Details

analyze6.0ms (0.3%)

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)

sample1.1s (47.8%)

Results

887.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify144.0ms (6.5%)

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

28.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	27.1b	(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))

rewrite7.0ms (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)))

simplify115.0ms (5.2%)

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

prune180.0ms (8.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	57	9	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	10	67

Error

0.1b

Counts

67 → 10

Alt Table

Status	Error	Program
	28.3b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))
✓	28.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	46.1b	(sqrt.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 x) 2)) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 x) 2))))
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	28.5b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))
	2.8b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.8b	(*.f64 (sqrt.f64 2) x)
	28.4b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))

Compiler

Compiled 893 to 657 computations (26.4% saved)

localize4.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.2b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series18.0ms (0.8%)

Counts

3 → 24

Calls

3 calls:

10.0ms	(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 (0.5%)

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 (3.7%)

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

prune58.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	5	3	8
Picked	1	0	1
Done	1	0	1
Total	103	11	114

Error

Counts

114 → 11

Alt Table

Status	Error	Program
	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (fabs.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))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	18.9b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	28.3b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))
	4.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (exp.f64 (log.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.8b	(*.f64 (sqrt.f64 2) x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
▶	0.2b	(hypot.f64 x x)

Compiler

Compiled 1620 to 432 computations (73.3% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.2b	(hypot.f64 x x)

prune11.0ms (0.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	4	11	15

Error

Counts

15 → 11

Alt Table

Status	Error	Program
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (fabs.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))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	18.9b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	28.3b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))
	4.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (exp.f64 (log.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.8b	(*.f64 (sqrt.f64 2) x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.2b	(hypot.f64 x x)

Compiler

Compiled 297 to 146 computations (50.8% saved)

localize4.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (hypot.f64 x x))
	0.2b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (fabs.f64 (sqrt.f64 (hypot.f64 x x))))

series18.0ms (0.8%)

Counts

1 → 0

Calls

1 calls:

18.0ms

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

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
20×	`sqrt-prod_binary64`
11×	`associate-r_binary64`
10×	`fabs-sqr_binary64`
10×	`fabs-mul_binary64`

Counts

1 → 46

Calls

1 calls:

6.0ms

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

simplify64.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-/r/_binary64`
421×	`associate-/l/_binary64`
396×	`cube-div_binary64`
396×	`log-div_binary64`
357×	`times-frac_binary64`

Counts

46 → 50

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	52	1100
1	90	455
2	148	455
3	295	455
4	470	455
5	778	455
6	1622	455
7	3705	441
8	5014	441

prune42.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	92	11	103

Error

Counts

103 → 11

Alt Table

Status	Error	Program
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (fabs.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))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	18.9b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	28.3b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))
	4.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (exp.f64 (log.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.8b	(*.f64 (sqrt.f64 2) x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.2b	(hypot.f64 x x)

Compiler

Compiled 1538 to 323 computations (79% saved)

regimes179.0ms (8%)

Accuracy

Total 0.1b remaining (85.7%)

Threshold costs 0.1b (85.7%)

Counts

49 → 1

Compiler

Compiled 2901 to 1725 computations (40.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	4	6

end195.0ms (8.8%)

Compiler: Compiled 140 to 73 computations (47.9% saved)

Details

analyze6.0ms (0.3%)

sample1.1s (47.8%)

simplify144.0ms (6.5%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite7.0ms (0.3%)

simplify115.0ms (5.2%)

prune180.0ms (8.1%)

localize4.0ms (0.2%)

series18.0ms (0.8%)

rewrite10.0ms (0.5%)

simplify82.0ms (3.7%)

prune58.0ms (2.6%)

localize2.0ms (0.1%)

prune11.0ms (0.5%)

localize4.0ms (0.2%)

series18.0ms (0.8%)

rewrite9.0ms (0.4%)

simplify64.0ms (2.9%)

prune42.0ms (1.9%)

regimes179.0ms (8%)

simplify2.0ms (0.1%)

end195.0ms (8.8%)

Profiling