Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
87.5%	87.5%	12.5%	0%	0%	0%	0%	5
93.8%	93.7%	6.2%	0%	0%	0%	0%	6
96.9%	96.8%	3.1%	0%	0%	0%	0%	7
98.4%	98.4%	1.6%	0%	0%	0%	0%	8
99.2%	99.2%	0.8%	0%	0%	0%	0%	9
99.6%	99.6%	0.4%	0%	0%	0%	0%	10
99.8%	99.8%	0.2%	0%	0%	0%	0%	11
99.9%	99.9%	0.1%	0%	0%	0%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.3s (40.3%)

Results

1.3s	8256×	body	256	valid
0.0ms	1×	body	256	infinite

Bogosity

preprocess240.0ms (7.2%)

Algorithm

2×	egg-herbie

Rules

2858×	`sqr-pow`
1496×	`pow-sqr`
1054×	`cube-prod`
914×	`fabs-mul`
794×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	17
2	31	17
3	51	17
4	103	17
5	260	17
6	947	17
7	1549	17
8	1664	17
9	1834	17
10	2038	17
11	2314	17
12	2666	17
13	3094	17
14	3590	17
15	4182	17
16	4899	17
17	5153	17
18	5407	17
19	5545	17
20	5591	17
21	5615	17
22	6544	17
23	7672	17
24	7990	17
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify229.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

2858×	`sqr-pow`
1496×	`pow-sqr`
1054×	`cube-prod`
914×	`fabs-mul`
794×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	17
2	31	17
3	51	17
4	103	17
5	260	17
6	947	17
7	1549	17
8	1664	17
9	1834	17
10	2038	17
11	2314	17
12	2666	17
13	3094	17
14	3590	17
15	4182	17
16	4899	17
17	5153	17
18	5407	17
19	5545	17
20	5591	17
21	5615	17
22	6544	17
23	7672	17
24	7990	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))

eval1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

32.2b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	32.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	31.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 17 to 8 computations (52.9% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(sqrt.f64 (.f64 2 (.f64 x x)))
0.0ms	x	@	inf	(sqrt.f64 (.f64 2 (.f64 x x)))
0.0ms	x	@	0	(.f64 2 (.f64 x x))
0.0ms	x	@	inf	(.f64 2 (.f64 x x))
0.0ms	x	@	-inf	(.f64 2 (.f64 x x))

rewrite99.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

1372×	`add-sqr-sqrt`
1354×	`*-un-lft-identity`
1256×	`add-cube-cbrt`
1246×	`add-cbrt-cube`
1234×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	159	24
2	1829	24

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 2 (.f64 x x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 x (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 x) 1/2) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 2 (.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (sqrt.f64 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 4) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 x 4) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2 (*.f64 x x))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (*.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 x) 1/2) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (*.f64 x x))))))))

simplify70.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1326×	`distribute-lft-in`
1310×	`distribute-rgt-in`
1040×	`associate-+r+`
954×	`associate-+l+`
876×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	816
1	201	816
2	880	816
3	2375	688

Stop Event

1×	node limit

Counts

60 → 46

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 x (sqrt.f64 2)) 1)
(.f64 1 (.f64 x (sqrt.f64 2)))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 1 1/2) (.f64 x (sqrt.f64 2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/2))
(.f64 (pow.f64 (.f64 2 x) 1/2) (sqrt.f64 x))
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 1 (.f64 2 (.f64 x x))) 1)
(pow.f64 (.f64 2 (.f64 x x)) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 x x))))
(exp.f64 (log.f64 (.f64 2 (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 x x))))

Outputs
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (.f64 x (sqrt.f64 2)) 1)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 1 (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 1 1/2) (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 (.f64 2 x) 1/2) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(-.f64 (+.f64 1 (.f64 2 (.f64 x x))) 1)
(.f64 2 (.f64 x x))
(pow.f64 (.f64 2 (.f64 x x)) 1)
(.f64 2 (.f64 x x))
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(.f64 2 (.f64 x x))
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
(.f64 2 (.f64 x x))
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(.f64 2 (.f64 x x))
(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 3) 1/3)
(.f64 2 (.f64 x x))
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(.f64 2 (.f64 x x))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))
(.f64 2 (.f64 x x))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3))
(.f64 2 (.f64 x x))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))
(exp.f64 (log.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))

eval8.0ms (0.2%)

Compiler: Compiled 354 to 261 computations (26.3% saved)

prune7.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Error

0.0b

Counts

47 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(hypot.f64 x x)
▶	29.3b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 10 to 7 computations (30% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 12 to 8 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) (neg.f64 x))

rewrite170.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1266×	`add-sqr-sqrt`
1248×	`*-un-lft-identity`
1162×	`add-cube-cbrt`
1148×	`add-cbrt-cube`
1134×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	162	11
2	1917	11

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (neg.f64 x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))))))

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1082×	`*-commutative`
878×	`log-prod`
650×	`distribute-lft-in`
648×	`distribute-rgt-in`
646×	`distribute-lft-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	463
1	90	397
2	331	331
3	1789	331
4	4954	331
5	7952	331

Stop Event

1×	node limit

Counts

25 → 19

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(neg.f64 (*.f64 (sqrt.f64 2) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))

Outputs
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x x)

Compiler

Compiled 5 to 2 computations (60% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(hypot.f64 x x)
0.0ms	x	@	inf	(hypot.f64 x x)
0.0ms	x	@	0	(hypot.f64 x x)

rewrite46.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

918×	`associate-r`
744×	`add-sqr-sqrt`
738×	`*-un-lft-identity`
696×	`pow1`
682×	`add-cube-cbrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	80	7
2	916	7

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (hypot.f64 x x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x x)))))))

simplify73.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1144×	`distribute-lft-in`
1118×	`associate-r`
1046×	`distribute-rgt-in`
928×	`associate-l`
836×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	1038
1	194	864
2	596	854
3	3338	854
4	7923	854

Stop Event

1×	node limit

Counts

48 → 50

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(-.f64 (+.f64 (hypot.f64 x x) 1) 1)
(*.f64 (hypot.f64 x x) 1)
(*.f64 1 (hypot.f64 x x))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (hypot.f64 x x))))
(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
(.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (cbrt.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))
(.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (hypot.f64 x x)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(-.f64 (+.f64 (hypot.f64 x x) 1) 1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 (hypot.f64 x x) 1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 1 (hypot.f64 x x))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(.f64 (cbrt.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))
(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4))))
(.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (cbrt.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))
(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(pow.f64 (hypot.f64 x x) 1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(log.f64 (exp.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)

eval12.0ms (0.4%)

Compiler: Compiled 780 to 304 computations (61% saved)

prune8.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	68	3	71

Error

0.0b

Counts

71 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(hypot.f64 x x)
✓	29.3b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	1.3b	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))

Compiler

Compiled 23 to 15 computations (34.8% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))
✓	0.5b	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))
✓	0.6b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)

Compiler

Compiled 37 to 11 computations (70.3% saved)

series42.0ms (1.3%)

Counts

4 → 24

Calls

12 calls:

Time	Variable		Point	Expression
22.0ms	x	@	0	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
10.0ms	x	@	-inf	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
6.0ms	x	@	inf	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
1.0ms	x	@	0	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))

rewrite70.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1878×	`add-sqr-sqrt`
1840×	`*-un-lft-identity`
1732×	`add-cube-cbrt`
1708×	`add-cbrt-cube`
200×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	80
1	217	68
2	2503	68

Stop Event

1×	node limit

Counts

4 → 80

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
(cbrt.f64 (hypot.f64 x x))
(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 x x) 5/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (hypot.f64 x x) 5/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 x x) 5/12) (pow.f64 (hypot.f64 x x) 5/12))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 5/2) (pow.f64 (hypot.f64 x x) 5/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2) (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 5/2) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 5/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 x x) 1/6) (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (hypot.f64 x x) 1/6) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 x x)) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 x x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (hypot.f64 x x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 x x) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/3) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x x) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 x x) 1/6)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 1/6)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (hypot.f64 x x) 5/12) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 5/6)) (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))))))))

simplify68.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1812×	`associate-+l+`
886×	`unswap-sqr`
548×	`*-commutative`
470×	`sqr-pow`
418×	`exp-prod`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	1984
1	366	1860
2	1175	1644
3	3947	1548

Stop Event

1×	node limit

Counts

104 → 111

Calls

Call 1

Inputs
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6))) 1)
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) 1)
(*.f64 1 (pow.f64 (hypot.f64 x x) 5/6))
(*.f64 (pow.f64 (hypot.f64 x x) 5/12) (pow.f64 (hypot.f64 x x) 5/12))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(*.f64 (pow.f64 1 5/2) (pow.f64 (hypot.f64 x x) 5/6))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2) (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 5/2) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5/2))
(sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6))))
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3))
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)) 1))
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x)))) 1)
(*.f64 (cbrt.f64 (hypot.f64 x x)) 1)
(*.f64 (pow.f64 (hypot.f64 x x) 1/6) (pow.f64 (hypot.f64 x x) 1/6))
(*.f64 1 (cbrt.f64 (hypot.f64 x x)))
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6))
(.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (hypot.f64 x x) 1/6)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2))
(.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) (pow.f64 (hypot.f64 x x) 1/6)))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (pow.f64 (hypot.f64 x x) 1/6) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 (hypot.f64 x x)))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (*.f64 x x))) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(pow.f64 (hypot.f64 x x) 1/3)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 1)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2/3)
(pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 2)
(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 3)
(pow.f64 (.f64 2 (.f64 x x)) 1/6)
(sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))
(log.f64 (exp.f64 (cbrt.f64 (hypot.f64 x x))))
(log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (hypot.f64 x x)))))
(expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x))))
(exp.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1/3))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 1))
(log1p.f64 (expm1.f64 (cbrt.f64 (hypot.f64 x x))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 1/6))) 1)
(*.f64 (pow.f64 (hypot.f64 x x) 1/6) 1)
(*.f64 1 (pow.f64 (hypot.f64 x x) 1/6))
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(*.f64 (pow.f64 1 1/3) (pow.f64 (hypot.f64 x x) 1/6))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/3) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/3))
(pow.f64 (hypot.f64 x x) 1/6)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/2)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/3)
(pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1)
(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) 2)
(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) 3)
(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
(fabs.f64 (pow.f64 (hypot.f64 x x) 1/6))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x x) 1/6))))
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 1/3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 1/6)) 1))
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6)))) 1)
(pow.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6)) 1)
(pow.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/12) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6)) 2)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))) 3)
(pow.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3)) 1/3)
(sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 5/6)) (pow.f64 (hypot.f64 x x) 1/6)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6)))))
(cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))))
(exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))) 1))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))))

Outputs
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 (sqrt.f64 2) 1/6))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 (sqrt.f64 2) 1/6))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 (sqrt.f64 2) 1/6))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 (sqrt.f64 2) 1/6))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6))) 1)
(pow.f64 (hypot.f64 x x) 5/6)
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) 1)
(pow.f64 (hypot.f64 x x) 5/6)
(*.f64 1 (pow.f64 (hypot.f64 x x) 5/6))
(pow.f64 (hypot.f64 x x) 5/6)
(*.f64 (pow.f64 (hypot.f64 x x) 5/12) (pow.f64 (hypot.f64 x x) 5/12))
(pow.f64 (hypot.f64 x x) 5/6)
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)))
(*.f64 (pow.f64 1 5/2) (pow.f64 (hypot.f64 x x) 5/6))
(pow.f64 (hypot.f64 x x) 5/6)
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2) (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2))
(pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 5/2) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5/2))
(sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5))
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
(log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(pow.f64 (hypot.f64 x x) 5/6)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6))))
(pow.f64 (hypot.f64 x x) 5/6)
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3))
(pow.f64 (hypot.f64 x x) 5/6)
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(pow.f64 (hypot.f64 x x) 5/6)
(exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(pow.f64 (hypot.f64 x x) 5/6)
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)) 1))
(pow.f64 (hypot.f64 x x) 5/6)
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(pow.f64 (hypot.f64 x x) 5/6)
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x)))) 1)
(cbrt.f64 (hypot.f64 x x))
(*.f64 (cbrt.f64 (hypot.f64 x x)) 1)
(cbrt.f64 (hypot.f64 x x))
(*.f64 (pow.f64 (hypot.f64 x x) 1/6) (pow.f64 (hypot.f64 x x) 1/6))
(cbrt.f64 (hypot.f64 x x))
(*.f64 1 (cbrt.f64 (hypot.f64 x x)))
(cbrt.f64 (hypot.f64 x x))
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6))
(.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (hypot.f64 x x) 1/6)))
(cbrt.f64 (hypot.f64 x x))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2))
(cbrt.f64 (hypot.f64 x x))
(.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) (pow.f64 (hypot.f64 x x) 1/6)))
(cbrt.f64 (hypot.f64 x x))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(cbrt.f64 (hypot.f64 x x))
(.f64 (.f64 (pow.f64 (hypot.f64 x x) 1/6) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(cbrt.f64 (hypot.f64 x x))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 (hypot.f64 x x)))
(cbrt.f64 (hypot.f64 x x))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (*.f64 x x))) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
(.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (cbrt.f64 (.f64 x (*.f64 2 x)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(pow.f64 (hypot.f64 x x) 1/3)
(cbrt.f64 (hypot.f64 x x))
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 1)
(cbrt.f64 (hypot.f64 x x))
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2/3)
(cbrt.f64 (hypot.f64 x x))
(pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 2)
(cbrt.f64 (hypot.f64 x x))
(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 3)
(cbrt.f64 (hypot.f64 x x))
(pow.f64 (.f64 2 (.f64 x x)) 1/6)
(pow.f64 (.f64 x (.f64 2 x)) 1/6)
(sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))
(sqrt.f64 (cbrt.f64 (.f64 x (.f64 2 x))))
(log.f64 (exp.f64 (cbrt.f64 (hypot.f64 x x))))
(cbrt.f64 (hypot.f64 x x))
(log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (hypot.f64 x x)))))
(cbrt.f64 (hypot.f64 x x))
(expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x))))
(cbrt.f64 (hypot.f64 x x))
(exp.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))))
(cbrt.f64 (hypot.f64 x x))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1/3))
(cbrt.f64 (hypot.f64 x x))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 1))
(cbrt.f64 (hypot.f64 x x))
(log1p.f64 (expm1.f64 (cbrt.f64 (hypot.f64 x x))))
(cbrt.f64 (hypot.f64 x x))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 1/6))) 1)
(pow.f64 (hypot.f64 x x) 1/6)
(*.f64 (pow.f64 (hypot.f64 x x) 1/6) 1)
(pow.f64 (hypot.f64 x x) 1/6)
(*.f64 1 (pow.f64 (hypot.f64 x x) 1/6))
(pow.f64 (hypot.f64 x x) 1/6)
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6))
(pow.f64 (hypot.f64 x x) 1/6)
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(pow.f64 (hypot.f64 x x) 1/6)
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(pow.f64 (hypot.f64 x x) 1/6)
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(pow.f64 (hypot.f64 x x) 1/6)
(*.f64 (pow.f64 1 1/3) (pow.f64 (hypot.f64 x x) 1/6))
(pow.f64 (hypot.f64 x x) 1/6)
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/3) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/3))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/4)) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/4)))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/6) 4)
(pow.f64 (hypot.f64 x x) 1/6)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/2)
(pow.f64 (hypot.f64 x x) 1/6)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/3)
(pow.f64 (hypot.f64 x x) 1/6)
(pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1)
(pow.f64 (hypot.f64 x x) 1/6)
(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) 2)
(pow.f64 (hypot.f64 x x) 1/6)
(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) 3)
(pow.f64 (hypot.f64 x x) 1/6)
(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
(pow.f64 (hypot.f64 x x) 1/6)
(fabs.f64 (pow.f64 (hypot.f64 x x) 1/6))
(pow.f64 (hypot.f64 x x) 1/6)
(log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(pow.f64 (hypot.f64 x x) 1/6)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x x) 1/6))))
(pow.f64 (hypot.f64 x x) 1/6)
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(pow.f64 (hypot.f64 x x) 1/6)
(exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(pow.f64 (hypot.f64 x x) 1/6)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 1/3))
(pow.f64 (hypot.f64 x x) 1/6)
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 1/6)) 1))
(pow.f64 (hypot.f64 x x) 1/6)
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(pow.f64 (hypot.f64 x x) 1/6)
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6)))) 1)
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(pow.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6)) 1)
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(pow.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/12) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6)) 2)
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))) 3)
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(pow.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3)) 1/3)
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3) (sqrt.f64 (hypot.f64 x x))))
(sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)))
(sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 6))
(fabs.f64 (hypot.f64 x x))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 5/6)) (pow.f64 (hypot.f64 x x) 1/6)))
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6)))))
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3) (sqrt.f64 (hypot.f64 x x))))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))))
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))))
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))) 1))
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))))
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) (pow.f64 (hypot.f64 x x) 1/6))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)

eval54.0ms (1.6%)

Compiler: Compiled 1673 to 780 computations (53.4% saved)

prune14.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	110	4	114

Error

0.0b

Counts

114 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(hypot.f64 x x)
✓	29.3b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	2.2b	(.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2))
✓	1.3b	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))

Compiler

Compiled 45 to 27 computations (40% saved)

localize25.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
	0.5b	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
	0.6b	(cbrt.f64 (hypot.f64 x x))
✓	0.6b	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2)

Compiler

Compiled 81 to 24 computations (70.4% saved)

series41.0ms (1.2%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
28.0ms	x	@	0	(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
6.0ms	x	@	inf	(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
6.0ms	x	@	-inf	(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
0.0ms	x	@	0	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2)
0.0ms	x	@	-inf	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2)

rewrite59.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1846×	`add-sqr-sqrt`
1798×	`*-un-lft-identity`
1702×	`add-cube-cbrt`
1684×	`add-cbrt-cube`
204×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	249	28
2	2565	28

Stop Event

1×	node limit

Counts

2 → 40

Calls

Call 1

Inputs
(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2)
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 x x) 5/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (hypot.f64 x x) 5/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 x x) 5/12) (pow.f64 (hypot.f64 x x) 5/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 5/2) (pow.f64 (hypot.f64 x x) 5/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2) (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 5/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2) (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1/3) (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))))))

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Rules

892×	`*-commutative`
870×	`associate-r`
766×	`associate-l`
764×	`distribute-lft-in`
696×	`distribute-rgt-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1110
1	235	1096
2	612	1088
3	3149	1074
4	7808	1074

Stop Event

1×	node limit

Counts

52 → 55

Calls

Call 1

Inputs
(exp.f64 (*.f64 1/9 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/9 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/9 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/9 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6))) 1)
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) 1)
(*.f64 1 (pow.f64 (hypot.f64 x x) 5/6))
(*.f64 (pow.f64 (hypot.f64 x x) 5/12) (pow.f64 (hypot.f64 x x) 5/12))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(*.f64 (pow.f64 1 5/2) (pow.f64 (hypot.f64 x x) 5/6))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2) (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2))
(sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6))))
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3))
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)) 1))
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))) 1)
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 1)
(*.f64 1 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/6))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2) (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(*.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2)))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1/3) (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1/3))
(pow.f64 (hypot.f64 x x) 1/9)
(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 1)
(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 1/2)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/3)
(pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/6) 2)
(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 3)
(sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2))
(fabs.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(log.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))
(expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(exp.f64 (log.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 1/3))
(log1p.f64 (expm1.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))

Outputs
(exp.f64 (*.f64 1/9 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/9) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(exp.f64 (*.f64 1/9 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/9) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(exp.f64 (*.f64 1/9 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/9) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(exp.f64 (*.f64 1/9 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/9) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/9) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/9) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/9) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/9) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/9) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/9) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/9) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/9) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/9) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/9) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/9) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/9) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6))) 1)
(pow.f64 (hypot.f64 x x) 5/6)
(*.f64 (pow.f64 (hypot.f64 x x) 5/6) 1)
(pow.f64 (hypot.f64 x x) 5/6)
(*.f64 1 (pow.f64 (hypot.f64 x x) 5/6))
(pow.f64 (hypot.f64 x x) 5/6)
(*.f64 (pow.f64 (hypot.f64 x x) 5/12) (pow.f64 (hypot.f64 x x) 5/12))
(pow.f64 (hypot.f64 x x) 5/6)
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/6)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5))
(*.f64 (pow.f64 1 5/2) (pow.f64 (hypot.f64 x x) 5/6))
(pow.f64 (hypot.f64 x x) 5/6)
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2) (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5/2))
(pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 5)
(sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5))
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
(log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(pow.f64 (hypot.f64 x x) 5/6)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6))))
(pow.f64 (hypot.f64 x x) 5/6)
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/6) 3))
(pow.f64 (hypot.f64 x x) 5/6)
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(pow.f64 (hypot.f64 x x) 5/6)
(exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(pow.f64 (hypot.f64 x x) 5/6)
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 5/6)) 1))
(pow.f64 (hypot.f64 x x) 5/6)
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 5/6)))
(pow.f64 (hypot.f64 x x) 5/6)
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))) 1)
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 1)
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(*.f64 1 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/6))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2) (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(*.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2)))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 4))) (fabs.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))
(*.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 4))))
(*.f64 (pow.f64 1 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1/3) (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1/3))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1/6) 4)
(pow.f64 (hypot.f64 x x) 1/9)
(*.f64 (pow.f64 (hypot.f64 x x) 1/18) (pow.f64 (hypot.f64 x x) 1/18))
(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 1)
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 1/2)
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/3)
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/6) 2)
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 3)
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(fabs.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(log.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 1))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 1/3))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
(log1p.f64 (expm1.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))

eval61.0ms (1.8%)

Compiler: Compiled 4727 to 1955 computations (58.6% saved)

prune27.0ms (0.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	191	4	195

Error

0.0b

Counts

195 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(hypot.f64 x x)
✓	29.3b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	2.2b	(.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2))
✓	1.3b	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))

Compiler

Compiled 45 to 27 computations (40% saved)

regimes16.0ms (0.5%)

Accuracy

Total -46.2b remaining (-295962.9%)

Threshold costs -46.2b (-295962.9%)

Counts

6 → 1

Calls

Call 1

Inputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))
(.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2))

Outputs
(hypot.f64 x x)

Calls

4 calls:

4.0ms	x
4.0ms	(*.f64 2 (pow.f64 x 2))
3.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
3.0ms	(pow.f64 x 2)

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
0.0b	1	`(*.f64 2 (pow.f64 x 2))`
0.0b	1	`(pow.f64 x 2)`

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

soundness365.0ms (10.9%)

Algorithm

2×	egg-herbie

Rules

2858×	`sqr-pow`
1496×	`pow-sqr`
1326×	`distribute-lft-in`
1310×	`distribute-rgt-in`
1054×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	17
2	31	17
3	51	17
4	103	17
5	260	17
6	947	17
7	1549	17
8	1664	17
9	1834	17
10	2038	17
11	2314	17
12	2666	17
13	3094	17
14	3590	17
15	4182	17
16	4899	17
17	5153	17
18	5407	17
19	5545	17
20	5591	17
21	5615	17
22	6544	17
23	7672	17
24	7990	17
0	83	816
1	201	816
2	880	816
3	2375	688

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 105 to 73 computations (30.5% saved)

end10.0ms (0.3%)

Compiler: Compiled 4 to 2 computations (50% saved)

Details

analyze5.0ms (0.1%)

sample1.3s (40.3%)

preprocess240.0ms (7.2%)

simplify229.0ms (6.9%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series2.0ms (0.1%)

rewrite99.0ms (3%)

simplify70.0ms (2.1%)

eval8.0ms (0.2%)

prune7.0ms (0.2%)

localize5.0ms (0.2%)

series1.0ms (0%)

rewrite170.0ms (5.1%)

simplify67.0ms (2%)

localize3.0ms (0.1%)

series2.0ms (0%)

rewrite46.0ms (1.4%)

simplify73.0ms (2.2%)

eval12.0ms (0.4%)

prune8.0ms (0.2%)

localize15.0ms (0.5%)

series42.0ms (1.3%)

rewrite70.0ms (2.1%)

simplify68.0ms (2%)

eval54.0ms (1.6%)

prune14.0ms (0.4%)

localize25.0ms (0.8%)

series41.0ms (1.2%)

rewrite59.0ms (1.8%)

simplify67.0ms (2%)

eval61.0ms (1.8%)

prune27.0ms (0.8%)

regimes16.0ms (0.5%)

simplify3.0ms (0.1%)

soundness365.0ms (10.9%)

end10.0ms (0.3%)

Profiling