Details

analyze3.0ms (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 6 computations (25% saved)

sample1.1s (47%)

Results

1.1s	8256×	body	256	valid
0.0ms	3×	body	256	infinite

Bogosity

preprocess4.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

6×	`*-commutative`
2×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	11	17
2	13	17
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`
2×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	11	17
2	13	17

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.6b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.6b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	27.3b	(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))

rewrite80.0ms (3.5%)

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))))))))

simplify48.0ms (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 (0.4%)

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

prune8.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	4	47

Error

Counts

47 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(hypot.f64 x x)
▶	33.6b	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
▶	43.5b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
▶	30.1b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 34 to 25 computations (26.5% 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))

rewrite51.0ms (2.2%)

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 (3%)

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)

localize42.0ms (1.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
✓	13.1b	(sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4)))
✓	28.3b	(cbrt.f64 (.f64 2 (.f64 x x)))
✓	28.8b	(cbrt.f64 (*.f64 (pow.f64 x 4) 4))

Compiler

Compiled 61 to 41 computations (32.8% saved)

series45.0ms (2%)

Counts

4 → 12

Calls

12 calls:

Time	Variable		Point	Expression
38.0ms	x	@	0	(sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4)))
3.0ms	x	@	0	(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
1.0ms	x	@	inf	(cbrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	0	(cbrt.f64 (*.f64 (pow.f64 x 4) 4))
0.0ms	x	@	0	(cbrt.f64 (.f64 2 (.f64 x x)))

rewrite131.0ms (5.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1016×	`*-commutative`
874×	`sqrt-prod`
712×	`unswap-sqr`
620×	`swap-sqr`
454×	`sqr-pow`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	94
1	296	62
2	3419	62

Stop Event

1×	node limit

Counts

4 → 199

Calls

Call 1

Inputs
(cbrt.f64 (*.f64 (pow.f64 x 4) 4))
(cbrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4)))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (.f64 x (.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (sqrt.f64 2)) (cbrt.f64 (.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (cbrt.f64 (.f64 4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 2) (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 4) (cbrt.f64 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 4) (pow.f64 (cbrt.f64 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) (cbrt.f64 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (.f64 x 2)) (cbrt.f64 (.f64 x 2))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 2)) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)) (cbrt.f64 (.f64 4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6)) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)) (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6))) (cbrt.f64 (.f64 4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 1 1/2) (pow.f64 1 1/2)) (cbrt.f64 (.f64 4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6)) (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 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1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))) 1/2)) (fabs.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 2))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6))) (cbrt.f64 (.f64 x (.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) 1) (+.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 4 (pow.f64 x 4)) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (sqrt.f64 2)) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (.f64 x 2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 (.f64 x (.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 1 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (.f64 x (.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 x (.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (.f64 x (*.f64 x 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2))))) 1) (+.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 3/2)))) (#(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 (.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 (pow.f64 (.f64 x (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (.f64 x 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 x (.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 1 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 (.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x (sqrt.f64 2)))))))) (#(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))))))))

simplify109.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1276×	`associate-+r+`
1156×	`unswap-sqr`
1122×	`associate-+l+`
446×	`fma-def`
440×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	6263
1	625	6075
2	2014	5835
3	6159	5835

Stop Event

1×	node limit

Counts

211 → 196

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(+.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))) -1)
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))) 1)
(.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) 1)
(.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) (*.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)))
(.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (.f64 x (*.f64 x 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (*.f64 x (sqrt.f64 2)))
(.f64 (.f64 x (sqrt.f64 2)) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 1 (cbrt.f64 (.f64 4 (pow.f64 x 4))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 (cbrt.f64 x) 4) (cbrt.f64 4))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))) (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))
(*.f64 (cbrt.f64 4) (pow.f64 (cbrt.f64 x) 4))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 16))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 x (*.f64 x 2))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 16)) 1/6)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 2)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) (cbrt.f64 4))))
(.f64 (.f64 (cbrt.f64 (.f64 x 2)) (cbrt.f64 (.f64 x 2))) (pow.f64 (cbrt.f64 x) 2))
(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))))) (cbrt.f64 (cbrt.f64 (.f64 x (*.f64 x 2)))))
(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 2)) (pow.f64 (cbrt.f64 x) 2))
(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))
(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 2))
(.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)) (cbrt.f64 (*.f64 4 (pow.f64 x 4))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6)) (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))
(.f64 (.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)) (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6))) (cbrt.f64 (*.f64 4 (pow.f64 x 4))))
(.f64 (.f64 (pow.f64 1 1/2) (pow.f64 1 1/2)) (cbrt.f64 (*.f64 4 (pow.f64 x 4))))
(.f64 (.f64 (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6)) (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6))) (pow.f64 (cbrt.f64 x) 2))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) 3/2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) 3/2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/4) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 16)) 1/4))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))) 2)) (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 4))) (cbrt.f64 2))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))))) (exp.f64 (log1p.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))) 1) (+.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))))) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))))) (exp.f64 (log1p.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))))) 1))))
(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/3)
(pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) 1)
(pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 4)
(pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 6)
(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) 3)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 16)) 1/2)
(pow.f64 (.f64 x (.f64 x 2)) 2/3)
(sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 16)))
(fabs.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))
(log.f64 (exp.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))
(log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))
(expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))
(exp.f64 (log.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))
(log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))
(+.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) -1)
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 1)
(.f64 (cbrt.f64 (.f64 x (*.f64 x 2))) 1)
(.f64 (cbrt.f64 (.f64 x (*.f64 x 2))) (pow.f64 1 1/2))
(.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 1 (cbrt.f64 (.f64 x (*.f64 x 2))))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (fabs.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x 2)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6)))
(.f64 (sqrt.f64 (cbrt.f64 2)) (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (pow.f64 (cbrt.f64 x) 2))))
(.f64 (cbrt.f64 (.f64 x 2)) (cbrt.f64 x))
(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(.f64 (pow.f64 1 1/2) (cbrt.f64 (.f64 x (*.f64 x 2))))
(.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6)) (cbrt.f64 x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 4) 1/2) (pow.f64 (cbrt.f64 4) 1/2))
(*.f64 (pow.f64 (cbrt.f64 4) 1/2) (pow.f64 (pow.f64 (cbrt.f64 x) 4) 1/2))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))) 1/2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) 1/2))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) 1/2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 16))) 1/2))
(.f64 (.f64 (pow.f64 1 1/2) (pow.f64 1 1/2)) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (pow.f64 (.f64 4 (pow.f64 x 4)) 1/12) (pow.f64 (*.f64 4 (pow.f64 x 4)) 1/12))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 3/2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (*.f64 x 2)))) 3/2))
(.f64 (fabs.f64 (pow.f64 1 1/2)) (cbrt.f64 (.f64 x (*.f64 x 2))))
(.f64 (fabs.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (fabs.f64 (cbrt.f64 (.f64 x 2))) (cbrt.f64 x))
(.f64 (fabs.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6))) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (fabs.f64 (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6))) (cbrt.f64 x))
(*.f64 (fabs.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 4) 1/2)) (fabs.f64 (pow.f64 (cbrt.f64 4) 1/2)))
(.f64 (fabs.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))) 1/2)) (fabs.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) 1/2)))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 2))) (cbrt.f64 x))
(.f64 (sqrt.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6))) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) 1) (+.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (*.f64 x 2))))) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 1))))
(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/6)
(pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) 1/2)
(pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2/3)
(pow.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 4)
(pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 3)
(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 6)
(pow.f64 (.f64 x (.f64 x 2)) 1/3)
(sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))
(fabs.f64 (cbrt.f64 (.f64 x (.f64 x 2))))
(fabs.f64 (-.f64 1 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))
(fabs.f64 (neg.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(log.f64 (exp.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (.f64 x (.f64 x 2))))))
(expm1.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(exp.f64 (log.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(log1p.f64 (expm1.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(+.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) -1)
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 1)
(.f64 (cbrt.f64 (.f64 x (*.f64 x 2))) 1)
(.f64 (cbrt.f64 (.f64 x (*.f64 x 2))) (pow.f64 1 1/2))
(.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 1 (cbrt.f64 (.f64 x (*.f64 x 2))))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (fabs.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x 2)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6)))
(.f64 (sqrt.f64 (cbrt.f64 2)) (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (pow.f64 (cbrt.f64 x) 2))))
(.f64 (cbrt.f64 (.f64 x 2)) (cbrt.f64 x))
(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(.f64 (pow.f64 1 1/2) (cbrt.f64 (.f64 x (*.f64 x 2))))
(.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6)) (cbrt.f64 x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 4) 1/2) (pow.f64 (cbrt.f64 4) 1/2))
(*.f64 (pow.f64 (cbrt.f64 4) 1/2) (pow.f64 (pow.f64 (cbrt.f64 x) 4) 1/2))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))) 1/2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) 1/2))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) 1/2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 16))) 1/2))
(.f64 (.f64 (pow.f64 1 1/2) (pow.f64 1 1/2)) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (pow.f64 (.f64 4 (pow.f64 x 4)) 1/12) (pow.f64 (*.f64 4 (pow.f64 x 4)) 1/12))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 3/2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (*.f64 x 2)))) 3/2))
(.f64 (fabs.f64 (pow.f64 1 1/2)) (cbrt.f64 (.f64 x (*.f64 x 2))))
(.f64 (fabs.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (fabs.f64 (cbrt.f64 (.f64 x 2))) (cbrt.f64 x))
(.f64 (fabs.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6))) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (fabs.f64 (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6))) (cbrt.f64 x))
(*.f64 (fabs.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 4) 1/2)) (fabs.f64 (pow.f64 (cbrt.f64 4) 1/2)))
(.f64 (fabs.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))) 1/2)) (fabs.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) 1/2)))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 2))) (cbrt.f64 x))
(.f64 (sqrt.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6))) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) 1) (+.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (*.f64 x 2))))) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 1))))
(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/6)
(pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) 1/2)
(pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2/3)
(pow.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 4)
(pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 3)
(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 6)
(pow.f64 (.f64 x (.f64 x 2)) 1/3)
(fabs.f64 (cbrt.f64 (.f64 x (.f64 x 2))))
(fabs.f64 (-.f64 1 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))
(fabs.f64 (neg.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(log.f64 (exp.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (.f64 x (.f64 x 2))))))
(cbrt.f64 (.f64 x (.f64 x 2)))
(expm1.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(exp.f64 (log.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(log1p.f64 (expm1.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(+.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) -1)
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) 1)
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2))))) 1) (+.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 1))))
(pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 3/2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (.f64 x (.f64 x 2)) 1/2)
(sqrt.f64 (.f64 x (.f64 x 2)))
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(fabs.f64 (-.f64 1 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))))
(fabs.f64 (neg.f64 (*.f64 x (sqrt.f64 2))))
(log.f64 (exp.f64 (*.f64 x (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (sqrt.f64 2)))))
(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))))

Outputs
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(neg.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(neg.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(neg.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(neg.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) (neg.f64 x))
(+.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))) -1)
(cbrt.f64 (*.f64 4 (pow.f64 x 4)))
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))) 1)
(cbrt.f64 (*.f64 4 (pow.f64 x 4)))
(.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) 1)
(cbrt.f64 (*.f64 4 (pow.f64 x 4)))
(.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) (*.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)))
(cbrt.f64 (*.f64 4 (pow.f64 x 4)))
(.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (.f64 x (*.f64 x 2))))
(pow.f64 (cbrt.f64 (.f64 x (.f64 2 x))) 2)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (*.f64 x (sqrt.f64 2)))
(.f64 (.f64 x (sqrt.f64 2)) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 4)
(.f64 (.f64 x (sqrt.f64 2)) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 4)
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(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 2 x))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 4))
(.f64 (pow.f64 1 1/2) (cbrt.f64 (.f64 x (*.f64 x 2))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6)) (cbrt.f64 (.f64 x (.f64 x 2))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(.f64 (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6)) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 2 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 4) 1/2) (pow.f64 (cbrt.f64 4) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 4)) (sqrt.f64 (cbrt.f64 4)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (cbrt.f64 4)))
(*.f64 (pow.f64 (cbrt.f64 4) 1/2) (pow.f64 (pow.f64 (cbrt.f64 x) 4) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 4)) (sqrt.f64 (cbrt.f64 4)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (cbrt.f64 4)))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))) 1/2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (sqrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) 1/2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 16))) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (sqrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))
(.f64 (.f64 (pow.f64 1 1/2) (pow.f64 1 1/2)) (cbrt.f64 (.f64 x (.f64 x 2))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(.f64 (pow.f64 (.f64 4 (pow.f64 x 4)) 1/12) (pow.f64 (*.f64 4 (pow.f64 x 4)) 1/12))
(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/6)
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 3/2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (*.f64 x 2)))) 3/2))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(.f64 (fabs.f64 (pow.f64 1 1/2)) (cbrt.f64 (.f64 x (*.f64 x 2))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(.f64 (fabs.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (fabs.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 2 x)))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (fabs.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 4) (fabs.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))))
(.f64 (fabs.f64 (cbrt.f64 (.f64 x 2))) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 2 x)))
(.f64 (fabs.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6))) (cbrt.f64 (.f64 x (.f64 x 2))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(.f64 (fabs.f64 (.f64 (pow.f64 (.f64 x 2) 1/6) (pow.f64 (.f64 x 2) 1/6))) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 2 x)))
(*.f64 (fabs.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 4) 1/2)) (fabs.f64 (pow.f64 (cbrt.f64 4) 1/2)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 4)) (sqrt.f64 (cbrt.f64 4)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (cbrt.f64 4)))
(.f64 (fabs.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16))) 1/2)) (fabs.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) 1/2)))
(.f64 (sqrt.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (sqrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (sqrt.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))))))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (cbrt.f64 2))) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (.f64 x (.f64 2 x))))))
(.f64 (cbrt.f64 x) (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (.f64 2 (.f64 x x))))))
(.f64 (sqrt.f64 (.f64 (pow.f64 1 1/6) (pow.f64 1 1/6))) (cbrt.f64 (.f64 x (.f64 x 2))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6) (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6))) (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 2 x)))) (fabs.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 16)) 1/6))
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) 1) (+.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (*.f64 x 2))))) 1))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2))))) 1))))
(/.f64 (+.f64 (pow.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 2 x))))) 3) -1) (+.f64 (exp.f64 (+.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 2 x)))) (log1p.f64 (cbrt.f64 (.f64 x (.f64 2 x)))))) (+.f64 1 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 2 x))))))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 2 (.f64 x x))))) 3)) (+.f64 (exp.f64 (.f64 2 (log1p.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))) (+.f64 1 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 2 (*.f64 x x))))))))
(/.f64 (expm1.f64 (.f64 3 (log1p.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))) (+.f64 1 (+.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 2 (.f64 x x))))) (pow.f64 (exp.f64 2) (log1p.f64 (cbrt.f64 (.f64 2 (*.f64 x x))))))))
(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/6)
(pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) 1/2)
(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/6)
(pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 1)
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2/3)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 4)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 3)
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 6)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (.f64 x (.f64 x 2)) 1/3)
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(fabs.f64 (cbrt.f64 (.f64 x (.f64 x 2))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(fabs.f64 (-.f64 1 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(fabs.f64 (neg.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (exp.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (.f64 x (.f64 x 2))))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(cbrt.f64 (.f64 x (.f64 x 2)))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(expm1.f64 (log1p.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(exp.f64 (log.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(log1p.f64 (expm1.f64 (cbrt.f64 (.f64 x (.f64 x 2)))))
(cbrt.f64 (.f64 x (.f64 2 x)))
(cbrt.f64 (.f64 2 (.f64 x x)))
(+.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) -1)
(*.f64 x (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) 1)
(*.f64 x (sqrt.f64 2))
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2))))) 1) (+.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 1))
(*.f64 x (sqrt.f64 2))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 1))))
(/.f64 (+.f64 (pow.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 3) -1) (+.f64 (+.f64 (exp.f64 (+.f64 (log1p.f64 (.f64 x (sqrt.f64 2))) (log1p.f64 (.f64 x (sqrt.f64 2))))) 1) (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2))))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) 3)) (+.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) (+.f64 1 (exp.f64 (.f64 2 (log1p.f64 (.f64 x (sqrt.f64 2))))))))
(/.f64 (expm1.f64 (.f64 3 (log1p.f64 (.f64 x (sqrt.f64 2))))) (+.f64 1 (+.f64 (exp.f64 (log1p.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (exp.f64 2) (log1p.f64 (.f64 x (sqrt.f64 2)))))))
(pow.f64 (cbrt.f64 (.f64 x (.f64 x 2))) 3/2)
(pow.f64 (cbrt.f64 (.f64 x (.f64 2 x))) 3/2)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (.f64 x (.f64 x 2)) 1/2)
(sqrt.f64 (.f64 x (.f64 2 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 x 2)))
(sqrt.f64 (.f64 x (.f64 2 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(fabs.f64 (-.f64 1 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))))
(*.f64 x (sqrt.f64 2))
(fabs.f64 (neg.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(log.f64 (exp.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (sqrt.f64 2)))))
(*.f64 x (sqrt.f64 2))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(*.f64 x (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))

Compiler

Compiled 18 to 5 computations (72.2% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
0.0ms	x	@	0	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))

rewrite48.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1358×	`add-sqr-sqrt`
1344×	`*-un-lft-identity`
1256×	`add-cube-cbrt`
1236×	`add-cbrt-cube`
1228×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	165	17
2	2187	17

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))

Outputs

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

simplify63.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

934×	`*-commutative`
908×	`associate-+r+`
812×	`associate-+l+`
784×	`associate-+l-`
752×	`associate-+r-`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	523
1	118	457
2	316	397
3	975	391
4	2478	359
5	6694	359

Stop Event

1×	node limit

Counts

25 → 33

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 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(-.f64 (+.f64 1 (*.f64 (+.f64 x x) (sqrt.f64 x))) 1)
(pow.f64 (*.f64 (+.f64 x x) (sqrt.f64 x)) 1)
(pow.f64 (*.f64 (+.f64 x x) (pow.f64 x 1/4)) 2)
(pow.f64 (*.f64 (+.f64 x x) (cbrt.f64 (sqrt.f64 x))) 3)
(pow.f64 (*.f64 (+.f64 x x) (pow.f64 x 3/2)) 1/3)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 2) x) (sqrt.f64 x)))
(cbrt.f64 (*.f64 (+.f64 x x) (pow.f64 x 3/2)))
(expm1.f64 (log1p.f64 (*.f64 (+.f64 x x) (sqrt.f64 x))))
(exp.f64 (log.f64 (*.f64 (+.f64 x x) (sqrt.f64 x))))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 x x) (sqrt.f64 x))) 1))
(log1p.f64 (expm1.f64 (*.f64 (+.f64 x x) (sqrt.f64 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 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (sqrt.f64 -1) (.f64 x (sqrt.f64 -2))))
(.f64 (sqrt.f64 -1) (neg.f64 (.f64 x (sqrt.f64 -2))))
(.f64 (sqrt.f64 -1) (.f64 x (neg.f64 (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (sqrt.f64 -1) (.f64 x (sqrt.f64 -2))))
(.f64 (sqrt.f64 -1) (neg.f64 (.f64 x (sqrt.f64 -2))))
(.f64 (sqrt.f64 -1) (.f64 x (neg.f64 (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (sqrt.f64 -1) (.f64 x (sqrt.f64 -2))))
(.f64 (sqrt.f64 -1) (neg.f64 (.f64 x (sqrt.f64 -2))))
(.f64 (sqrt.f64 -1) (.f64 x (neg.f64 (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (sqrt.f64 -1) (.f64 x (sqrt.f64 -2))))
(.f64 (sqrt.f64 -1) (neg.f64 (.f64 x (sqrt.f64 -2))))
(.f64 (sqrt.f64 -1) (.f64 x (neg.f64 (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(-.f64 (+.f64 1 (*.f64 (+.f64 x x) (sqrt.f64 x))) 1)
(+.f64 (+.f64 1 (*.f64 (+.f64 x x) (sqrt.f64 x))) -1)
(+.f64 (.f64 2 (.f64 x (sqrt.f64 x))) 0)
(.f64 2 (.f64 x (sqrt.f64 x)))
(*.f64 (+.f64 x x) (sqrt.f64 x))
(*.f64 2 (pow.f64 x 3/2))
(pow.f64 (*.f64 (+.f64 x x) (sqrt.f64 x)) 1)
(+.f64 (+.f64 1 (*.f64 (+.f64 x x) (sqrt.f64 x))) -1)
(+.f64 (.f64 2 (.f64 x (sqrt.f64 x))) 0)
(.f64 2 (.f64 x (sqrt.f64 x)))
(*.f64 (+.f64 x x) (sqrt.f64 x))
(*.f64 2 (pow.f64 x 3/2))
(pow.f64 (*.f64 (+.f64 x x) (pow.f64 x 1/4)) 2)
(pow.f64 (.f64 2 (.f64 x (pow.f64 x 1/4))) 2)
(pow.f64 (*.f64 2 (pow.f64 x 5/4)) 2)
(*.f64 (pow.f64 x 5/2) 4)
(pow.f64 (*.f64 (+.f64 x x) (cbrt.f64 (sqrt.f64 x))) 3)
(.f64 (sqrt.f64 x) (.f64 8 (pow.f64 x 3)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 3))
(.f64 x (.f64 (pow.f64 x 5/2) 8))
(pow.f64 (*.f64 (+.f64 x x) (pow.f64 x 3/2)) 1/3)
(cbrt.f64 (*.f64 (+.f64 x x) (pow.f64 x 3/2)))
(cbrt.f64 (*.f64 2 (pow.f64 x 5/2)))
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(hypot.f64 x x)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(hypot.f64 x x)
(log.f64 (pow.f64 (pow.f64 (exp.f64 2) x) (sqrt.f64 x)))
(+.f64 (+.f64 1 (*.f64 (+.f64 x x) (sqrt.f64 x))) -1)
(+.f64 (.f64 2 (.f64 x (sqrt.f64 x))) 0)
(.f64 2 (.f64 x (sqrt.f64 x)))
(*.f64 (+.f64 x x) (sqrt.f64 x))
(*.f64 2 (pow.f64 x 3/2))
(cbrt.f64 (*.f64 (+.f64 x x) (pow.f64 x 3/2)))
(cbrt.f64 (*.f64 2 (pow.f64 x 5/2)))
(expm1.f64 (log1p.f64 (*.f64 (+.f64 x x) (sqrt.f64 x))))
(+.f64 (+.f64 1 (*.f64 (+.f64 x x) (sqrt.f64 x))) -1)
(+.f64 (.f64 2 (.f64 x (sqrt.f64 x))) 0)
(.f64 2 (.f64 x (sqrt.f64 x)))
(*.f64 (+.f64 x x) (sqrt.f64 x))
(*.f64 2 (pow.f64 x 3/2))
(exp.f64 (log.f64 (*.f64 (+.f64 x x) (sqrt.f64 x))))
(+.f64 (+.f64 1 (*.f64 (+.f64 x x) (sqrt.f64 x))) -1)
(+.f64 (.f64 2 (.f64 x (sqrt.f64 x))) 0)
(.f64 2 (.f64 x (sqrt.f64 x)))
(*.f64 (+.f64 x x) (sqrt.f64 x))
(*.f64 2 (pow.f64 x 3/2))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 x x) (sqrt.f64 x))) 1))
(+.f64 (+.f64 1 (*.f64 (+.f64 x x) (sqrt.f64 x))) -1)
(+.f64 (.f64 2 (.f64 x (sqrt.f64 x))) 0)
(.f64 2 (.f64 x (sqrt.f64 x)))
(*.f64 (+.f64 x x) (sqrt.f64 x))
(*.f64 2 (pow.f64 x 3/2))
(log1p.f64 (expm1.f64 (*.f64 (+.f64 x x) (sqrt.f64 x))))
(+.f64 (+.f64 1 (*.f64 (+.f64 x x) (sqrt.f64 x))) -1)
(+.f64 (.f64 2 (.f64 x (sqrt.f64 x))) 0)
(.f64 2 (.f64 x (sqrt.f64 x)))
(*.f64 (+.f64 x x) (sqrt.f64 x))
(*.f64 2 (pow.f64 x 3/2))

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)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite52.0ms (2.3%)

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)))))))

simplify57.0ms (2.5%)

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)

eval137.0ms (6%)

Compiler: Compiled 5280 to 3855 computations (27% saved)

prune76.0ms (3.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	298	0	298
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	298	4	302

Error

Counts

302 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(hypot.f64 x x)
✓	33.6b	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	43.5b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
✓	30.1b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 34 to 25 computations (26.5% saved)

regimes16.0ms (0.7%)

Accuracy

Total -63.4b remaining (-405989.7%)

Threshold costs -63.4b (-405989.7%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

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

Results

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

Compiler

Compiled 56 to 37 computations (33.9% saved)

simplify3.0ms (0.2%)

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)

soundness101.0ms (4.5%)

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

Compiler

Compiled 92 to 63 computations (31.5% saved)

end10.0ms (0.5%)

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

Details

analyze3.0ms (0.1%)

sample1.1s (47%)

preprocess4.0ms (0.2%)

simplify13.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.3%)

series2.0ms (0.1%)

rewrite80.0ms (3.5%)

simplify48.0ms (2.1%)

eval8.0ms (0.4%)

prune8.0ms (0.4%)

localize5.0ms (0.2%)

series1.0ms (0%)

rewrite51.0ms (2.2%)

simplify67.0ms (3%)

localize42.0ms (1.8%)

series45.0ms (2%)

rewrite131.0ms (5.8%)

simplify109.0ms (4.8%)

localize6.0ms (0.3%)

series2.0ms (0.1%)

rewrite48.0ms (2.1%)

simplify63.0ms (2.8%)

localize3.0ms (0.1%)

series1.0ms (0.1%)

rewrite52.0ms (2.3%)

simplify57.0ms (2.5%)

eval137.0ms (6%)

prune76.0ms (3.3%)

regimes16.0ms (0.7%)

simplify3.0ms (0.2%)

soundness101.0ms (4.5%)

end10.0ms (0.5%)

Profiling