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 10 to 5 computations (50% saved)

sample869.0ms (24%)

Results

859.0ms	8256×	body	256	valid
0.0ms	1×	body	256	infinite

Bogosity

preprocess4.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

6×	`*-commutative`
4×	`count-2`
2×	`associate-r`
2×	`fma-def`
2×	`hypot-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	14	7
2	18	7
3	19	7
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)

Compiler

Compiled 10 to 5 computations (50% saved)

simplify42.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`
4×	`count-2`
2×	`associate-r`
2×	`fma-def`
2×	`hypot-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	14	7
2	18	7
3	19	7

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)

eval0.0ms (0%)

Compiler: Compiled 12 to 5 computations (58.3% 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

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

localize2.0ms (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 (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite48.0ms (1.3%)

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)))))))

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)))))))

simplify64.0ms (1.8%)

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)

eval9.0ms (0.2%)

Compiler: Compiled 662 to 207 computations (68.7% saved)

prune10.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	6	51

Error

Counts

51 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.6b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
✓	0.0b	(hypot.f64 x x)
▶	0.6b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
▶	0.9b	(.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))))
▶	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	1.4b	(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))

Compiler

Compiled 128 to 70 computations (45.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 x x)
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 16 to 6 computations (62.5% saved)

series4.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
0.0ms	x	@	inf	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
0.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
0.0ms	x	@	0	(sqrt.f64 (hypot.f64 x x))
0.0ms	x	@	-inf	(sqrt.f64 (hypot.f64 x x))

rewrite56.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1198×	`add-sqr-sqrt`
1182×	`*-un-lft-identity`
1116×	`pow1`
1096×	`add-cube-cbrt`
1086×	`add-cbrt-cube`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	162	18
2	1556	18

Stop Event

1×	node limit

Counts

2 → 38

Calls

Call 1

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

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

Outputs

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

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

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

778×	`associate-/l*`
728×	`*-commutative`
726×	`distribute-lft-out`
702×	`unswap-sqr`
676×	`associate-+r+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	800
1	148	584
2	578	368
3	2146	368
4	6123	368

Stop Event

1×	node limit

Counts

38 → 45

Calls

Call 1

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

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

localize7.0ms (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)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(*.f64 (sqrt.f64 2) (neg.f64 x))
1.0ms	x	@	0	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) (neg.f64 x))

rewrite50.0ms (1.4%)

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)))))))

simplify71.0ms (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)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.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))
✓	0.7b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)

Compiler

Compiled 37 to 11 computations (70.3% saved)

series41.0ms (1.1%)

Counts

4 → 24

Calls

12 calls:

Time	Variable		Point	Expression
24.0ms	x	@	0	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
6.0ms	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))

rewrite75.0ms (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))))))))

simplify98.0ms (2.7%)

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)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 40 to 6 computations (85% saved)

series80.0ms (2.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
62.0ms	x	@	0	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
9.0ms	x	@	-inf	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
6.0ms	x	@	inf	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
0.0ms	x	@	inf	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
0.0ms	x	@	0	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

rewrite61.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1306×	`add-sqr-sqrt`
1296×	`*-un-lft-identity`
1196×	`add-cube-cbrt`
1180×	`add-cbrt-cube`
1168×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	49
1	177	37
2	1745	37

Stop Event

1×	node limit

Counts

3 → 47

Calls

Call 1

Inputs

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

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 x x)) 1)))) (#(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 (*.f64 x (+.f64 x x)) 1/2)))) (#(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 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 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)))))))

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

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1042×	`unswap-sqr`
1018×	`distribute-lft-in`
980×	`distribute-rgt-in`
836×	`associate-+r+`
726×	`associate-+l+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	2141
1	300	1863
2	970	1465
3	3394	1393

Stop Event

1×	node limit

Counts

83 → 78

Calls

Call 1

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

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

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
✓	0.4b	(.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))))
✓	0.5b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
	0.6b	(cbrt.f64 (hypot.f64 x x))

Compiler

Compiled 60 to 16 computations (73.3% saved)

series50.0ms (1.4%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
38.0ms	x	@	0	(.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))))
10.0ms	x	@	0	(*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
0.0ms	x	@	0	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
0.0ms	x	@	inf	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
0.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)

rewrite107.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

1626×	`add-sqr-sqrt`
1604×	`*-un-lft-identity`
1488×	`add-cube-cbrt`
1472×	`add-cbrt-cube`
218×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	77
1	261	41
2	2751	41

Stop Event

1×	node limit

Counts

3 → 55

Calls

Call 1

Inputs

(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)

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

Outputs

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

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

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

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1150×	`associate-r`
1048×	`associate-l`
916×	`log-prod`
686×	`unswap-sqr`
530×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	100	1103
1	205	1103
2	602	1103
3	3719	1103

Stop Event

1×	node limit

Counts

67 → 52

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

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

eval147.0ms (4.1%)

Compiler: Compiled 8604 to 3213 computations (62.7% saved)

prune71.0ms (2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	524	3	527
Fresh	0	0	0
Picked	1	0	1
Done	2	3	5
Total	527	6	533

Error

Counts

533 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	33.4b	(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
✓	0.6b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
✓	0.0b	(hypot.f64 x x)
▶	0.5b	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	0.9b	(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

Compiler

Compiled 56 to 34 computations (39.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 43 to 7 computations (83.7% saved)

series1.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite54.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1442×	`add-sqr-sqrt`
1424×	`*-un-lft-identity`
1324×	`add-cube-cbrt`
1306×	`add-cbrt-cube`
1298×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	78
1	192	24
2	2321	24

Stop Event

1×	node limit

Counts

2 → 28

Calls

Call 1

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

Outputs

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

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

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

892×	`*-commutative`
804×	`log-prod`
606×	`distribute-lft-out`
486×	`exp-sum`
474×	`sqr-pow`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	820
1	133	652
2	409	484
3	1749	484
4	4751	484

Stop Event

1×	node limit

Counts

40 → 37

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

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.3b	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓	0.4b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)

Compiler

Compiled 33 to 10 computations (69.7% saved)

series48.0ms (1.3%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
45.0ms	x	@	0	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
1.0ms	x	@	0	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)
1.0ms	x	@	inf	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)
1.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)
0.0ms	x	@	inf	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))

rewrite57.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1534×	`add-sqr-sqrt`
1510×	`*-un-lft-identity`
1414×	`add-cube-cbrt`
1396×	`add-cbrt-cube`
1384×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	46
1	203	20
2	2368	20

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))

Outputs

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

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

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

818×	`associate-/l*`
690×	`associate-r`
654×	`distribute-rgt-in`
640×	`log-prod`
634×	`distribute-lft-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1066
1	191	870
2	546	708
3	2394	684
4	6787	684

Stop Event

1×	node limit

Counts

48 → 57

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 1 (pow.f64 (hypot.f64 x x) 3/4)) 1)
(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/4))
(*.f64 (pow.f64 (hypot.f64 x x) 3/4) 1)
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (sqrt.f64 (hypot.f64 x x)))
(*.f64 1 (pow.f64 (hypot.f64 x x) 3/4))
(*.f64 (pow.f64 (hypot.f64 x x) 3/8) (pow.f64 (hypot.f64 x x) 3/8))
(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (hypot.f64 x x) 1/4)))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/4)) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/4))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/4)))
(*.f64 (pow.f64 1 3/4) (pow.f64 (hypot.f64 x x) 3/4))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) 3/4) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3/4))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3/2) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3/2))
(*.f64 (pow.f64 1 3/2) (pow.f64 (hypot.f64 x x) 3/4))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3/2) (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2))
(sqrt.f64 (pow.f64 (hypot.f64 x x) 3/2))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 3/4)))
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/4) 3))
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 3/4)))
(exp.f64 (*.f64 3/4 (log.f64 (hypot.f64 x x))))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 3/4))
(exp.f64 (.f64 (.f64 3/4 (log.f64 (hypot.f64 x x))) 1))
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 3/4)))
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(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 2 (.f64 x x)) 1/2)
(sqrt.f64 (.f64 2 (.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)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(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 1 (pow.f64 (hypot.f64 x x) 3/4)) 1)
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/4))
(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)
(*.f64 (pow.f64 (hypot.f64 x x) 3/4) 1)
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (sqrt.f64 (hypot.f64 x x)))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/4))
(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)
(*.f64 1 (pow.f64 (hypot.f64 x x) 3/4))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(*.f64 (pow.f64 (hypot.f64 x x) 3/8) (pow.f64 (hypot.f64 x x) 3/8))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (hypot.f64 x x) 1/4)))
(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (pow.f64 (hypot.f64 x x) 1/4) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (pow.f64 (hypot.f64 x x) 1/4) (cbrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 (hypot.f64 x x) 1/4) (.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)) 7/4))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/4)) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/4))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/4))
(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/4)))
(.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/4))))
(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/4))))
(*.f64 (pow.f64 1 3/4) (pow.f64 (hypot.f64 x x) 3/4))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) 3/4) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3/4))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) 3/4) (pow.f64 (hypot.f64 x x) 1/4))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3/2) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3/2))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/4))
(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)
(*.f64 (pow.f64 1 3/2) (pow.f64 (hypot.f64 x x) 3/4))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3/2) (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2))
(sqrt.f64 (pow.f64 (hypot.f64 x x) 3/2))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 3/4)))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/4) 3))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 3/4)))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(exp.f64 (*.f64 3/4 (log.f64 (hypot.f64 x x))))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 3/4))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(exp.f64 (.f64 (.f64 3/4 (log.f64 (hypot.f64 x x))) 1))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 3/4)))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 x x) 3/4) 1))
(+.f64 (pow.f64 (hypot.f64 x x) 3/4) 0)
(pow.f64 (hypot.f64 x x) 3/4)
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(+.f64 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (hypot.f64 x x) 1)
(+.f64 1 (-.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 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(+.f64 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(+.f64 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 x (.f64 2 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 x (.f64 2 x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(+.f64 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(+.f64 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(+.f64 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(hypot.f64 x x)
(+.f64 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(exp.f64 (log.f64 (hypot.f64 x x)))
(+.f64 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(+.f64 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(+.f64 1 (-.f64 (hypot.f64 x x) 1))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)

localize14.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
✓	33.0b	(pow.f64 (.f64 x (.f64 x 2)) 1/4)

Compiler

Compiled 28 to 20 computations (28.6% saved)

series20.0ms (0.5%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	x	@	0	(pow.f64 (.f64 x (.f64 x 2)) 1/4)
9.0ms	x	@	inf	(pow.f64 (.f64 x (.f64 x 2)) 1/4)
0.0ms	x	@	0	(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
0.0ms	x	@	inf	(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
0.0ms	x	@	-inf	(pow.f64 (.f64 x (.f64 x 2)) 1/4)

rewrite61.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1620×	`add-sqr-sqrt`
1598×	`*-un-lft-identity`
1496×	`add-cube-cbrt`
1482×	`add-cbrt-cube`
176×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	196	26
2	2240	26

Stop Event

1×	node limit

Counts

2 → 53

Calls

Call 1

Inputs
(pow.f64 (.f64 x (.f64 x 2)) 1/4)
(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)

Outputs

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

simplify95.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1264×	`associate-r`
1214×	`fma-def`
1122×	`associate-l`
992×	`+-commutative`
802×	`associate-+r-`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	2617
1	305	2417
2	859	1955
3	3970	1531
4	7651	1531

Stop Event

1×	node limit

Counts

77 → 93

Calls

Call 1

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

Outputs
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (sqrt.f64 x) (pow.f64 2 1/4))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (sqrt.f64 x) (pow.f64 2 1/4))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (sqrt.f64 x) (pow.f64 2 1/4))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (sqrt.f64 x) (pow.f64 2 1/4))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (sqrt.f64 x) (pow.f64 2 1/4))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (sqrt.f64 x) (pow.f64 2 1/4))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (sqrt.f64 x) (pow.f64 2 1/4))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (sqrt.f64 x) (pow.f64 2 1/4))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 -2 (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/4) (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 (/.f64 -1 x) -1/2))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 -2 (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/4) (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 (/.f64 -1 x) -1/2))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 -2 (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/4) (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 (/.f64 -1 x) -1/2))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 -2 (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/4) (fma.f64 -2 (log.f64 (/.f64 -1 x)) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 (/.f64 -1 x) -1/2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (exp.f64 1/4) (*.f64 2 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/4)) 2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x))))) 2)
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(pow.f64 (exp.f64 1/4) (*.f64 2 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/4)) 2)
(*.f64 x (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (exp.f64 1/4) (*.f64 2 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/4)) 2)
(*.f64 x (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (exp.f64 1/4) (*.f64 2 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/4)) 2)
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (.f64 x (*.f64 x 2))) 1/2))
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (exp.f64 1/4) (*.f64 2 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/4)) 2)
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 1))
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (exp.f64 1/4) (*.f64 2 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/4)) 2)
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (exp.f64 1/4) (*.f64 2 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/4)) 2)
(*.f64 x (sqrt.f64 2))

eval340.0ms (9.4%)

Compiler: Compiled 4784 to 2276 computations (52.4% saved)

prune44.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	335	3	338
Fresh	0	0	0
Picked	1	0	1
Done	3	2	5
Total	339	5	344

Error

Counts

344 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(hypot.f64 x x)
▶	0.4b	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (pow.f64 (hypot.f64 x x) 1/4))
▶	32.4b	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))
✓	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	33.3b	(sqrt.f64 (*.f64 2 (pow.f64 (/.f64 -1 x) -2)))

Compiler

Compiled 40 to 29 computations (27.5% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 (/.f64 -1 x) -2))
✓	0.2b	(pow.f64 (/.f64 -1 x) -2)
✓	32.2b	(sqrt.f64 (*.f64 2 (pow.f64 (/.f64 -1 x) -2)))

Compiler

Compiled 28 to 23 computations (17.9% saved)

series2.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(pow.f64 (/.f64 -1 x) -2)
0.0ms	x	@	0	(pow.f64 (/.f64 -1 x) -2)
0.0ms	x	@	-inf	(pow.f64 (/.f64 -1 x) -2)
0.0ms	x	@	0	(sqrt.f64 (*.f64 2 (pow.f64 (/.f64 -1 x) -2)))
0.0ms	x	@	inf	(sqrt.f64 (*.f64 2 (pow.f64 (/.f64 -1 x) -2)))

rewrite68.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1868×	`add-sqr-sqrt`
1842×	`*-un-lft-identity`
1710×	`add-cube-cbrt`
1694×	`add-cbrt-cube`
202×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	55
1	226	49
2	2493	49

Stop Event

1×	node limit

Counts

3 → 55

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (pow.f64 (/.f64 -1 x) -2)))
(pow.f64 (/.f64 -1 x) -2)
(*.f64 2 (pow.f64 (/.f64 -1 x) -2))

Outputs

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

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

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

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

674×	`unswap-sqr`
534×	`associate-*r/`
480×	`distribute-lft-neg-out`
454×	`distribute-lft-in`
444×	`distribute-rgt-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1149
1	271	1149
2	1046	1125
3	4054	1101

Stop Event

1×	node limit

Counts

91 → 66

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

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

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))
0.0ms	x	@	0	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))
0.0ms	x	@	inf	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))

rewrite56.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1554×	`add-sqr-sqrt`
1538×	`*-un-lft-identity`
1424×	`add-cube-cbrt`
1406×	`add-cbrt-cube`
1392×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	178	11
2	2018	11

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

simplify67.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

892×	`*-commutative`
830×	`log-prod`
818×	`associate-*r/`
618×	`associate--l+`
596×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	331
1	98	331
2	342	331
3	1791	331
4	4221	331
5	6315	331

Stop Event

1×	node limit

Counts

25 → 19

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 x (sqrt.f64 2))) 1)
(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 (.f64 x (.f64 x 2)) 1/2)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(sqrt.f64 (.f64 x (.f64 x 2)))
(log.f64 (exp.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))))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 1))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))

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

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (hypot.f64 x x) 1/4)
	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.3b	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (pow.f64 (hypot.f64 x x) 1/4))
	0.4b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)

Compiler

Compiled 34 to 14 computations (58.8% saved)

series0.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (pow.f64 (hypot.f64 x x) 1/4))
0.0ms	x	@	inf	(pow.f64 (hypot.f64 x x) 1/4)
0.0ms	x	@	-inf	(pow.f64 (hypot.f64 x x) 1/4)
0.0ms	x	@	inf	(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (pow.f64 (hypot.f64 x x) 1/4))
0.0ms	x	@	0	(pow.f64 (hypot.f64 x x) 1/4)

rewrite56.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1732×	`add-sqr-sqrt`
1704×	`*-un-lft-identity`
1604×	`add-cube-cbrt`
1584×	`add-cbrt-cube`
210×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	231	20
2	2674	20

Stop Event

1×	node limit

Counts

2 → 34

Calls

Call 1

Inputs
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (pow.f64 (hypot.f64 x x) 1/4))
(pow.f64 (hypot.f64 x x) 1/4)

Outputs

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

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

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1294×	`distribute-lft-in`
1202×	`distribute-rgt-in`
890×	`*-commutative`
718×	`associate-r`
634×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	986
1	208	978
2	561	906
3	2716	834

Stop Event

1×	node limit

Counts

58 → 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))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x x))) 1)
(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)))
(log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x x))))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 1/4))) 1)
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) 1)
(*.f64 1 (pow.f64 (hypot.f64 x x) 1/4))
(*.f64 (pow.f64 (hypot.f64 x x) 1/8) (pow.f64 (hypot.f64 x x) 1/8))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/4)))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/4)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/4) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/4))
(*.f64 (pow.f64 1 1/4) (pow.f64 (hypot.f64 x x) 1/4))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) 1/4) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/4))
(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
(fabs.f64 (pow.f64 (hypot.f64 x x) 1/4))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 1/4)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x x) 1/4))))
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3))
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 1/4)))
(exp.f64 (*.f64 1/4 (log.f64 (hypot.f64 x x))))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (hypot.f64 x x))) 1))
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 1/4)))

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

eval45.0ms (1.3%)

Compiler: Compiled 2421 to 1496 computations (38.2% saved)

prune28.0ms (0.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	195	5	200

Error

Counts

200 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(hypot.f64 x x)
✓	32.4b	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))
✓	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	33.3b	(sqrt.f64 (*.f64 2 (pow.f64 (/.f64 -1 x) -2)))
	49.0b	(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (/.f64 -1 x)) -4)))

Compiler

Compiled 37 to 30 computations (18.9% saved)

regimes29.0ms (0.8%)

Accuracy

Total -64.0b remaining (-233957.1%)

Threshold costs -64.0b (-233957.1%)

Counts

14 → 1

Calls

Call 1

Inputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))
(sqrt.f64 (*.f64 2 (pow.f64 (/.f64 -1 x) -2)))
(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (/.f64 -1 x)) -4)))
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (pow.f64 (hypot.f64 x x) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.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 (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))))

Outputs
(hypot.f64 x x)

Calls

4 calls:

9.0ms	(*.f64 x x)
8.0ms	x
4.0ms	(+.f64 (.f64 x x) (.f64 x x))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Results

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

Compiler

Compiled 164 to 73 computations (55.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

soundness12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`
4×	`count-2`
2×	`associate-r`
2×	`fma-def`
2×	`hypot-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	14	7
2	18	7
3	19	7

Stop Event

1×

saturated

Compiler

Compiled 12 to 5 computations (58.3% saved)

end10.0ms (0.3%)

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

Details

analyze3.0ms (0.1%)

sample869.0ms (24%)

preprocess4.0ms (0.1%)

simplify42.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize2.0ms (0.1%)

series2.0ms (0.1%)

rewrite48.0ms (1.3%)

simplify64.0ms (1.8%)

eval9.0ms (0.2%)

prune10.0ms (0.3%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite56.0ms (1.5%)

simplify55.0ms (1.5%)

localize7.0ms (0.2%)

series2.0ms (0%)

rewrite50.0ms (1.4%)

simplify71.0ms (2%)

localize20.0ms (0.5%)

series41.0ms (1.1%)

rewrite75.0ms (2.1%)

simplify98.0ms (2.7%)

localize10.0ms (0.3%)

series80.0ms (2.2%)

rewrite61.0ms (1.7%)

simplify65.0ms (1.8%)

localize16.0ms (0.5%)

series50.0ms (1.4%)

rewrite107.0ms (3%)

simplify55.0ms (1.5%)

eval147.0ms (4.1%)

prune71.0ms (2%)

localize12.0ms (0.3%)

series1.0ms (0%)

rewrite54.0ms (1.5%)

simplify57.0ms (1.6%)

localize14.0ms (0.4%)

series48.0ms (1.3%)

rewrite57.0ms (1.6%)

simplify65.0ms (1.8%)

localize14.0ms (0.4%)

series20.0ms (0.5%)

rewrite61.0ms (1.7%)

simplify95.0ms (2.6%)

eval340.0ms (9.4%)

prune44.0ms (1.2%)

localize12.0ms (0.3%)

series2.0ms (0%)

rewrite68.0ms (1.9%)

simplify61.0ms (1.7%)

localize8.0ms (0.2%)

series1.0ms (0%)

rewrite56.0ms (1.5%)

simplify67.0ms (1.9%)

localize18.0ms (0.5%)

series0.0ms (0%)

rewrite56.0ms (1.6%)

simplify61.0ms (1.7%)

eval45.0ms (1.3%)

prune28.0ms (0.8%)

regimes29.0ms (0.8%)

simplify3.0ms (0.1%)

soundness12.0ms (0.3%)

end10.0ms (0.3%)

Profiling