Details

analyze125.0ms (6.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
40.6%	40.6%	59.3%	0.1%	0%	0%	0%	7
46%	45.3%	53.1%	0.1%	1.6%	0%	0%	8
65.3%	63.2%	33.6%	0.1%	3.1%	0%	0%	9
69.5%	66%	28.9%	0.1%	5.1%	0%	0%	10
80.9%	75.1%	17.8%	0.1%	7%	0%	0%	11
83.6%	76.6%	15%	0.1%	8.3%	0%	0%	12

Compiler

Compiled 10 to 6 computations (40% saved)

sample977.0ms (53.5%)

Results

935.0ms	8256×	body	256	valid
30.0ms	377×	body	256	infinite

Bogosity

preprocess6.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

8×	`associate-/r*`
4×	`*-commutative`
4×	`count-2`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	14	38
2	19	38
3	23	38
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 y x) (+.f64 x x))

Outputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 y x) (+.f64 x x))
(/.f64 (+.f64 x y) (+.f64 x x))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify12.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

4×	`associate-/r*`
2×	`*-commutative`
2×	`count-2`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	10	19
2	13	19
3	15	19

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))

Outputs
(/.f64 (+.f64 x y) (+.f64 y y))

eval0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.5b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.f64 (+.f64 x y) (+.f64 y y))

Compiler

Compiled 9 to 5 computations (44.4% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (+.f64 x y) (+.f64 y y))

Compiler

Compiled 17 to 5 computations (70.6% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/.f64 (+.f64 x y) (+.f64 y y))
0.0ms	y	@	0	(/.f64 (+.f64 x y) (+.f64 y y))
0.0ms	x	@	0	(/.f64 (+.f64 x y) (+.f64 y y))
0.0ms	y	@	inf	(/.f64 (+.f64 x y) (+.f64 y y))
0.0ms	x	@	-inf	(/.f64 (+.f64 x y) (+.f64 y y))

rewrite56.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1820×	`add-sqr-sqrt`
1802×	`*-un-lft-identity`
1692×	`add-cube-cbrt`
1674×	`add-cbrt-cube`
174×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	162	19
2	2568	19

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))

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

Outputs

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

simplify18.0ms (1%)

Algorithm

1×	egg-herbie

Rules

44×	`*-commutative`
22×	`sqr-pow`
20×	`associate-*r/`
18×	`associate-*l/`
16×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	890
1	291	890

Stop Event

1×

unsound

Counts

58 → 48

Calls

Call 1

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

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

eval8.0ms (0.5%)

Compiler: Compiled 483 to 282 computations (41.6% saved)

prune9.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Error

Counts

49 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (+.f64 x y) (+.f64 y y))
▶	37.5b	(/.f64 (*.f64 1/2 x) y)
▶	0.0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	26.4b	1/2
	62.4b	-1

Compiler

Compiled 31 to 23 computations (25.8% saved)

localize8.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))

Compiler

Compiled 20 to 13 computations (35% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
0.0ms	x	@	0	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
0.0ms	y	@	0	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
0.0ms	y	@	inf	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
0.0ms	y	@	-inf	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))

rewrite67.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1440×	`associate-*r/`
1268×	`associate-/r*`
990×	`associate-/l*`
886×	`associate-*l/`
882×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	178	19
2	2458	19

Stop Event

1×	node limit

Counts

1 → 70

Calls

Call 1

Inputs
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))

Outputs
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Outputs

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(/.f64 x y))) 2) (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 1/2)))))

simplify70.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1352×	`associate-/l*`
1288×	`associate-/r*`
1028×	`associate-*r/`
1010×	`distribute-lft-in`
914×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	4876
1	586	4364
2	2236	4360

Stop Event

1×	node limit

Counts

94 → 130

Calls

Call 1

Inputs
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y)))) 1/2)
(-.f64 (exp.f64 (log.f64 (+.f64 3/2 (*.f64 1/2 (/.f64 x y))))) 1)
(-.f64 (/.f64 1/4 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))) (/.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))
(-.f64 (+.f64 1/2 (exp.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y))))) 1)
(.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y))) 1)
(.f64 1 (+.f64 1/2 (.f64 1/2 (/.f64 x y))))
(.f64 (sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) (sqrt.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))))
(.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))) 2))
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(.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (/.f64 1 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))
(.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (/.f64 1 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(.f64 (/.f64 1 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))) (-.f64 1/4 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2)))
(.f64 (/.f64 1 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))) (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))))
(.f64 (/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))) (+.f64 1/2 (.f64 1/2 (/.f64 x y))))
(.f64 (/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (-.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))) (+.f64 1/4 (/.f64 (+.f64 1/4 (*.f64 (/.f64 1/4 y) x)) (/.f64 y x))))
(.f64 (/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (-.f64 1/16 (.f64 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))) (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))))) (+.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (.f64 (/.f64 1/4 y) x)))
(.f64 (/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (+.f64 1/64 (pow.f64 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))) 3))) (+.f64 1/16 (.f64 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))) (-.f64 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))) 1/4))))
(/.f64 1 (/.f64 1 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))))
(/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (+.f64 1/2 (.f64 -1/2 (/.f64 x y))))
(/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))))
(/.f64 (sqrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))) (/.f64 (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))) (sqrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))))))
(/.f64 (sqrt.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))) (/.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y))) (sqrt.f64 (-.f64 1/4 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2)))))
(/.f64 (.f64 (cbrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))) (cbrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))))) (/.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))) (cbrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))))))
(/.f64 (.f64 (cbrt.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))) (cbrt.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)))) (/.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y))) (cbrt.f64 (-.f64 1/4 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2)))))
(/.f64 (-.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) 1/4) (-.f64 (.f64 1/2 (/.f64 x y)) 1/2))
(/.f64 (-.f64 1/64 (/.f64 (/.f64 1/64 (pow.f64 (/.f64 y x) 3)) (pow.f64 (/.f64 y x) 3))) (.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))) (-.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))))
(/.f64 (-.f64 1/16 (/.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) (.f64 y (/.f64 2 x)))) (.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y))) (+.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))))
(/.f64 (+.f64 1/512 (pow.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) 3)) (.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))) (+.f64 1/64 (*.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) (-.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) 1/8)))))
(/.f64 (-.f64 1/64 (pow.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) 3)) (.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y))) (+.f64 1/16 (.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (+.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))))))
(/.f64 (neg.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))) (neg.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))))
(/.f64 (neg.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))) (neg.f64 (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (.f64 1 (-.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) 1/4)) (-.f64 (*.f64 1/2 (/.f64 x y)) 1/2))
(/.f64 (.f64 1 (neg.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)))) (neg.f64 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))
(/.f64 (.f64 1 (neg.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))))) (neg.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) (sqrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))))) (sqrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) (sqrt.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)))) (sqrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) 2) (cbrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))))) (cbrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) 2) (cbrt.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)))) (cbrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) 1/4) 1) (-.f64 (*.f64 1/2 (/.f64 x y)) 1/2))
(/.f64 (.f64 (neg.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))) 1) (neg.f64 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))
(/.f64 (.f64 (neg.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))) 1) (neg.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (.f64 (sqrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))) (sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y))))) (sqrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (.f64 (sqrt.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))) (sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y))))) (sqrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))))
(/.f64 (.f64 (cbrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) 2)) (cbrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (.f64 (cbrt.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))) (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) 2)) (cbrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))))
(/.f64 (.f64 (-.f64 1/16 (/.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) (.f64 y (/.f64 2 x)))) (/.f64 1 (+.f64 1/2 (.f64 -1/2 (/.f64 x y))))) (+.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)))
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(/.f64 (.f64 (+.f64 1/512 (pow.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) 3)) (/.f64 1 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))))) (+.f64 1/64 (*.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) (-.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) 1/8))))
(/.f64 (/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) 1) (+.f64 1/2 (.f64 -1/2 (/.f64 x y))))
(/.f64 (/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (sqrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y))))) (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))
(/.f64 (/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (.f64 (cbrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))) (cbrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))))) (cbrt.f64 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))
(/.f64 (/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) 1) (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))))
(/.f64 (/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (sqrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))))) (sqrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (.f64 (cbrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))) (cbrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))) (cbrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(pow.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y))) 1)
(pow.f64 (sqrt.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))) 2)
(pow.f64 (cbrt.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))) 3)
(pow.f64 (pow.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y))) 3) 1/3)
(sqrt.f64 (pow.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y))) 2))
(log.f64 (exp.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y))))))
(cbrt.f64 (pow.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y))) 3))
(expm1.f64 (log.f64 (+.f64 3/2 (*.f64 1/2 (/.f64 x y)))))
(exp.f64 (log.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))))
(log1p.f64 (expm1.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))))
(fma.f64 (*.f64 1/2 x) (/.f64 1 y) 1/2)
(fma.f64 1 (*.f64 1/2 (/.f64 x y)) 1/2)
(fma.f64 (sqrt.f64 (.f64 1/2 (/.f64 x y))) (sqrt.f64 (.f64 1/2 (/.f64 x y))) 1/2)
(fma.f64 (pow.f64 (cbrt.f64 (.f64 1/2 (/.f64 x y))) 2) (cbrt.f64 (.f64 1/2 (/.f64 x y))) 1/2)

Outputs
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
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(fma.f64 1/2 (/.f64 x y) 1/2)
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(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
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(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y)))) 1/2)
(+.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y)))) -1/2)
(+.f64 1/2 (expm1.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y)))))
(+.f64 1/2 (expm1.f64 (log1p.f64 (*.f64 x (/.f64 1/2 y)))))
(-.f64 (exp.f64 (log.f64 (+.f64 3/2 (*.f64 1/2 (/.f64 x y))))) 1)
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(/.f64 (-.f64 1/4 (pow.f64 (*.f64 x (/.f64 1/2 y)) 2)) (fma.f64 (/.f64 x y) -1/2 1/2))
(-.f64 (+.f64 1/2 (exp.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y))))) 1)
(+.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y)))) -1/2)
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(+.f64 1/2 (expm1.f64 (log1p.f64 (*.f64 x (/.f64 1/2 y)))))
(.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y))) 1)
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(.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))) 2))
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(/.f64 1 (/.f64 1 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))))
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(/.f64 (sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 (/.f64 x y) -1/2))) (sqrt.f64 (-.f64 1/4 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2)))))
(.f64 (/.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) (sqrt.f64 (fma.f64 (/.f64 x y) -1/2 1/2))) (sqrt.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))))
(.f64 (sqrt.f64 (-.f64 1/4 (pow.f64 (.f64 x (/.f64 1/2 y)) 2))) (/.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) (sqrt.f64 (fma.f64 (/.f64 x y) -1/2 1/2))))
(/.f64 (.f64 (cbrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) 2)) (cbrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) 2) (/.f64 (cbrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (*.f64 (/.f64 -1/4 y) x)))) (cbrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))))))
(.f64 (/.f64 (cbrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))) (cbrt.f64 (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (.f64 1/2 (/.f64 x y)) 2))))) (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 2))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 2) (/.f64 (cbrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))) (cbrt.f64 (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (.f64 x (/.f64 1/2 y)) 2))))))
(/.f64 (.f64 (cbrt.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))) (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) 2)) (cbrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))))
(/.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x y)))) 2) (/.f64 (cbrt.f64 (+.f64 1/2 (.f64 (/.f64 x y) -1/2))) (cbrt.f64 (-.f64 1/4 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 2) (cbrt.f64 (fma.f64 (/.f64 x y) -1/2 1/2))) (cbrt.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))))
(.f64 (cbrt.f64 (-.f64 1/4 (pow.f64 (.f64 x (/.f64 1/2 y)) 2))) (/.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 2) (cbrt.f64 (fma.f64 (/.f64 x y) -1/2 1/2))))
(/.f64 (.f64 (-.f64 1/16 (/.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) (.f64 y (/.f64 2 x)))) (/.f64 1 (+.f64 1/2 (.f64 -1/2 (/.f64 x y))))) (+.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)))
(/.f64 (-.f64 1/16 (/.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) (.f64 y (/.f64 2 x)))) (.f64 (+.f64 1/2 (.f64 (/.f64 x y) -1/2)) (+.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))))
(/.f64 (-.f64 1/16 (/.f64 1/8 (.f64 y (.f64 (/.f64 2 x) (pow.f64 (/.f64 y x) 3))))) (.f64 (fma.f64 (/.f64 x y) -1/2 1/2) (+.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))))
(/.f64 (+.f64 1/16 (/.f64 (/.f64 -1/8 y) (.f64 (pow.f64 (/.f64 y x) 3) (/.f64 2 x)))) (.f64 (fma.f64 (/.f64 x y) -1/2 1/2) (+.f64 1/4 (pow.f64 (*.f64 x (/.f64 1/2 y)) 2))))
(/.f64 (.f64 (-.f64 1/64 (pow.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) 3)) (/.f64 1 (+.f64 1/2 (.f64 -1/2 (/.f64 x y))))) (+.f64 1/16 (.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (+.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)))))
(/.f64 (-.f64 1/64 (pow.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) 3)) (.f64 (+.f64 1/2 (.f64 (/.f64 x y) -1/2)) (+.f64 1/16 (.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (+.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2))))))
(/.f64 (-.f64 1/64 (pow.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) 3)) (.f64 (fma.f64 (/.f64 x y) -1/2 1/2) (+.f64 1/16 (fma.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (pow.f64 (.f64 1/2 (/.f64 x y)) 4)))))
(/.f64 (-.f64 1/64 (pow.f64 (pow.f64 (.f64 x (/.f64 1/2 y)) 2) 3)) (.f64 (fma.f64 (/.f64 x y) -1/2 1/2) (+.f64 1/16 (fma.f64 1/4 (pow.f64 (.f64 x (/.f64 1/2 y)) 2) (pow.f64 (.f64 x (/.f64 1/2 y)) 4)))))
(/.f64 (.f64 (-.f64 1/64 (/.f64 (/.f64 1/64 (pow.f64 (/.f64 y x) 3)) (pow.f64 (/.f64 y x) 3))) (/.f64 1 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))))) (-.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))))
(/.f64 (-.f64 1/64 (/.f64 1/64 (.f64 (pow.f64 (/.f64 y x) 3) (pow.f64 (/.f64 y x) 3)))) (.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (.f64 (/.f64 -1/4 y) x))) (-.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)))))
(/.f64 (+.f64 1/64 (/.f64 -1/64 (pow.f64 (/.f64 y x) 6))) (.f64 (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (.f64 1/2 (/.f64 x y)) 2))) (+.f64 1/8 (/.f64 -1/8 (pow.f64 (/.f64 y x) 3)))))
(/.f64 (-.f64 1/64 (/.f64 1/64 (pow.f64 (/.f64 y x) 6))) (.f64 (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (.f64 x (/.f64 1/2 y)) 2))) (+.f64 1/8 (/.f64 -1/8 (pow.f64 (/.f64 y x) 3)))))
(/.f64 (.f64 (+.f64 1/512 (pow.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) 3)) (/.f64 1 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))))) (+.f64 1/64 (*.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) (-.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) 1/8))))
(/.f64 (+.f64 1/512 (/.f64 1/512 (pow.f64 (pow.f64 (/.f64 y x) 3) 3))) (.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (.f64 (/.f64 -1/4 y) x))) (+.f64 1/64 (.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) (+.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) -1/8)))))
(/.f64 (+.f64 1/512 (/.f64 1/512 (pow.f64 (pow.f64 (/.f64 y x) 3) 3))) (.f64 (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (.f64 1/2 (/.f64 x y)) 2))) (fma.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) (+.f64 (/.f64 1/8 (pow.f64 (/.f64 y x) 3)) -1/8) 1/64)))
(/.f64 (/.f64 (+.f64 1/512 (/.f64 1/512 (pow.f64 (pow.f64 (/.f64 y x) 3) 3))) (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (*.f64 x (/.f64 1/2 y)) 2)))) (+.f64 (+.f64 1/64 (/.f64 1/64 (pow.f64 (/.f64 y x) 6))) (/.f64 -1/64 (pow.f64 (/.f64 y x) 3))))
(/.f64 (/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) 1) (+.f64 1/2 (.f64 -1/2 (/.f64 x y))))
(/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (+.f64 1/2 (.f64 (/.f64 x y) -1/2)))
(/.f64 (-.f64 1/4 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2)) (fma.f64 (/.f64 x y) -1/2 1/2))
(/.f64 (-.f64 1/4 (pow.f64 (*.f64 x (/.f64 1/2 y)) 2)) (fma.f64 (/.f64 x y) -1/2 1/2))
(/.f64 (/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (sqrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y))))) (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))
(/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (+.f64 1/2 (.f64 (/.f64 x y) -1/2)))
(/.f64 (-.f64 1/4 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2)) (fma.f64 (/.f64 x y) -1/2 1/2))
(/.f64 (-.f64 1/4 (pow.f64 (*.f64 x (/.f64 1/2 y)) 2)) (fma.f64 (/.f64 x y) -1/2 1/2))
(/.f64 (/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (.f64 (cbrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))) (cbrt.f64 (+.f64 1/2 (.f64 -1/2 (/.f64 x y)))))) (cbrt.f64 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))
(/.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (/.f64 x y)) 2)) (+.f64 1/2 (.f64 (/.f64 x y) -1/2)))
(/.f64 (-.f64 1/4 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2)) (fma.f64 (/.f64 x y) -1/2 1/2))
(/.f64 (-.f64 1/4 (pow.f64 (*.f64 x (/.f64 1/2 y)) 2)) (fma.f64 (/.f64 x y) -1/2 1/2))
(/.f64 (/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) 1) (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))))
(/.f64 (.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) 1) (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (*.f64 (/.f64 -1/4 y) x))))
(/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (*.f64 1/2 (/.f64 x y)) 2))))
(/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (*.f64 x (/.f64 1/2 y)) 2))))
(/.f64 (/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (sqrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x)))))) (sqrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) 1) (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (*.f64 (/.f64 -1/4 y) x))))
(/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (*.f64 1/2 (/.f64 x y)) 2))))
(/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (*.f64 x (/.f64 1/2 y)) 2))))
(/.f64 (/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (.f64 (cbrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))) (cbrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))) (cbrt.f64 (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (/.f64 -1/4 (/.f64 y x))))))
(/.f64 (.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) 1) (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x y)) 2) (*.f64 (/.f64 -1/4 y) x))))
(/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (*.f64 1/2 (/.f64 x y)) 2))))
(/.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (/.f64 y x) 3))) (+.f64 1/4 (fma.f64 (/.f64 -1/4 y) x (pow.f64 (*.f64 x (/.f64 1/2 y)) 2))))
(pow.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y))) 1)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(pow.f64 (sqrt.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))) 2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(pow.f64 (cbrt.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))) 3)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(pow.f64 (pow.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y))) 3) 1/3)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(sqrt.f64 (pow.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y))) 2))
(fabs.f64 (fma.f64 1/2 (/.f64 x y) 1/2))
(log.f64 (exp.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y))))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(cbrt.f64 (pow.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y))) 3))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(expm1.f64 (log.f64 (+.f64 3/2 (*.f64 1/2 (/.f64 x y)))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(exp.f64 (log.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(log1p.f64 (expm1.f64 (+.f64 1/2 (*.f64 1/2 (/.f64 x y)))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(fma.f64 (*.f64 1/2 x) (/.f64 1 y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(fma.f64 1 (*.f64 1/2 (/.f64 x y)) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(fma.f64 (sqrt.f64 (.f64 1/2 (/.f64 x y))) (sqrt.f64 (.f64 1/2 (/.f64 x y))) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(fma.f64 (pow.f64 (cbrt.f64 (.f64 1/2 (/.f64 x y))) 2) (cbrt.f64 (.f64 1/2 (/.f64 x y))) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)

localize5.0ms (0.3%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

eval63.0ms (3.4%)

Compiler: Compiled 3656 to 2502 computations (31.6% saved)

prune20.0ms (1.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	129	6	135

Error

Counts

135 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (+.f64 x y) (+.f64 y y))
✓	37.5b	(/.f64 (*.f64 1/2 x) y)
✓	0.0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
▶	37.6b	(*.f64 x (/.f64 1/2 y))
	26.4b	1/2
	62.4b	-1

Compiler

Compiled 38 to 28 computations (26.3% saved)

localize9.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (/.f64 1/2 y))

Compiler

Compiled 13 to 8 computations (38.5% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite51.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1450×	`add-sqr-sqrt`
1426×	`*-un-lft-identity`
1332×	`add-cube-cbrt`
1316×	`add-cbrt-cube`
1302×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	148	13
2	1796	13

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(*.f64 x (/.f64 1/2 y))

Outputs

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

simplify47.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1702×	`distribute-lft-in`
1574×	`associate-/r/`
1164×	`associate-r`
1042×	`associate-l`
726×	`associate-+l+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	605
1	142	605
2	537	605
3	4171	605

Stop Event

1×	node limit

Counts

45 → 25

Calls

Call 1

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

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

eval5.0ms (0.3%)

Compiler: Compiled 197 to 125 computations (36.5% saved)

prune5.0ms (0.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	25	6	31

Error

Counts

31 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (+.f64 x y) (+.f64 y y))
✓	37.5b	(/.f64 (*.f64 1/2 x) y)
✓	0.0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
✓	37.6b	(*.f64 x (/.f64 1/2 y))
	26.4b	1/2
	62.4b	-1

Compiler

Compiled 38 to 28 computations (26.3% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	4	4
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (+.f64 x y) (+.f64 y y))
✓	37.5b	(/.f64 (*.f64 1/2 x) y)
✓	0.0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
✓	37.6b	(*.f64 x (/.f64 1/2 y))
	26.4b	1/2
	62.4b	-1

Compiler

Compiled 38 to 28 computations (26.3% saved)

regimes15.0ms (0.8%)

Counts

6 → 1

Calls

Call 1

Inputs
-1
1/2
(*.f64 x (/.f64 1/2 y))
(/.f64 (*.f64 1/2 x) y)
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(/.f64 (+.f64 x y) (+.f64 y y))

Outputs
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))

Calls

3 calls:

5.0ms	x
4.0ms	y
4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 43 to 27 computations (37.2% saved)

regimes38.0ms (2.1%)

Counts

4 → 5

Calls

Call 1

Inputs
-1
1/2
(*.f64 x (/.f64 1/2 y))
(/.f64 (*.f64 1/2 x) y)

Outputs
1/2
(/.f64 (*.f64 1/2 x) y)
1/2
(/.f64 (*.f64 1/2 x) y)
1/2

Calls

2 calls:

20.0ms	x
17.0ms	y

Results

Error	Segments	Branch
16.1b	5	`x`
15.3b	5	`y`

Compiler

Compiled 20 to 14 computations (30% saved)

bsearch43.0ms (2.3%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
7.0ms	7.496289847181478e+78	1.2476957871432609e+79
10.0ms	18602638049556416.0	1431552957006553900.0
17.0ms	1.3490586795095852e-86	4.829755626483052e-58
8.0ms	-3.288700410405478e+109	-1.2471618721007155e+109

Results

37.0ms	432×	body	256	valid
0.0ms	3×	body	256	infinite

Compiler

Compiled 338 to 279 computations (17.5% saved)

regimes34.0ms (1.9%)

Counts

3 → 5

Calls

Call 1

Inputs
-1
1/2
(*.f64 x (/.f64 1/2 y))

Outputs
1/2
(*.f64 x (/.f64 1/2 y))
1/2
(*.f64 x (/.f64 1/2 y))
1/2

Calls

2 calls:

18.0ms	x
15.0ms	y

Results

Error	Segments	Branch
16.2b	5	`x`
15.3b	5	`y`

Compiler

Compiled 15 to 11 computations (26.7% saved)

bsearch43.0ms (2.3%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
6.0ms	7.496289847181478e+78	1.2476957871432609e+79
11.0ms	18602638049556416.0	1431552957006553900.0
17.0ms	1.3490586795095852e-86	4.829755626483052e-58
8.0ms	-3.288700410405478e+109	-1.2471618721007155e+109

Results

37.0ms	432×	body	256	valid
0.0ms	4×	body	256	infinite

Compiler

Compiled 338 to 279 computations (17.5% saved)

regimes8.0ms (0.4%)

Accuracy

Total -36.7b remaining (-139.2%)

Threshold costs -36.7b (-139.2%)

Counts

2 → 1

Calls

Call 1

Inputs
-1
1/2

Outputs
1/2

Calls

2 calls:

4.0ms	y
3.0ms	x

Results

Error	Segments	Branch
26.4b	1	`x`
26.4b	1	`y`

Compiler

Compiled 10 to 8 computations (20% saved)

simplify10.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

16×	`not-or`
12×	`not-not`
12×	`if-if-or-not`
12×	`if-not`
4×	`not-and`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	151
1	49	151
2	55	151
3	67	143
4	75	143
5	83	143
6	85	143
7	87	143

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(if (<=.f64 y -13500000000000000067875480669316803468202086541523516722249383066451556046124244973410802266579253932725370880) 1/2 (if (<=.f64 y 6216540455122333/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176) (/.f64 (.f64 1/2 x) y) (if (<=.f64 y 140000000000000000) 1/2 (if (<=.f64 y 7499999999999999343793916924645128878317507065649858689265552055579786579279872) (/.f64 (.f64 1/2 x) y) 1/2))))
(if (<=.f64 y -12500000000000000294617093927128197915619159938211023289123906740853520855827021657478867019905618878278926336) 1/2 (if (<=.f64 y 242445077749771/124330809102446660538845562036705210025114037699336929360115994223289874253133343883264) (.f64 x (/.f64 1/2 y)) (if (<=.f64 y 650000000000000000) 1/2 (if (<=.f64 y 9999999999999999673560075006595519222746403606649979913266024618633003221909504) (.f64 x (/.f64 1/2 y)) 1/2))))
1/2
-1

Outputs
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(if (<=.f64 y -13500000000000000067875480669316803468202086541523516722249383066451556046124244973410802266579253932725370880) 1/2 (if (<=.f64 y 6216540455122333/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176) (/.f64 (.f64 1/2 x) y) (if (<=.f64 y 140000000000000000) 1/2 (if (<=.f64 y 7499999999999999343793916924645128878317507065649858689265552055579786579279872) (/.f64 (.f64 1/2 x) y) 1/2))))
(if (<=.f64 y -13500000000000000067875480669316803468202086541523516722249383066451556046124244973410802266579253932725370880) 1/2 (if (or (<=.f64 y 6216540455122333/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176) (and (not (<=.f64 y 140000000000000000)) (<=.f64 y 7499999999999999343793916924645128878317507065649858689265552055579786579279872))) (/.f64 (*.f64 1/2 x) y) 1/2))
(if (<=.f64 y -12500000000000000294617093927128197915619159938211023289123906740853520855827021657478867019905618878278926336) 1/2 (if (<=.f64 y 242445077749771/124330809102446660538845562036705210025114037699336929360115994223289874253133343883264) (.f64 x (/.f64 1/2 y)) (if (<=.f64 y 650000000000000000) 1/2 (if (<=.f64 y 9999999999999999673560075006595519222746403606649979913266024618633003221909504) (.f64 x (/.f64 1/2 y)) 1/2))))
(if (<=.f64 y -12500000000000000294617093927128197915619159938211023289123906740853520855827021657478867019905618878278926336) 1/2 (if (or (<=.f64 y 242445077749771/124330809102446660538845562036705210025114037699336929360115994223289874253133343883264) (and (not (<=.f64 y 650000000000000000)) (<=.f64 y 9999999999999999673560075006595519222746403606649979913266024618633003221909504))) (*.f64 x (/.f64 1/2 y)) 1/2))
1/2
-1

Compiler

Compiled 67 to 53 computations (20.9% saved)

soundness16.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

44×	`*-commutative`
22×	`sqr-pow`
20×	`associate-*r/`
18×	`associate-*l/`
16×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	890
1	291	890

Stop Event

1×

unsound

Compiler

Compiled 16 to 12 computations (25% saved)

end42.0ms (2.3%)

Compiler: Compiled 59 to 45 computations (23.7% saved)

Details

analyze125.0ms (6.9%)

sample977.0ms (53.5%)

preprocess6.0ms (0.3%)

simplify12.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.3%)

series3.0ms (0.1%)

rewrite56.0ms (3.1%)

simplify18.0ms (1%)

eval8.0ms (0.5%)

prune9.0ms (0.5%)

localize8.0ms (0.5%)

series2.0ms (0.1%)

rewrite67.0ms (3.7%)

simplify70.0ms (3.9%)

localize5.0ms (0.3%)

eval63.0ms (3.4%)

prune20.0ms (1.1%)

localize9.0ms (0.5%)

series2.0ms (0.1%)

rewrite51.0ms (2.8%)

simplify47.0ms (2.6%)

eval5.0ms (0.3%)

prune5.0ms (0.3%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes15.0ms (0.8%)

regimes38.0ms (2.1%)

bsearch43.0ms (2.3%)

regimes34.0ms (1.9%)

bsearch43.0ms (2.3%)

regimes8.0ms (0.4%)

simplify10.0ms (0.5%)

soundness16.0ms (0.9%)

end42.0ms (2.3%)

Profiling