Details

analyze130.0ms (3.6%)

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
12.5%	12.5%	87.4%	0.1%	0%	0%	0%	5
26.7%	25%	68.7%	0.1%	0%	6.2%	0%	6
39.3%	34.3%	53.1%	0.1%	0%	12.5%	0%	7
54.5%	46.8%	39%	0.1%	0%	14%	0%	8
64.8%	53.1%	28.9%	0.1%	0%	18%	0%	9
74.4%	60.1%	20.7%	0.1%	0%	19.1%	0%	10
80.9%	63.6%	15%	0.1%	0%	21.3%	0%	11
86.4%	67.3%	10.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.1s (31.2%)

Results

1.1s	8256×	body	256	valid
26.0ms	357×	body	256	invalid

Bogosity

preprocess4.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

4×	`fma-def`
4×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	16	26
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (fma.f64 x x y))
(sqrt.f64 (+.f64 (*.f64 y y) x))
(sqrt.f64 (fma.f64 y y x))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	11	13

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (fma.f64 x x y))

eval0.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

20.2b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	20.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 8 to 5 computations (37.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 x x) y)
✓	18.9b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 18 to 5 computations (72.2% saved)

series6.0ms (0.2%)

Counts

2 → 40

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	x	@	0	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	y	@	inf	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	x	@	inf	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	y	@	-inf	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite66.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1714×	`add-sqr-sqrt`
1692×	`*-un-lft-identity`
1580×	`add-cube-cbrt`
1566×	`add-cbrt-cube`
172×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	168	20
2	2191	20

Stop Event

1×	node limit

Counts

2 → 67

Calls

Call 1

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

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

Outputs

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

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

simplify117.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1540×	`associate-+r+`
1270×	`associate-+l+`
680×	`fma-def`
632×	`unswap-sqr`
588×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	2195
1	452	2101
2	1559	2093
3	5580	2093

Stop Event

1×	node limit

Counts

107 → 115

Calls

Call 1

Inputs
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y)))
(+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6))) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(*.f64 -1 x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y)))) 1)
(*.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(*.f64 1 (hypot.f64 x (sqrt.f64 y)))
(*.f64 (pow.f64 (fma.f64 x x y) 1/4) (pow.f64 (fma.f64 x x y) 1/4))
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 y)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 1/2))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (sqrt.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (sqrt.f64 (-.f64 (.f64 x x) y)))
(pow.f64 (fma.f64 x x y) 1/2)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)
(pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 3)
(pow.f64 (pow.f64 (fma.f64 x x y) 3/2) 1/3)
(fabs.f64 (hypot.f64 x (sqrt.f64 y)))
(log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 y))))
(log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 y)))))
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) 1/2))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))) 1))
(log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 y))))
(-.f64 (exp.f64 (log1p.f64 (fma.f64 x x y))) 1)
(-.f64 (/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y)))
(*.f64 (fma.f64 x x y) 1)
(*.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))
(*.f64 1 (fma.f64 x x y))
(.f64 (pow.f64 (fma.f64 x x y) 1/4) (.f64 (pow.f64 (fma.f64 x x y) 1/4) (hypot.f64 x (sqrt.f64 y))))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))
(.f64 (cbrt.f64 (fma.f64 x x y)) (.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (hypot.f64 x (sqrt.f64 y))))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))
(.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (-.f64 (*.f64 x x) y)))
(.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (*.f64 x x))))))
(.f64 (.f64 (hypot.f64 x (sqrt.f64 y)) (pow.f64 (fma.f64 x x y) 1/4)) (pow.f64 (fma.f64 x x y) 1/4))
(.f64 (.f64 (hypot.f64 x (sqrt.f64 y)) (cbrt.f64 (fma.f64 x x y))) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))
(/.f64 1 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (pow.f64 x 4) (.f64 y y))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 x 4) (.f64 x (*.f64 x y)))))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (neg.f64 (-.f64 (.f64 x x) y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(pow.f64 (fma.f64 x x y) 1)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)
(pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)
(pow.f64 (pow.f64 (fma.f64 x x y) 2) 1/2)
(pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)
(sqrt.f64 (pow.f64 (fma.f64 x x y) 2))
(log.f64 (exp.f64 (fma.f64 x x y)))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x y))))
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3))
(expm1.f64 (log1p.f64 (fma.f64 x x y)))
(exp.f64 (log.f64 (fma.f64 x x y)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) 1))
(log1p.f64 (expm1.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(fma.f64 1 (*.f64 x x) y)
(fma.f64 1 y (*.f64 x x))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) y)
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) (*.f64 x x))

Outputs
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))
(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (sqrt.f64 y))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y)))
(fma.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x)) (sqrt.f64 y)))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (.f64 1/2 (.f64 x x)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 -1/8 (pow.f64 x 4)) (sqrt.f64 y)))
(+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6))) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))))
(fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6)) (fma.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (sqrt.f64 y))))
(fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6)) (fma.f64 (sqrt.f64 (/.f64 1 y)) (.f64 1/2 (.f64 x x)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 -1/8 (pow.f64 x 4)) (sqrt.f64 y))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(fma.f64 1/2 (/.f64 y x) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (*.f64 (/.f64 y (pow.f64 x 3)) y) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (*.f64 (/.f64 y (pow.f64 x 3)) y) x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 -1 x))
(fma.f64 -1/2 (/.f64 y x) (neg.f64 x))
(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
(-.f64 (*.f64 (/.f64 y x) -1/2) x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (fma.f64 -1 x (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) 1/8)))
(fma.f64 (/.f64 y x) -1/2 (-.f64 (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) 1/8) x))
(-.f64 (fma.f64 (/.f64 y x) -1/2 (.f64 (.f64 (/.f64 y (pow.f64 x 3)) y) 1/8)) x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 y x) (fma.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1 x (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) 1/8))))
(fma.f64 (/.f64 y x) -1/2 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (-.f64 (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) 1/8) x)))
(fma.f64 (/.f64 y x) -1/2 (fma.f64 (*.f64 (/.f64 y (pow.f64 x 3)) y) 1/8 (-.f64 (/.f64 (pow.f64 y 3) (/.f64 (pow.f64 x 5) -1/16)) x)))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(fma.f64 1/2 (/.f64 y x) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (*.f64 (/.f64 y (pow.f64 x 3)) y) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (*.f64 (/.f64 y (pow.f64 x 3)) y) x)))
y
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
y
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
y
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y)))) 1)
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(*.f64 1 (hypot.f64 x (sqrt.f64 y)))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (pow.f64 (fma.f64 x x y) 1/4) (pow.f64 (fma.f64 x x y) 1/4))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 y) x)) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 y) x)) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 y)))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (sqrt.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (hypot.f64 (pow.f64 x 3) (pow.f64 y 3/2)) (sqrt.f64 (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (sqrt.f64 (-.f64 (.f64 x x) y)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (sqrt.f64 (fma.f64 x x (neg.f64 y))))
(pow.f64 (fma.f64 x x y) 1/2)
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 3)
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(pow.f64 (pow.f64 (fma.f64 x x y) 3/2) 1/3)
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(fabs.f64 (hypot.f64 x (sqrt.f64 y)))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 y))))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 y)))))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(hypot.f64 (sqrt.f64 y) x)
(hypot.f64 x (sqrt.f64 y))
(exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) 1/2))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(exp.f64 (*.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))) 1))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 y))))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(-.f64 (exp.f64 (log1p.f64 (fma.f64 x x y))) 1)
(fma.f64 x x y)
(-.f64 (/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (fma.f64 x x (neg.f64 y)))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))
(*.f64 (fma.f64 x x y) 1)
(fma.f64 x x y)
(*.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))
(fma.f64 x x y)
(*.f64 1 (fma.f64 x x y))
(fma.f64 x x y)
(.f64 (pow.f64 (fma.f64 x x y) 1/4) (.f64 (pow.f64 (fma.f64 x x y) 1/4) (hypot.f64 x (sqrt.f64 y))))
(fma.f64 x x y)
(*.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))
(fma.f64 x x y)
(.f64 (cbrt.f64 (fma.f64 x x y)) (.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (hypot.f64 x (sqrt.f64 y))))
(.f64 (cbrt.f64 (fma.f64 x x y)) (.f64 (hypot.f64 x (sqrt.f64 y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y)))))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 4))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 y) x)) 4))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (-.f64 (*.f64 x x) y)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (fma.f64 x x (neg.f64 y)))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))
(.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (*.f64 x x))))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 y 3) (pow.f64 x 6))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6)) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4)))
(.f64 (.f64 (hypot.f64 x (sqrt.f64 y)) (pow.f64 (fma.f64 x x y) 1/4)) (pow.f64 (fma.f64 x x y) 1/4))
(fma.f64 x x y)
(.f64 (.f64 (hypot.f64 x (sqrt.f64 y)) (cbrt.f64 (fma.f64 x x y))) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))
(.f64 (cbrt.f64 (fma.f64 x x y)) (.f64 (hypot.f64 x (sqrt.f64 y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y)))))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 4))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 y) x)) 4))
(/.f64 1 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (pow.f64 x 4) (.f64 y y))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (fma.f64 x x (neg.f64 y)))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 y 3) (pow.f64 x 6))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6)) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (fma.f64 x x (neg.f64 y)))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 y 3) (pow.f64 x 6))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6)) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4)))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 x 4) (.f64 x (*.f64 x y)))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 y 3) (pow.f64 x 6))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6)) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4)))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (fma.f64 x x (neg.f64 y)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (neg.f64 (-.f64 (.f64 x x) y)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (fma.f64 x x (neg.f64 y)))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 y 3) (pow.f64 x 6))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6)) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4)))
(pow.f64 (fma.f64 x x y) 1)
(fma.f64 x x y)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)
(fma.f64 x x y)
(pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)
(fma.f64 x x y)
(pow.f64 (pow.f64 (fma.f64 x x y) 2) 1/2)
(fma.f64 x x y)
(pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)
(fma.f64 x x y)
(sqrt.f64 (pow.f64 (fma.f64 x x y) 2))
(fma.f64 x x y)
(log.f64 (exp.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x y))))
(fma.f64 x x y)
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3))
(fma.f64 x x y)
(expm1.f64 (log1p.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(exp.f64 (log.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) 1))
(fma.f64 x x y)
(log1p.f64 (expm1.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(fma.f64 x x y)
(fma.f64 1 (*.f64 x x) y)
(fma.f64 x x y)
(fma.f64 1 y (*.f64 x x))
(fma.f64 x x y)
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 x x))
(fma.f64 x x y)
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) y)
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) (*.f64 x x))
(fma.f64 x x y)

eval26.0ms (0.7%)

Compiler: Compiled 1488 to 734 computations (50.7% saved)

prune19.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	109	6	115
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	109	7	116

Error

Counts

116 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	42.2b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
▶	42.2b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
▶	42.1b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	20.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	41.4b	(sqrt.f64 y)
▶	42.0b	(neg.f64 x)
	42.0b	x

Compiler

Compiled 81 to 55 computations (32.1% saved)

localize3.0ms (0.1%)

Compiler: Compiled 5 to 3 computations (40% saved)

localize3.0ms (0.1%)

Compiler: Compiled 5 to 3 computations (40% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 9 computations (55% saved)

series4.0ms (0.1%)

Counts

1 → 0

Calls

6 calls:

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

rewrite68.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1518×	`add-sqr-sqrt`
1500×	`*-un-lft-identity`
1400×	`add-cube-cbrt`
1384×	`add-cbrt-cube`
1370×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	147	13
2	1848	13

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

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

Outputs

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

simplify45.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1696×	`distribute-lft-in`
1686×	`distribute-rgt-in`
1042×	`associate-r`
928×	`associate-l`
658×	`associate-+r+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	61	531
1	145	417
2	542	297
3	3910	297

Stop Event

1×	node limit

Counts

21 → 28

Calls

Call 1

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

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

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 9 computations (55% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(*.f64 (/.f64 y x) -1/2)
0.0ms	y	@	0	(*.f64 (/.f64 y x) -1/2)
0.0ms	x	@	0	(*.f64 (/.f64 y x) -1/2)
0.0ms	y	@	-inf	(*.f64 (/.f64 y x) -1/2)
0.0ms	y	@	inf	(*.f64 (/.f64 y x) -1/2)

rewrite52.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1522×	`add-sqr-sqrt`
1504×	`*-un-lft-identity`
1404×	`add-cube-cbrt`
1388×	`add-cbrt-cube`
1374×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	147	13
2	1852	13

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

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

simplify51.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1558×	`distribute-rgt-in`
1554×	`distribute-lft-in`
1526×	`associate-/r/`
910×	`associate-r`
792×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	608
1	148	608
2	559	602
3	3657	602

Stop Event

1×	node limit

Counts

46 → 28

Calls

Call 1

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

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

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 -1/2 (/.f64 x y))

Compiler

Compiled 20 to 9 computations (55% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite75.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1612×	`add-sqr-sqrt`
1588×	`*-un-lft-identity`
1488×	`add-cube-cbrt`
1472×	`add-cbrt-cube`
152×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	154	13
2	2008	13

Stop Event

1×	node limit

Counts

1 → 28

Calls

Call 1

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

Outputs

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

simplify45.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1276×	`associate-/l*`
1110×	`distribute-lft-in`
1022×	`distribute-rgt-in`
896×	`associate-+r+`
828×	`associate-+l+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	706
1	163	706
2	648	706
3	2574	706

Stop Event

1×	node limit

Counts

52 → 29

Calls

Call 1

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

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

eval16.0ms (0.4%)

Compiler: Compiled 830 to 470 computations (43.4% saved)

prune14.0ms (0.4%)

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	1	1
Picked	0	1	1
Done	0	5	5
Total	82	10	92

Error

Counts

92 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	42.2b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
▶	42.3b	(-.f64 (-.f64 (+.f64 1 (*.f64 (/.f64 y x) -1/2)) 1) x)
✓	42.2b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
▶	42.2b	(-.f64 (*.f64 (/.f64 -1/2 x) y) x)
▶	42.1b	(+.f64 (/.f64 1/2 (/.f64 x y)) x)
✓	42.1b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	20.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	41.4b	(sqrt.f64 y)
✓	42.0b	(neg.f64 x)
	42.0b	x

Compiler

Compiled 77 to 53 computations (31.2% saved)

localize51.0ms (1.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 1/2 (/.f64 x y))

Compiler

Compiled 20 to 9 computations (55% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite52.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1616×	`add-sqr-sqrt`
1592×	`*-un-lft-identity`
1492×	`add-cube-cbrt`
1476×	`add-cbrt-cube`
152×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	154	13
2	2008	13

Stop Event

1×	node limit

Counts

1 → 28

Calls

Call 1

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

Outputs

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

simplify43.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1176×	`associate-/l*`
1130×	`distribute-lft-in`
1038×	`distribute-rgt-in`
894×	`associate-+r+`
842×	`associate-+l+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	706
1	162	706
2	647	706
3	2594	706

Stop Event

1×	node limit

Counts

52 → 29

Calls

Call 1

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

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

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 12 computations (40% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite52.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1448×	`add-sqr-sqrt`
1424×	`*-un-lft-identity`
1330×	`add-cube-cbrt`
1314×	`add-cbrt-cube`
1302×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	148	13
2	1798	13

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

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

simplify56.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1852×	`distribute-rgt-in`
1842×	`distribute-lft-in`
1076×	`associate-r`
966×	`associate-l`
650×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	598
1	145	598
2	552	598
3	4252	598

Stop Event

1×	node limit

Counts

46 → 23

Calls

Call 1

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

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

localize24.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (/.f64 y x) -1/2)
✓	2.7b	(-.f64 (+.f64 1 (*.f64 (/.f64 y x) -1/2)) 1)

Compiler

Compiled 41 to 24 computations (41.5% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite81.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1056×	`associate-/r*`
922×	`*-commutative`
758×	`associate-/l*`
624×	`distribute-lft-in`
590×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	223	13
2	3071	13

Stop Event

1×	node limit

Counts

1 → 140

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 (/.f64 y x) -1/2 -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 y x) -1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 y x) -1/2 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 y x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 y x) -1/2 -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 (/.f64 y x) -1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (/.f64 y x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (*.f64 -1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 y x) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (/.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 y x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 y x) -1/2)) (sqrt.f64 (*.f64 (/.f64 y x) -1/2)))))) (#(struct:change #<rule 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/2 (pow.f64 (cbrt.f64 x) 2)) (/.f64 y (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/2 (neg.f64 x)) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/2 (/.f64 x 1)) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/2 (/.f64 x (cbrt.f64 (*.f64 y y)))) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2) -1) (-.f64 1 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2))) (-.f64 0 (*.f64 (/.f64 y x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2) -1) (+.f64 1 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 3))) (+.f64 (fma.f64 (/.f64 y x) -1/2 1) (*.f64 (pow.f64 (/.f64 y x) 2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 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(/.f64 y x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 y x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 y x) 3) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 y x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 y x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 y x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 (/.f64 y x) -1/2 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 (/.f64 y x) -1/2 1)) (sqrt.f64 (fma.f64 (/.f64 y x) -1/2 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y x) -1/2 1)) 2) (cbrt.f64 (fma.f64 (/.f64 y x) -1/2 1)) -1)))))

simplify152.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1450×	`associate-/r/`
764×	`associate-+r+`
682×	`associate-+l+`
486×	`associate-/l/`
396×	`+-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	384	5268
1	1002	5176
2	3857	5172

Stop Event

1×	node limit

Counts

164 → 212

Calls

Call 1

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

Outputs
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(+.f64 1 (fma.f64 (/.f64 y x) -1/2 -1))
(*.f64 -1/2 (/.f64 y x))
(+.f64 (*.f64 (/.f64 y x) -1/2) 0)
(*.f64 -1/2 (/.f64 y x))
(+.f64 (fma.f64 (/.f64 y x) -1/2 1) -1)
(*.f64 -1/2 (/.f64 y x))
(+.f64 0 (*.f64 (/.f64 y x) -1/2))
(*.f64 -1/2 (/.f64 y x))
(+.f64 (fma.f64 (/.f64 y x) -1/2 -1) 1)
(*.f64 -1/2 (/.f64 y x))
(+.f64 -1 (fma.f64 (/.f64 y x) -1/2 1))
(*.f64 -1/2 (/.f64 y x))
(.f64 1 (.f64 (/.f64 y x) -1/2))
(*.f64 -1/2 (/.f64 y x))
(.f64 y (.f64 -1/2 (/.f64 1 x)))
(*.f64 -1/2 (/.f64 y x))
(*.f64 (/.f64 y x) -1/2)
(*.f64 -1/2 (/.f64 y x))
(*.f64 -1/2 (/.f64 y x))
(.f64 (.f64 (/.f64 y x) -1/2) 1)
(*.f64 -1/2 (/.f64 y x))
(.f64 (sqrt.f64 (.f64 (/.f64 y x) -1/2)) (sqrt.f64 (*.f64 (/.f64 y x) -1/2)))
(*.f64 -1/2 (/.f64 y x))
(.f64 (sqrt.f64 (/.f64 y x)) (.f64 -1/2 (sqrt.f64 (/.f64 y x))))
(*.f64 -1/2 (/.f64 y x))
(.f64 (cbrt.f64 (.f64 (/.f64 y x) -1/2)) (pow.f64 (cbrt.f64 (*.f64 (/.f64 y x) -1/2)) 2))
(*.f64 -1/2 (/.f64 y x))
(.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 y x) -1/2)) 2) (cbrt.f64 (*.f64 (/.f64 y x) -1/2)))
(*.f64 -1/2 (/.f64 y x))
(.f64 (cbrt.f64 (/.f64 y x)) (.f64 -1/2 (pow.f64 (cbrt.f64 (/.f64 y x)) 2)))
(*.f64 -1/2 (/.f64 y x))
(.f64 (pow.f64 (cbrt.f64 (/.f64 y x)) 2) (.f64 -1/2 (cbrt.f64 (/.f64 y x))))
(*.f64 -1/2 (/.f64 y x))
(.f64 (.f64 y -1/2) (/.f64 1 x))
(*.f64 -1/2 (/.f64 y x))
(.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2) -1) (/.f64 1 (+.f64 (.f64 (/.f64 y x) -1/2) 2)))
(*.f64 -1/2 (/.f64 y x))
(.f64 (/.f64 1 x) (.f64 y -1/2))
(*.f64 -1/2 (/.f64 y x))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2) (+.f64 (.f64 (/.f64 y x) -1/2) 2))))
(/.f64 (*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 3)) 1) (+.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2) (fma.f64 (/.f64 y x) -1/2 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 3)) (+.f64 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 2) (fma.f64 -1/2 (/.f64 y x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 3)) (+.f64 1 (*.f64 (fma.f64 -1/2 (/.f64 y x) 1) (fma.f64 -1/2 (/.f64 y x) 2))))
(.f64 (.f64 -1/2 (sqrt.f64 (/.f64 y x))) (sqrt.f64 (/.f64 y x)))
(*.f64 -1/2 (/.f64 y x))
(.f64 (.f64 -1/2 (pow.f64 (cbrt.f64 (/.f64 y x)) 2)) (cbrt.f64 (/.f64 y x)))
(*.f64 -1/2 (/.f64 y x))
(.f64 (.f64 -1/2 (/.f64 1 x)) y)
(*.f64 -1/2 (/.f64 y x))
(.f64 (.f64 -1/2 (cbrt.f64 (/.f64 y x))) (pow.f64 (cbrt.f64 (/.f64 y x)) 2))
(*.f64 -1/2 (/.f64 y x))
(*.f64 (/.f64 y 1) (/.f64 -1/2 x))
(*.f64 -1/2 (/.f64 y x))
(*.f64 (/.f64 y (sqrt.f64 x)) (/.f64 -1/2 (sqrt.f64 x)))
(.f64 y (/.f64 -1/2 (.f64 (sqrt.f64 x) (sqrt.f64 x))))
(*.f64 (/.f64 y (pow.f64 (cbrt.f64 x) 2)) (/.f64 -1/2 (cbrt.f64 x)))
(*.f64 -1/2 (/.f64 y x))
(*.f64 (+.f64 1 (sqrt.f64 (fma.f64 (/.f64 y x) -1/2 1))) (-.f64 (sqrt.f64 (fma.f64 (/.f64 y x) -1/2 1)) 1))
(*.f64 -1/2 (/.f64 y x))
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(/.f64 (+.f64 -1 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 3)) (+.f64 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 2) (fma.f64 -1/2 (/.f64 y x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 3)) (+.f64 1 (*.f64 (fma.f64 -1/2 (/.f64 y x) 1) (fma.f64 -1/2 (/.f64 y x) 2))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 3)) (.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2) (+.f64 (.f64 (/.f64 y x) -1/2) 2))) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2) (+.f64 (.f64 (/.f64 y x) -1/2) 2))))) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2) (+.f64 (.f64 (/.f64 y x) -1/2) 2))))
(/.f64 (*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 3)) 1) (+.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2) (fma.f64 (/.f64 y x) -1/2 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 3)) (+.f64 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 2) (fma.f64 -1/2 (/.f64 y x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 3)) (+.f64 1 (*.f64 (fma.f64 -1/2 (/.f64 y x) 1) (fma.f64 -1/2 (/.f64 y x) 2))))
(/.f64 (/.f64 (/.f64 y -2) 1) x)
(*.f64 -1/2 (/.f64 y x))
(/.f64 (/.f64 (/.f64 y -2) (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (/.f64 (/.f64 y (/.f64 (sqrt.f64 x) -1/2)) 1) (sqrt.f64 x))
(*.f64 (/.f64 y (sqrt.f64 x)) (/.f64 -1/2 (sqrt.f64 x)))
(.f64 y (/.f64 -1/2 (.f64 (sqrt.f64 x) (sqrt.f64 x))))
(/.f64 (/.f64 (/.f64 y (/.f64 (sqrt.f64 x) -1/2)) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
(/.f64 (.f64 (/.f64 y (sqrt.f64 x)) -1/2) (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x)))
(/.f64 y (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 x) -1/2)))
(/.f64 (/.f64 (*.f64 y (/.f64 -1/2 (sqrt.f64 x))) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
(/.f64 (/.f64 (/.f64 y (/.f64 (sqrt.f64 x) -1/2)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (/.f64 y (sqrt.f64 x)) (/.f64 -1/2 (sqrt.f64 x)))
(.f64 y (/.f64 -1/2 (.f64 (sqrt.f64 x) (sqrt.f64 x))))
(/.f64 (/.f64 (/.f64 y (/.f64 (sqrt.f64 x) -1/2)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2))) (sqrt.f64 (cbrt.f64 x)))
(/.f64 (.f64 (/.f64 y (sqrt.f64 x)) -1/2) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2))))
(*.f64 (/.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 (cbrt.f64 x))) (/.f64 -1/2 (fabs.f64 (cbrt.f64 x))))
(/.f64 (/.f64 (/.f64 (*.f64 y -1/2) (pow.f64 (cbrt.f64 x) 2)) 1) (cbrt.f64 x))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (/.f64 (/.f64 (*.f64 y -1/2) (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (/.f64 (/.f64 (.f64 y -1/2) (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x)))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (/.f64 (/.f64 (*.f64 y -1/2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 (sqrt.f64 x)))
(/.f64 (/.f64 y (/.f64 (pow.f64 (cbrt.f64 x) 2) -1/2)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))))
(/.f64 y (.f64 (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))) (/.f64 (pow.f64 (cbrt.f64 x) 2) -1/2)))
(/.f64 (/.f64 (/.f64 (*.f64 y -1/2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 (cbrt.f64 x)))
(/.f64 (/.f64 y (/.f64 (pow.f64 (cbrt.f64 x) 2) -1/2)) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))))
(/.f64 y (.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))) (/.f64 (pow.f64 (cbrt.f64 x) 2) -1/2)))
(/.f64 (/.f64 (*.f64 y 1/2) 1) (neg.f64 x))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (/.f64 (*.f64 y 1/2) (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))
(*.f64 (/.f64 y (sqrt.f64 x)) (/.f64 -1/2 (sqrt.f64 x)))
(.f64 y (/.f64 -1/2 (.f64 (sqrt.f64 x) (sqrt.f64 x))))
(/.f64 (/.f64 (*.f64 y 1/2) (pow.f64 (cbrt.f64 x) 2)) (neg.f64 (cbrt.f64 x)))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (/.f64 (*.f64 y 1/2) -1) x)
(*.f64 -1/2 (/.f64 y x))
(/.f64 (/.f64 (*.f64 y 1/2) (sqrt.f64 (neg.f64 x))) (sqrt.f64 (neg.f64 x)))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (/.f64 (.f64 y 1/2) (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 (neg.f64 x)))) (cbrt.f64 (neg.f64 x)))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (/.f64 (*.f64 y 1/2) (neg.f64 (sqrt.f64 x))) (sqrt.f64 x))
(*.f64 (/.f64 y (sqrt.f64 x)) (/.f64 -1/2 (sqrt.f64 x)))
(.f64 y (/.f64 -1/2 (.f64 (sqrt.f64 x) (sqrt.f64 x))))
(/.f64 (/.f64 (*.f64 y 1/2) (neg.f64 (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 x))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (+.f64 (neg.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2)) 1) (+.f64 (*.f64 (/.f64 y x) 1/2) -2))
(/.f64 (-.f64 1 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2)) (fma.f64 (/.f64 y x) 1/2 -2))
(/.f64 (-.f64 1 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 2)) (fma.f64 (/.f64 y x) 1/2 -2))
(/.f64 (+.f64 (neg.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 3)) 1) (+.f64 (+.f64 (*.f64 (/.f64 y x) 1/2) -2) (neg.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2))))
(/.f64 (+.f64 1 (neg.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 3))) (-.f64 (fma.f64 (/.f64 y x) 1/2 -2) (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2)))
(/.f64 (-.f64 1 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 3)) (-.f64 (fma.f64 (/.f64 y x) 1/2 -2) (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 2)))
(pow.f64 (*.f64 (/.f64 y x) -1/2) 1)
(*.f64 -1/2 (/.f64 y x))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 y x) -1/2)) 2)
(*.f64 -1/2 (/.f64 y x))
(pow.f64 (cbrt.f64 (*.f64 (/.f64 y x) -1/2)) 3)
(*.f64 -1/2 (/.f64 y x))
(pow.f64 (*.f64 (pow.f64 (/.f64 y x) 3) -1/8) 1/3)
(cbrt.f64 (*.f64 (pow.f64 (/.f64 y x) 3) -1/8))
(neg.f64 (*.f64 (/.f64 y x) 1/2))
(*.f64 -1/2 (/.f64 y x))
(neg.f64 (/.f64 (*.f64 y -1/2) (neg.f64 x)))
(*.f64 -1/2 (/.f64 y x))
(neg.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2) -1) (+.f64 (*.f64 (/.f64 y x) 1/2) -2)))
(/.f64 (-.f64 1 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2)) (fma.f64 (/.f64 y x) 1/2 -2))
(/.f64 (-.f64 1 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 2)) (fma.f64 (/.f64 y x) 1/2 -2))
(neg.f64 (/.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 3)) (+.f64 (+.f64 (*.f64 (/.f64 y x) 1/2) -2) (neg.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2)))))
(/.f64 (+.f64 1 (neg.f64 (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 3))) (-.f64 (fma.f64 (/.f64 y x) 1/2 -2) (pow.f64 (fma.f64 (/.f64 y x) -1/2 1) 2)))
(/.f64 (-.f64 1 (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 3)) (-.f64 (fma.f64 (/.f64 y x) 1/2 -2) (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1) 2)))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4))
(log.f64 (pow.f64 (exp.f64 (/.f64 y x)) -1/2))
(*.f64 -1/2 (/.f64 y x))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 y x) -1/2))))
(*.f64 -1/2 (/.f64 y x))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 y x) 3) -1/8))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 y x) -1/2)))
(*.f64 -1/2 (/.f64 y x))
(exp.f64 (log.f64 (*.f64 (/.f64 y x) -1/2)))
(*.f64 -1/2 (/.f64 y x))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 y x) -1/2)))
(*.f64 -1/2 (/.f64 y x))
(fma.f64 1 (fma.f64 (/.f64 y x) -1/2 1) -1)
(*.f64 -1/2 (/.f64 y x))
(fma.f64 (sqrt.f64 (fma.f64 (/.f64 y x) -1/2 1)) (sqrt.f64 (fma.f64 (/.f64 y x) -1/2 1)) -1)
(*.f64 -1/2 (/.f64 y x))
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y x) -1/2 1)) 2) (cbrt.f64 (fma.f64 (/.f64 y x) -1/2 1)) -1)
(*.f64 -1/2 (/.f64 y x))

eval132.0ms (3.6%)

Compiler: Compiled 5728 to 3543 computations (38.1% saved)

prune59.0ms (1.6%)

Pruning

12 alts after pruning (3 fresh and 9 done)

	Pruned	Kept	Total
New	290	2	292
Fresh	0	1	1
Picked	0	1	1
Done	0	8	8
Total	290	12	302

Error

Counts

302 → 12

Alt Table

Click to see full alt table

Status	Error	Program
▶	42.2b	(-.f64 (/.f64 (/.f64 -1/2 x) (/.f64 1 y)) x)
✓	42.2b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
✓	42.3b	(-.f64 (-.f64 (+.f64 1 (*.f64 (/.f64 y x) -1/2)) 1) x)
✓	42.2b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	42.2b	(-.f64 (*.f64 (/.f64 -1/2 x) y) x)
✓	42.1b	(+.f64 (/.f64 1/2 (/.f64 x y)) x)
▶	42.1b	(+.f64 (*.f64 (/.f64 1/2 x) y) x)
✓	42.1b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	20.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	41.4b	(sqrt.f64 y)
✓	42.0b	(neg.f64 x)
	42.0b	x

Compiler

Compiled 97 to 67 computations (30.9% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 12 computations (40% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite87.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1452×	`add-sqr-sqrt`
1428×	`*-un-lft-identity`
1334×	`add-cube-cbrt`
1318×	`add-cbrt-cube`
1304×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	148	13
2	1798	13

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

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

simplify50.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1854×	`distribute-rgt-in`
1842×	`distribute-lft-in`
1122×	`associate-r`
976×	`associate-l`
650×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	598
1	144	598
2	550	598
3	4244	598

Stop Event

1×	node limit

Counts

46 → 23

Calls

Call 1

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

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

localize63.0ms (1.7%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 28 to 19 computations (32.1% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite58.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1966×	`add-sqr-sqrt`
1942×	`*-un-lft-identity`
1818×	`add-cube-cbrt`
1798×	`add-cbrt-cube`
184×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	195	13
2	2562	13

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

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

Outputs

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

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1640×	`associate-+l+`
1116×	`associate-*r/`
822×	`associate-*l/`
596×	`associate-/l*`
540×	`associate-+l-`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	114	970
1	307	934
2	1087	934
3	5229	934

Stop Event

1×	node limit

Counts

64 → 47

Calls

Call 1

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

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

eval18.0ms (0.5%)

Compiler: Compiled 813 to 542 computations (33.3% saved)

prune45.0ms (1.2%)

Pruning

12 alts after pruning (1 fresh and 11 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	1	1
Picked	0	1	1
Done	0	10	10
Total	70	12	82

Error

Counts

82 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	42.2b	(-.f64 (/.f64 (/.f64 -1/2 x) (/.f64 1 y)) x)
✓	42.2b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
✓	42.3b	(-.f64 (-.f64 (+.f64 1 (*.f64 (/.f64 y x) -1/2)) 1) x)
✓	42.2b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	42.2b	(-.f64 (*.f64 (/.f64 -1/2 x) y) x)
✓	42.1b	(+.f64 (/.f64 1/2 (/.f64 x y)) x)
✓	42.1b	(+.f64 (*.f64 (/.f64 1/2 x) y) x)
✓	42.1b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	20.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	41.4b	(sqrt.f64 y)
✓	42.0b	(neg.f64 x)
	42.0b	x

Compiler

Compiled 97 to 67 computations (30.9% saved)

regimes130.0ms (3.6%)

Counts

12 → 3

Calls

Call 1

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

Outputs
(neg.f64 x)
(sqrt.f64 (+.f64 (*.f64 x x) y))
x

Calls

5 calls:

62.0ms	y
23.0ms	x
20.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
13.0ms	(+.f64 (*.f64 x x) y)
10.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0b	3	`x`
16.5b	5	`y`
9.5b	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
9.5b	2	`(+.f64 (*.f64 x x) y)`
9.5b	2	`(*.f64 x x)`

Compiler

Compiled 101 to 58 computations (42.6% saved)

bsearch16.0ms (0.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
12.0ms	6.171526533950804e+46	6.893766661713218e+64
3.0ms	-1.0103766754973097e+155	-4.720132630970031e+153

Results

14.0ms	128×	body	256	valid
1.0ms	10×	body	256	invalid

Compiler

Compiled 119 to 83 computations (30.3% saved)

regimes64.0ms (1.7%)

Counts

11 → 3

Calls

Call 1

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

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

Calls

2 calls:

42.0ms	y
20.0ms	x

Results

Error	Segments	Branch
5.3b	3	`x`
25.6b	6	`y`

Compiler

Compiled 75 to 43 computations (42.7% saved)

bsearch29.0ms (0.8%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
11.0ms	1.1102968013602658e-90	1.1690425920107805e-89
17.0ms	-2.1546137099933924e-8	-2.4250587760037416e-13

Results

23.0ms	240×	body	256	valid
3.0ms	38×	body	256	invalid

Compiler

Compiled 238 to 174 computations (26.9% saved)

regimes109.0ms (3%)

Counts

10 → 2

Calls

Call 1

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

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

Calls

2 calls:

74.0ms	x
33.0ms	y

Results

Error	Segments	Branch
20.8b	2	`x`
35.4b	4	`y`

Compiler

Compiled 73 to 42 computations (42.5% saved)

bsearch38.0ms (1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
38.0ms	-8.583704052603535e-232	-7.786362076071373e-234

Results

32.0ms	112×	body	256	valid
4.0ms	49×	body	256	invalid

Compiler

Compiled 111 to 79 computations (28.8% saved)

regimes32.0ms (0.9%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

21.0ms	y
9.0ms	x

Results

Error	Segments	Branch
20.8b	2	`x`
35.5b	4	`y`

Compiler

Compiled 32 to 19 computations (40.6% saved)

bsearch8.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
8.0ms	9.814351557675573e-259	1.8010055087069885e-258

Results

6.0ms	64×	body	256	valid
2.0ms	22×	body	256	invalid

Compiler

Compiled 73 to 53 computations (27.4% saved)

regimes24.0ms (0.6%)

Accuracy

Total -42.3b remaining (-202.6%)

Threshold costs -42.3b (-202.6%)

Counts

2 → 2

Calls

Call 1

Inputs
x
(neg.f64 x)

Outputs
(neg.f64 x)
x

Calls

2 calls:

16.0ms	y
7.0ms	x

Results

Error	Segments	Branch
20.9b	2	`x`
35.5b	4	`y`

Compiler

Compiled 11 to 7 computations (36.4% saved)

bsearch15.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
15.0ms	-2.9270499895908444e-308	3.745372484723043e-308

Results

9.0ms	96×	body	256	valid
5.0ms	55×	body	256	invalid

Compiler

Compiled 67 to 51 computations (23.9% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative`
6×	`*-commutative`
4×	`sub-neg`
2×	`neg-mul-1`
2×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	180
1	51	180
2	54	180
3	55	180

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 x -20000000000000000738950913761164530819618359659685376903845557104301087318694439194433026219410816654893023507374465334628674006699146808342092384896548864) (neg.f64 x) (if (<=.f64 x 20000000000000000426408380189087937446025157425359298935486676992) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -7737125245533627/618970019642690137449562112) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (if (<=.f64 x 3010216933486969/286687326998758938951352611912760867599570623646035140467198604923365359511060601008752319138765710819328) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x)))
(if (<=.f64 x -3495959950985713/6991919901971426075297554671307333615898862102580725715195666431228287110681861367027657291461090911970058473930419853533788296083269867358507086435928852446414275954096487329654980776728266302794199220759703429559553357814144917874843453883416576) (-.f64 (*.f64 (/.f64 -1/2 x) y) x) x)
(if (<=.f64 x 7790019838314065/4327788799063369698118367518036104040602397294887907509272254128346512609744690048814426160231687683233172643784762398137404191207445999921156415311568401014033503715319849649510248592805285405106374515984066055406780647774220793764564147394699562815402300054714269682368512) (neg.f64 x) (+.f64 (*.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x -5060056332683/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (neg.f64 x) x)
x

Outputs
(if (<=.f64 x -20000000000000000738950913761164530819618359659685376903845557104301087318694439194433026219410816654893023507374465334628674006699146808342092384896548864) (neg.f64 x) (if (<=.f64 x 20000000000000000426408380189087937446025157425359298935486676992) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -7737125245533627/618970019642690137449562112) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (if (<=.f64 x 3010216933486969/286687326998758938951352611912760867599570623646035140467198604923365359511060601008752319138765710819328) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x)))
(if (<=.f64 x -7737125245533627/618970019642690137449562112) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (if (<=.f64 x 3010216933486969/286687326998758938951352611912760867599570623646035140467198604923365359511060601008752319138765710819328) (sqrt.f64 y) (+.f64 x (.f64 1/2 (/.f64 y x)))))
(if (<=.f64 x -3495959950985713/6991919901971426075297554671307333615898862102580725715195666431228287110681861367027657291461090911970058473930419853533788296083269867358507086435928852446414275954096487329654980776728266302794199220759703429559553357814144917874843453883416576) (-.f64 (*.f64 (/.f64 -1/2 x) y) x) x)
(if (<=.f64 x -3495959950985713/6991919901971426075297554671307333615898862102580725715195666431228287110681861367027657291461090911970058473930419853533788296083269867358507086435928852446414275954096487329654980776728266302794199220759703429559553357814144917874843453883416576) (-.f64 (*.f64 y (/.f64 -1/2 x)) x) x)
(if (<=.f64 x 7790019838314065/4327788799063369698118367518036104040602397294887907509272254128346512609744690048814426160231687683233172643784762398137404191207445999921156415311568401014033503715319849649510248592805285405106374515984066055406780647774220793764564147394699562815402300054714269682368512) (neg.f64 x) (+.f64 (*.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x 7790019838314065/4327788799063369698118367518036104040602397294887907509272254128346512609744690048814426160231687683233172643784762398137404191207445999921156415311568401014033503715319849649510248592805285405106374515984066055406780647774220793764564147394699562815402300054714269682368512) (neg.f64 x) (+.f64 x (*.f64 1/2 (/.f64 y x))))
(if (<=.f64 x -5060056332683/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (neg.f64 x) x)
x

Compiler

Compiled 86 to 56 computations (34.9% saved)

soundness85.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1540×	`associate-+r+`
1270×	`associate-+l+`
680×	`fma-def`
632×	`unswap-sqr`
588×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	2195
1	452	2101
2	1559	2093
3	5580	2093

Stop Event

1×	node limit

Compiler

Compiled 7 to 5 computations (28.6% saved)

end60.0ms (1.7%)

Compiler: Compiled 76 to 43 computations (43.4% saved)

Details

analyze130.0ms (3.6%)

sample1.1s (31.2%)

preprocess4.0ms (0.1%)

simplify13.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series6.0ms (0.2%)

rewrite66.0ms (1.8%)

simplify117.0ms (3.2%)

eval26.0ms (0.7%)

prune19.0ms (0.5%)

localize3.0ms (0.1%)

localize3.0ms (0.1%)

localize7.0ms (0.2%)

series4.0ms (0.1%)

rewrite68.0ms (1.9%)

simplify45.0ms (1.2%)

localize7.0ms (0.2%)

series3.0ms (0.1%)

rewrite52.0ms (1.4%)

simplify51.0ms (1.4%)

localize9.0ms (0.3%)

series1.0ms (0%)

rewrite75.0ms (2.1%)

simplify45.0ms (1.2%)

eval16.0ms (0.4%)

prune14.0ms (0.4%)

localize51.0ms (1.4%)

series1.0ms (0%)

rewrite52.0ms (1.4%)

simplify43.0ms (1.2%)

localize8.0ms (0.2%)

series2.0ms (0.1%)

rewrite52.0ms (1.4%)

simplify56.0ms (1.5%)

localize24.0ms (0.7%)

series2.0ms (0%)

rewrite81.0ms (2.2%)

simplify152.0ms (4.2%)

eval132.0ms (3.6%)

prune59.0ms (1.6%)

localize9.0ms (0.3%)

series1.0ms (0%)

rewrite87.0ms (2.4%)

simplify50.0ms (1.4%)

localize63.0ms (1.7%)

series1.0ms (0%)

rewrite58.0ms (1.6%)

simplify55.0ms (1.5%)

eval18.0ms (0.5%)

prune45.0ms (1.2%)

regimes130.0ms (3.6%)

bsearch16.0ms (0.4%)

regimes64.0ms (1.7%)

bsearch29.0ms (0.8%)

regimes109.0ms (3%)

bsearch38.0ms (1%)

regimes32.0ms (0.9%)

bsearch8.0ms (0.2%)

regimes24.0ms (0.6%)

bsearch15.0ms (0.4%)

simplify8.0ms (0.2%)

soundness85.0ms (2.3%)

end60.0ms (1.7%)

Profiling