Details

analyze101.0ms (3.7%)

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)

sample871.0ms (32.3%)

Results

830.0ms	8256×	body	256	valid
31.0ms	367×	body	256	invalid

Bogosity

preprocess6.0ms (0.2%)

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)

simplify11.0ms (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)

prune2.0ms (0.1%)

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

21.8b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.8b	(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)
✓	20.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 18 to 5 computations (72.2% saved)

series3.0ms (0.1%)

Counts

2 → 40

Calls

12 calls:

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

rewrite59.0ms (2.2%)

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))))))

simplify71.0ms (2.6%)

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)

eval24.0ms (0.9%)

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

prune20.0ms (0.7%)

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
▶	41.9b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
▶	41.9b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
▶	42.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	21.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	41.5b	(sqrt.f64 y)
▶	41.8b	(neg.f64 x)
	42.4b	x

Compiler

Compiled 81 to 55 computations (32.1% saved)

localize2.0ms (0.1%)

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

localize2.0ms (0.1%)

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

localize8.0ms (0.3%)

Compiler: Compiled 20 to 9 computations (55% saved)

localize7.0ms (0.3%)

Compiler: Compiled 20 to 9 computations (55% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 -1/2 (/.f64 x y))

Compiler

Compiled 20 to 9 computations (55% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite64.0ms (2.4%)

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))))))))

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))))))))

simplify44.0ms (1.6%)

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))

eval5.0ms (0.2%)

Compiler: Compiled 300 to 175 computations (41.7% saved)

prune9.0ms (0.3%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	1	1
Picked	0	1	1
Done	0	5	5
Total	28	8	36

Error

Counts

36 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	41.9b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
✓	41.9b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
▶	41.9b	(-.f64 (*.f64 (/.f64 -1/2 x) y) x)
✓	42.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	21.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	41.5b	(sqrt.f64 y)
✓	41.8b	(neg.f64 x)
	42.4b	x

Compiler

Compiled 55 to 37 computations (32.7% saved)

localize8.0ms (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)

series0.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite52.0ms (1.9%)

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))))))))

simplify66.0ms (2.4%)

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))

eval4.0ms (0.2%)

Compiler: Compiled 215 to 129 computations (40% saved)

prune6.0ms (0.2%)

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	22	1	23
Fresh	0	1	1
Picked	0	1	1
Done	0	6	6
Total	22	9	31

Error

Counts

31 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	41.9b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
▶	42.0b	(-.f64 (-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 y x))) 1) x)
✓	41.9b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	41.9b	(-.f64 (*.f64 (/.f64 -1/2 x) y) x)
✓	42.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	21.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	41.5b	(sqrt.f64 y)
✓	41.8b	(neg.f64 x)
	42.4b	x

Compiler

Compiled 68 to 47 computations (30.9% saved)

localize68.0ms (2.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.3b	(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 y x))) 1)

Compiler

Compiled 41 to 24 computations (41.5% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite71.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1044×	`associate-/r*`
914×	`*-commutative`
740×	`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	3068	13

Stop Event

1×	node limit

Counts

1 → 133

Calls

Call 1

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

Outputs

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

simplify93.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1518×	`associate-/l/`
1416×	`associate-/r/`
770×	`associate-+r+`
682×	`associate-+l+`
398×	`distribute-lft-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	5063
1	969	4967
2	3701	4963

Stop Event

1×	node limit

Counts

157 → 204

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

eval128.0ms (4.8%)

Compiler: Compiled 4774 to 3014 computations (36.9% saved)

prune113.0ms (4.2%)

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	0	1	1
Picked	0	1	1
Done	0	7	7
Total	202	11	213

Error

Counts

213 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	41.9b	(-.f64 (/.f64 (/.f64 -1/2 x) (/.f64 1 y)) x)
	41.9b	(-.f64 (/.f64 (+.f64 (.f64 -1/2 (/.f64 y x)) 2) (/.f64 (+.f64 (.f64 -1/2 (/.f64 y x)) 2) (*.f64 -1/2 (/.f64 y x)))) x)
✓	41.9b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
✓	42.0b	(-.f64 (-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 y x))) 1) x)
✓	41.9b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	41.9b	(-.f64 (*.f64 (/.f64 -1/2 x) y) x)
✓	42.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	21.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	41.5b	(sqrt.f64 y)
✓	41.8b	(neg.f64 x)
	42.4b	x

Compiler

Compiled 104 to 71 computations (31.7% saved)

regimes129.0ms (4.8%)

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

75.0ms	y
18.0ms	x
12.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
11.0ms	(*.f64 x x)
11.0ms	(+.f64 (*.f64 x x) y)

Results

Error	Segments	Branch
0b	3	`x`
17.8b	6	`y`
10.0b	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
10.0b	2	`(+.f64 (*.f64 x x) y)`
10.0b	2	`(*.f64 x x)`

Compiler

Compiled 110 to 64 computations (41.8% saved)

bsearch44.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
32.0ms	8.579133192245223e+110	5.3388413257018765e+116
11.0ms	-1.634874678358553e+161	-1.11707927987533e+153

Results

42.0ms	160×	body	256	valid
0.0ms	2×	body	256	invalid

Compiler

Compiled 150 to 106 computations (29.3% saved)

regimes113.0ms (4.2%)

Counts

10 → 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 (/.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 -1/2 (/.f64 y x))) 1) x)
(-.f64 (/.f64 (+.f64 (.f64 -1/2 (/.f64 y x)) 2) (/.f64 (+.f64 (.f64 -1/2 (/.f64 y x)) 2) (*.f64 -1/2 (/.f64 y x)))) 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:

67.0ms	x
44.0ms	y

Results

Error	Segments	Branch
4.8b	3	`x`
24.1b	7	`y`

Compiler

Compiled 84 to 49 computations (41.7% saved)

bsearch22.0ms (0.8%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	2.6915206755510028e-36	2.7614499085772823e-30
4.0ms	-1.5443131710590441e-55	-1.4411413922965182e-55

Results

15.0ms	176×	body	256	valid
4.0ms	40×	body	256	invalid

Compiler

Compiled 178 to 130 computations (27% saved)

regimes115.0ms (4.3%)

Counts

9 → 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 (/.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 -1/2 (/.f64 y x))) 1) x)
(-.f64 (/.f64 (+.f64 (.f64 -1/2 (/.f64 y x)) 2) (/.f64 (+.f64 (.f64 -1/2 (/.f64 y x)) 2) (*.f64 -1/2 (/.f64 y x)))) x)

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

Calls

2 calls:

102.0ms	y
11.0ms	x

Results

Error	Segments	Branch
20.8b	2	`x`
34.9b	10	`y`

Compiler

Compiled 82 to 48 computations (41.5% saved)

bsearch24.0ms (0.9%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	3.6382086891930544e-298	9.160154573793071e-286

Results

16.0ms	160×	body	256	valid
6.0ms	84×	body	256	invalid

Compiler

Compiled 213 to 149 computations (30% saved)

regimes76.0ms (2.8%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

2 calls:

67.0ms	y
8.0ms	x

Results

Error	Segments	Branch
20.8b	2	`x`
34.9b	10	`y`

Compiler

Compiled 18 to 11 computations (38.9% saved)

bsearch24.0ms (0.9%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	6.847724053816816e-247	2.790270237627558e-234

Results

16.0ms	160×	body	256	valid
6.0ms	78×	body	256	invalid

Compiler

Compiled 163 to 119 computations (27% saved)

regimes36.0ms (1.3%)

Accuracy

Total -42.3b remaining (-202.1%)

Threshold costs -42.3b (-202.1%)

Counts

2 → 2

Calls

Call 1

Inputs
x
(neg.f64 x)

Outputs
(neg.f64 x)
x

Calls

2 calls:

30.0ms	y
5.0ms	x

Results

Error	Segments	Branch
20.9b	2	`x`
35.0b	10	`y`

Compiler

Compiled 11 to 7 computations (36.4% saved)

bsearch27.0ms (1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
27.0ms	-2.360273784159186e-304	3.6382086891930544e-298

Results

16.0ms	160×	body	256	valid
9.0ms	97×	body	256	invalid

Compiler

Compiled 103 to 79 computations (23.3% saved)

simplify9.0ms (0.3%)

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	198
1	51	198
2	54	198
3	55	198

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 x -15000000000000001298496038999574854037221349022080675856012921172039509217266793356799400692677585977189403561424740135192327629840926310196001356373819392) (neg.f64 x) (if (<=.f64 x 20000000000000000311188322589336860485364027938421228667395411608616675623295114065299707798300948953524125617356800) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -4196261778848663/27606985387162255149739023449108101809804435888681546220650096895197184) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (if (<=.f64 x 6736609109572131/22835963083295358096932575511191922182123945984) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x)))
(if (<=.f64 x 4359103839594459/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (+.f64 (.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x 5498669552347193/458222462695599379270700542938797415851547826754730440471063195236977024085646466549524548253194054006869752147503995521190349772113174027207120416665033273928205988927667393636268820183663660419920640131707923959614888857707801337845740593703588724736) (neg.f64 x) (+.f64 (*.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) (neg.f64 x) x)
x

Outputs
(if (<=.f64 x -15000000000000001298496038999574854037221349022080675856012921172039509217266793356799400692677585977189403561424740135192327629840926310196001356373819392) (neg.f64 x) (if (<=.f64 x 20000000000000000311188322589336860485364027938421228667395411608616675623295114065299707798300948953524125617356800) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -4196261778848663/27606985387162255149739023449108101809804435888681546220650096895197184) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (if (<=.f64 x 6736609109572131/22835963083295358096932575511191922182123945984) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x)))
(if (<=.f64 x -4196261778848663/27606985387162255149739023449108101809804435888681546220650096895197184) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (if (<=.f64 x 6736609109572131/22835963083295358096932575511191922182123945984) (sqrt.f64 y) (+.f64 x (.f64 1/2 (/.f64 y x)))))
(if (<=.f64 x 4359103839594459/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (+.f64 (.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x 4359103839594459/11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056587776) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (+.f64 x (.f64 1/2 (/.f64 y x))))
(if (<=.f64 x 5498669552347193/458222462695599379270700542938797415851547826754730440471063195236977024085646466549524548253194054006869752147503995521190349772113174027207120416665033273928205988927667393636268820183663660419920640131707923959614888857707801337845740593703588724736) (neg.f64 x) (+.f64 (*.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x 5498669552347193/458222462695599379270700542938797415851547826754730440471063195236977024085646466549524548253194054006869752147503995521190349772113174027207120416665033273928205988927667393636268820183663660419920640131707923959614888857707801337845740593703588724736) (neg.f64 x) (+.f64 x (*.f64 1/2 (/.f64 y x))))
(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) (neg.f64 x) x)
x

Compiler

Compiled 92 to 60 computations (34.8% saved)

soundness94.0ms (3.5%)

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)

end51.0ms (1.9%)

Compiler: Compiled 82 to 46 computations (43.9% saved)

Details

analyze101.0ms (3.7%)

sample871.0ms (32.3%)

preprocess6.0ms (0.2%)

simplify11.0ms (0.4%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite59.0ms (2.2%)

simplify71.0ms (2.6%)

eval24.0ms (0.9%)

prune20.0ms (0.7%)

localize2.0ms (0.1%)

localize2.0ms (0.1%)

localize8.0ms (0.3%)

localize7.0ms (0.3%)

localize7.0ms (0.2%)

series3.0ms (0.1%)

rewrite64.0ms (2.4%)

simplify44.0ms (1.6%)

eval5.0ms (0.2%)

prune9.0ms (0.3%)

localize8.0ms (0.3%)

series0.0ms (0%)

rewrite52.0ms (1.9%)

simplify66.0ms (2.4%)

eval4.0ms (0.2%)

prune6.0ms (0.2%)

localize68.0ms (2.5%)

series1.0ms (0%)

rewrite71.0ms (2.6%)

simplify93.0ms (3.4%)

eval128.0ms (4.8%)

prune113.0ms (4.2%)

regimes129.0ms (4.8%)

bsearch44.0ms (1.6%)

regimes113.0ms (4.2%)

bsearch22.0ms (0.8%)

regimes115.0ms (4.3%)

bsearch24.0ms (0.9%)

regimes76.0ms (2.8%)

bsearch24.0ms (0.9%)

regimes36.0ms (1.3%)

bsearch27.0ms (1%)

simplify9.0ms (0.3%)

soundness94.0ms (3.5%)

end51.0ms (1.9%)

Profiling