Details

analyze96.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
25%	68.7%	6.3%	6
34.3%	53.1%	12.6%	7
46.8%	39%	14.1%	8
53.1%	28.9%	18%	9
60.1%	20.7%	19.2%	10
63.6%	15%	21.4%	11
67.3%	10.6%	22%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.4s (23.1%)

Results

1.3s	8256×	body	256	valid
48.0ms	356×	body	256	invalid

preprocess20.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
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)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

23.8b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	23.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	23.8b	(sqrt.f64 (fma.f64 x x y))

Compiler

Compiled 15 to 9 computations (40% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 x x) y)
✓	22.1b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 18 to 5 computations (72.2% saved)

series17.0ms (0.3%)

Counts

2 → 40

Calls

12 calls:

Time	Variable		Point	Expression
11.0ms	y	@	inf	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	x	@	0	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	x	@	inf	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	y	@	-inf	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	y	@	0	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite58.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

662×	`pow1_binary64`
619×	`add-log-exp_binary64`
619×	`log1p-expm1-u_binary64`
619×	`expm1-log1p-u_binary64`
602×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	130	11
2	1751	11

Stop Event

1×	node limit

Counts

2 → 62

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

Outputs

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

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

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

759×	`times-frac_binary64`
599×	`associate-/l*_binary64`
502×	`unswap-sqr_binary64`
498×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	454
1	161	416
2	444	416
3	1586	414
4	5763	414

Stop Event

1×	node limit

Counts

102 → 88

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))

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 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 1/16 (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))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 -1/8 (pow.f64 x 4)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 1/16 (pow.f64 x 6)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (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 y (/.f64 (pow.f64 x 3) y)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) x))
(fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) (fma.f64 1/2 (/.f64 y x) 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 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) 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 y (/.f64 (pow.f64 x 3) y)) 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 y (/.f64 y (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) (fma.f64 1/2 (/.f64 y x) 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 (/.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 y (/.f64 (pow.f64 x 3) y)) 1/8) x))
(-.f64 (fma.f64 (/.f64 y x) -1/2 (*.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8)) x)
(-.f64 (.f64 (/.f64 y x) (+.f64 -1/2 (.f64 (/.f64 y x) (/.f64 1/8 x)))) x)
(fma.f64 (/.f64 y x) (+.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 1/8 x))) (neg.f64 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 y (/.f64 (pow.f64 x 3) y)) 1/8) x)))
(fma.f64 (/.f64 y x) -1/2 (fma.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8 (-.f64 (/.f64 (*.f64 (pow.f64 y 3) -1/16) (pow.f64 x 5)) x)))
(fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (-.f64 (.f64 (/.f64 y x) (+.f64 -1/2 (.f64 (/.f64 y x) (/.f64 1/8 x)))) x))
(fma.f64 (pow.f64 y 3) (/.f64 -1/16 (pow.f64 x 5)) (fma.f64 (/.f64 y x) (+.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 1/8 x))) (neg.f64 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 y (/.f64 (pow.f64 x 3) y)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) x))
(fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) (fma.f64 1/2 (/.f64 y x) 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 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) 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 y (/.f64 (pow.f64 x 3) y)) 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 y (/.f64 y (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) (fma.f64 1/2 (/.f64 y x) x)))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	22.1b	(sqrt.f64 (fma.f64 x x y))

Compiler

Compiled 13 to 4 computations (69.2% saved)

series2.0ms (0%)

Counts

1 → 16

Calls

6 calls:

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

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`pow1_binary64`
421×	`add-sqr-sqrt_binary64`
414×	`*-un-lft-identity_binary64`
404×	`add-log-exp_binary64`
404×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	98	6
2	1121	6

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(sqrt.f64 (fma.f64 x x y))

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

Outputs

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

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

759×	`times-frac_binary64`
598×	`associate-/l*_binary64`
502×	`unswap-sqr_binary64`
498×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	313
1	159	311
2	440	311
3	1580	309
4	5737	309

Stop Event

1×	node limit

Counts

41 → 47

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)))

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 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 -1/8 (pow.f64 x 4)) (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 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 1/16 (pow.f64 x 6)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (sqrt.f64 y))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 -1/8 (pow.f64 x 4)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 1/16 (pow.f64 x 6)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (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))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (*.f64 y (/.f64 y (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)))
(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)))
(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 y (/.f64 y (pow.f64 x 3))) 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 (/.f64 y x) -1/2) x)
(fma.f64 (/.f64 y x) -1/2 (neg.f64 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 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x))))) x)
(fma.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x)))) (neg.f64 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 (-.f64 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (.f64 (.f64 (/.f64 y (pow.f64 x 3)) y) 1/8)) x))
(fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x))))) x))
(fma.f64 (pow.f64 y 3) (/.f64 -1/16 (pow.f64 x 5)) (fma.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x)))) (neg.f64 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))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (*.f64 y (/.f64 y (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)))
(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)))
(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 y (/.f64 y (pow.f64 x 3))) x)))

eval33.0ms (0.5%)

Compiler: Compiled 1630 to 805 computations (50.6% saved)

prune23.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	129	6	135
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	130	7	137

Error

Counts

137 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	39.1b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	23.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	43.1b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
	43.1b	x
▶	43.9b	(sqrt.f64 y)
▶	39.1b	(neg.f64 x)
▶	39.4b	(fma.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x)))) (neg.f64 x))

Compiler

Compiled 97 to 63 computations (35.1% saved)

localize46.0ms (0.8%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 20 to 9 computations (55% saved)

series6.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite67.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

907×	`pow1_binary64`
847×	`add-log-exp_binary64`
847×	`log1p-expm1-u_binary64`
847×	`expm1-log1p-u_binary64`
830×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	159	17
2	2241	17

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

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

Outputs

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

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

simplify113.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
410×	`fma-def_binary64`
277×	`associate-/l*_binary64`
248×	`div-sub_binary64`
186×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	378
1	16	378
2	26	378
3	35	378
4	58	378
5	102	378
6	197	378
7	352	378
8	542	378
9	834	378
10	1817	378
11	3011	378
12	3534	378
13	3734	378
14	3831	378
15	3863	378
16	3887	378
17	3887	378

Stop Event

1×

saturated

Counts

106 → 64

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

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

localize3.0ms (0%)

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

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 20 to 9 computations (55% saved)

series42.0ms (0.7%)

Counts

2 → 6

Calls

12 calls:

Time	Variable		Point	Expression
39.0ms	x	@	-inf	(*.f64 1/2 (/.f64 y x))
0.0ms	y	@	0	(*.f64 1/2 (/.f64 y x))
0.0ms	x	@	0	(*.f64 1/2 (/.f64 y x))
0.0ms	y	@	0	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
0.0ms	y	@	-inf	(+.f64 (*.f64 1/2 (/.f64 y x)) x)

rewrite71.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

902×	`pow1_binary64`
841×	`add-log-exp_binary64`
841×	`log1p-expm1-u_binary64`
841×	`expm1-log1p-u_binary64`
824×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	159	15
2	2248	15

Stop Event

1×	node limit

Counts

2 → 55

Calls

Call 1

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

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
1	9	24
2	13	24
3	17	24
4	18	24

Stop Event

1×

saturated

Counts

61 → 57

Calls

Call 1

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

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

localize3.0ms (0%)

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

localize37.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x)))) (neg.f64 x))
✓	0.1b	(/.f64 x (/.f64 y x))
✓	1.1b	(/.f64 1/8 (/.f64 x (/.f64 y x)))

Compiler

Compiled 47 to 18 computations (61.7% saved)

series12.0ms (0.2%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(/.f64 1/8 (/.f64 x (/.f64 y x)))
2.0ms	y	@	0	(/.f64 x (/.f64 y x))
1.0ms	y	@	0	(/.f64 1/8 (/.f64 x (/.f64 y x)))
1.0ms	x	@	0	(/.f64 1/8 (/.f64 x (/.f64 y x)))
1.0ms	y	@	-inf	(/.f64 1/8 (/.f64 x (/.f64 y x)))

rewrite186.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

570×	`log-prod_binary64`
324×	`prod-diff_binary64`
289×	`pow2_binary64`
250×	`pow-unpow_binary64`
202×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	254	35
2	3692	35

Stop Event

1×	node limit

Counts

3 → 177

Calls

Call 1

Inputs
(/.f64 1/8 (/.f64 x (/.f64 y x)))
(/.f64 x (/.f64 y x))
(fma.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x)))) (neg.f64 x))

Outputs

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

simplify114.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

861×	`distribute-rgt-neg-in_binary64`
757×	`distribute-lft-neg-in_binary64`
616×	`unswap-sqr_binary64`
589×	`distribute-neg-frac_binary64`
475×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	834
1	58	822
2	130	822
3	391	807
4	2272	777
5	4645	777

Stop Event

1×	node limit

Counts

249 → 189

Calls

Call 1

Inputs
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(/.f64 (pow.f64 x 2) y)
(*.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 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.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 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.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 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.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 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(*.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 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(*.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 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))

Outputs
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(*.f64 1/8 (/.f64 y (pow.f64 x 2)))
(.f64 1/8 (/.f64 y (.f64 x x)))
(/.f64 y (/.f64 (*.f64 x x) 1/8))
(/.f64 y (/.f64 x (/.f64 1/8 x)))
(/.f64 (*.f64 y (/.f64 1/8 x)) x)
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(*.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 y x)) x)
(-.f64 (/.f64 y (/.f64 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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x 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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) x)
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))
(/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3))
(/.f64 1/8 (/.f64 (pow.f64 x 3) (*.f64 y y)))
(.f64 1/8 (.f64 y (/.f64 y (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))))
(fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x)))
(*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x)))))
(.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2))
(+.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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x 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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) x)
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))
(/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3))
(/.f64 1/8 (/.f64 (pow.f64 x 3) (*.f64 y y)))
(.f64 1/8 (.f64 y (/.f64 y (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))))
(fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x)))
(*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x)))))
(.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2))
(+.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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x 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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) x)
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))
(/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3))
(/.f64 1/8 (/.f64 (pow.f64 x 3) (*.f64 y y)))
(.f64 1/8 (.f64 y (/.f64 y (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))))
(fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x)))
(*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x)))))
(.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2))
(+.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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x 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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) 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 y x)) x)
(-.f64 (/.f64 y (/.f64 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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x 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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) 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 y x)) x)
(-.f64 (/.f64 y (/.f64 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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x 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 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (-.f64 (.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3))) x))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 y y) (pow.f64 x 3)) (.f64 -1/2 (/.f64 y x))) x)
(-.f64 (*.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 y (/.f64 x (/.f64 1/8 x))))) x)
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) x)

eval102.0ms (1.7%)

Compiler: Compiled 6370 to 2940 computations (53.8% saved)

prune58.0ms (1%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	304	6	310
Fresh	0	1	1
Picked	1	0	1
Done	1	4	5
Total	306	11	317

Error

Counts

317 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	43.1b	x
▶	43.2b	(+.f64 (-.f64 (+.f64 1 (*.f64 1/2 (/.f64 y x))) 1) x)
	39.5b	(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) x)
✓	39.1b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	23.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	62.3b	(*.f64 1/2 (/.f64 y x))
▶	39.1b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
▶	39.1b	(-.f64 (-.f64 (+.f64 1 (*.f64 (/.f64 y x) -1/2)) 1) x)
▶	43.1b	(+.f64 (/.f64 1/2 (/.f64 x y)) x)
✓	43.9b	(sqrt.f64 y)
✓	39.1b	(neg.f64 x)

Compiler

Compiled 162 to 113 computations (30.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
✓	0.7b	(/.f64 -1/2 (/.f64 x y))

Compiler

Compiled 20 to 9 computations (55% saved)

series3.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite68.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

952×	`pow1_binary64`
893×	`add-log-exp_binary64`
892×	`log1p-expm1-u_binary64`
892×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	165	17
2	2409	17

Stop Event

1×	node limit

Counts

2 → 65

Calls

Call 1

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

simplify109.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
410×	`fma-def_binary64`
277×	`associate-/l*_binary64`
248×	`div-sub_binary64`
186×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	378
1	16	378
2	26	378
3	35	378
4	58	378
5	102	378
6	197	378
7	352	378
8	542	378
9	834	378
10	1817	378
11	3011	378
12	3534	378
13	3734	378
14	3831	378
15	3863	378
16	3887	378
17	3887	378

Stop Event

1×

saturated

Counts

113 → 70

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

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

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 13 to 6 computations (53.8% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 (/.f64 x y)) x)
✓	0.7b	(/.f64 1/2 (/.f64 x y))

Compiler

Compiled 20 to 9 computations (55% saved)

series3.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite68.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

952×	`pow1_binary64`
891×	`add-log-exp_binary64`
891×	`log1p-expm1-u_binary64`
891×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	165	15
2	2422	15

Stop Event

1×	node limit

Counts

2 → 63

Calls

Call 1

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

Outputs

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

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

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`+-commutative_binary64`
1×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	336
1	12	336
2	17	336
3	21	336
4	23	336
5	24	336

Stop Event

1×

saturated

Counts

111 → 65

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

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 1/2 (/.f64 y x)))
	0.0b	(*.f64 1/2 (/.f64 y x))
✓	2.8b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 y x))) 1)

Compiler

Compiled 41 to 24 computations (41.5% saved)

series4.0ms (0.1%)

Counts

2 → 39

Calls

12 calls:

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

rewrite81.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`unpow-prod-down_binary64`
490×	`prod-diff_binary64`
417×	`log-prod_binary64`
410×	`fma-def_binary64`
234×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	203	15
2	2844	15

Stop Event

1×	node limit

Counts

2 → 188

Calls

Call 1

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

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

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

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`+-commutative_binary64`
1×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	264
1	15	264
2	20	264
3	24	264
4	26	264
5	27	264

Stop Event

1×

saturated

Counts

227 → 190

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

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 (/.f64 y x) -1/2))
	0.0b	(*.f64 (/.f64 y x) -1/2)
✓	2.8b	(-.f64 (+.f64 1 (*.f64 (/.f64 y x) -1/2)) 1)

Compiler

Compiled 41 to 24 computations (41.5% saved)

series3.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite78.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

657×	`unpow-prod-down_binary64`
509×	`prod-diff_binary64`
418×	`log-prod_binary64`
416×	`fma-def_binary64`
234×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	203	15
2	2849	15

Stop Event

1×	node limit

Counts

2 → 193

Calls

Call 1

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

Outputs

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

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`+-commutative_binary64`
1×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	336
1	15	336
2	20	336
3	24	336
4	26	336
5	27	336

Stop Event

1×

saturated

Counts

241 → 195

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

eval270.0ms (4.5%)

Compiler: Compiled 8834 to 5450 computations (38.3% saved)

prune181.0ms (3%)

Pruning

13 alts after pruning (6 fresh and 7 done)

	Pruned	Kept	Total
New	578	5	583
Fresh	1	1	2
Picked	0	1	1
Done	2	6	8
Total	581	13	594

Error

Counts

594 → 13

Alt Table

Click to see full alt table

Status	Error	Program
✓	39.1b	(-.f64 (-.f64 (+.f64 1 (*.f64 (/.f64 y x) -1/2)) 1) x)
▶	62.4b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 y x))) 1)
✓	39.1b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	23.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	62.3b	(*.f64 1/2 (/.f64 y x))
	43.1b	x
✓	39.1b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
▶	62.3b	(/.f64 1/2 (/.f64 x y))
▶	43.1b	(+.f64 (*.f64 (/.f64 1/2 x) y) x)
▶	39.5b	(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) x)
✓	43.9b	(sqrt.f64 y)
✓	39.1b	(neg.f64 x)
▶	39.1b	(-.f64 (*.f64 (/.f64 -1/2 x) y) x)

Compiler

Compiled 161 to 112 computations (30.4% saved)

localize21.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 20 to 12 computations (40% saved)

series6.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite91.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

865×	`pow1_binary64`
809×	`add-log-exp_binary64`
808×	`log1p-expm1-u_binary64`
808×	`expm1-log1p-u_binary64`
793×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	160	17
2	2177	17

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

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

Outputs

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

simplify139.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
410×	`fma-def_binary64`
277×	`associate-/l*_binary64`
248×	`div-sub_binary64`
186×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	378
1	16	378
2	26	378
3	35	378
4	58	378
5	102	378
6	197	378
7	352	378
8	542	378
9	834	378
10	1817	378
11	3011	378
12	3534	378
13	3734	378
14	3831	378
15	3863	378
16	3887	378
17	3887	378

Stop Event

1×

saturated

Counts

106 → 64

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

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

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 13 to 6 computations (53.8% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (/.f64 1/2 x) y) x)
✓	0.2b	(*.f64 (/.f64 1/2 x) y)

Compiler

Compiled 20 to 12 computations (40% saved)

series3.0ms (0.1%)

Counts

2 → 48

Calls

12 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	y	@	inf	(*.f64 (/.f64 1/2 x) y)
0.0ms	x	@	-inf	(*.f64 (/.f64 1/2 x) y)
0.0ms	x	@	inf	(+.f64 (*.f64 (/.f64 1/2 x) y) x)

rewrite69.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

864×	`pow1_binary64`
806×	`add-log-exp_binary64`
806×	`log1p-expm1-u_binary64`
806×	`expm1-log1p-u_binary64`
790×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	160	15
2	2190	15

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

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

Outputs

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

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`+-commutative_binary64`
1×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	336
1	12	336
2	17	336
3	21	336
4	23	336
5	24	336

Stop Event

1×

saturated

Counts

104 → 60

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

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (*.f64 1/2 (/.f64 y x)))
	0.0b	(*.f64 1/2 (/.f64 y x))
	2.8b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 y x))) 1)

Compiler

Compiled 30 to 17 computations (43.3% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2))
✓	11.3b	(/.f64 y (*.f64 x x))

Compiler

Compiled 51 to 19 computations (62.7% saved)

series6.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2))
1.0ms	y	@	0	(.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2))
1.0ms	x	@	0	(.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2))
1.0ms	y	@	-inf	(/.f64 y (*.f64 x x))
1.0ms	y	@	inf	(.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2))

rewrite76.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
403×	`exp-prod_binary64`
319×	`pow-prod-down_binary64`
269×	`pow2_binary64`
191×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	215	24
2	2809	24

Stop Event

1×	node limit

Counts

2 → 111

Calls

Call 1

Inputs
(/.f64 y (*.f64 x x))
(.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 y (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 y (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 y x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 y (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (pow.f64 x -2))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 y) x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 y) x) 4)) (cbrt.f64 (*.f64 y (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 y) x) (/.f64 (sqrt.f64 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 y) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) 1) (/.f64 (cbrt.f64 y) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (/.f64 y x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (/.f64 y x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 y (sqrt.f64 x)) (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) x) (/.f64 (cbrt.f64 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (cbrt.f64 x) x)) (/.f64 y (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 y (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 1 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 x) x)) (cbrt.f64 (*.f64 y (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 x) x)) (/.f64 (sqrt.f64 y) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 y 1) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 y x)) 2) 1) (/.f64 (cbrt.f64 (/.f64 y x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 y x)) 1) (/.f64 (sqrt.f64 (/.f64 y x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 y x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (*.f64 y (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 y x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (/.f64 y x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 y x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 y x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 y) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 y) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 y) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 y x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 y (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (/.f64 y x) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 x y) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (/.f64 x y)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (/.f64 y x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 y (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (*.f64 y (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 y (pow.f64 x -2))))) (sqrt.f64 (log.f64 (*.f64 y (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 y (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 y) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 y (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 y) x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 y x) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 y (pow.f64 x -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (sqrt.f64 y) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 y (pow.f64 x -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 y) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (/.f64 y x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 y (pow.f64 x -2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 y) 1) (*.f64 2 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 y) (*.f64 (log.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 y) 1) (*.f64 (log.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 y) (*.f64 (*.f64 2 (log.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 y) 1) (*.f64 (*.f64 2 (log.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 y x)) 1) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (/.f64 y x)) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 y x)) 1) (*.f64 (log.f64 x) 1)))))))

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

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1223×	`associate-*l/_binary64`
999×	`associate-/l/_binary64`
632×	`associate-/r/_binary64`
569×	`unswap-sqr_binary64`
301×	`sqr-pow_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	588
1	39	588
2	92	588
3	306	570
4	1858	534
5	2557	534
6	3474	534
7	3661	534
8	3890	534
9	4167	534

Stop Event

1×	node limit

Counts

159 → 119

Calls

Call 1

Inputs
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(/.f64 y (pow.f64 x 2))
(*.f64 -1/2 (/.f64 y x))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(*.f64 -1/2 (/.f64 y x))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(*.f64 -1/2 (/.f64 y x))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))

Outputs
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(/.f64 y (pow.f64 x 2))
(/.f64 y (*.f64 x x))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (*.f64 y -1/2) x)
(/.f64 -1/2 (/.f64 x y))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3))
(*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)))
(*.f64 y (/.f64 1/8 (/.f64 (pow.f64 x 3) y)))
(.f64 y (.f64 y (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3))
(*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)))
(*.f64 y (/.f64 1/8 (/.f64 (pow.f64 x 3) y)))
(.f64 y (.f64 y (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))
(/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3))
(*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)))
(*.f64 y (/.f64 1/8 (/.f64 (pow.f64 x 3) y)))
(.f64 y (.f64 y (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (*.f64 y -1/2) x)
(/.f64 -1/2 (/.f64 x y))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(*.f64 -1/2 (/.f64 y x))
(/.f64 (*.f64 y -1/2) x)
(/.f64 -1/2 (/.f64 x y))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 y x) (/.f64 (.f64 1/8 (.f64 y y)) (pow.f64 x 3)))
(fma.f64 -1/2 (/.f64 y x) (*.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y))))
(fma.f64 1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) (*.f64 -1/2 (/.f64 y x)))
(.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 (.f64 x x) y))))
(.f64 (/.f64 y x) (fma.f64 (/.f64 y (.f64 x x)) 1/8 -1/2))
(*.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 1/8 x) -1/2))
(*.f64 y (fma.f64 y (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

eval157.0ms (2.6%)

Compiler: Compiled 7001 to 4262 computations (39.1% saved)

prune76.0ms (1.3%)

Pruning

13 alts after pruning (2 fresh and 11 done)

	Pruned	Kept	Total
New	479	1	480
Fresh	0	1	1
Picked	0	1	1
Done	1	10	11
Total	480	13	493

Error

Counts

493 → 13

Alt Table

Click to see full alt table

Status	Error	Program
✓	39.1b	(-.f64 (-.f64 (+.f64 1 (*.f64 (/.f64 y x) -1/2)) 1) x)
✓	62.4b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 y x))) 1)
✓	39.1b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	23.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))
	62.3b	(*.f64 (/.f64 1/2 x) y)
✓	43.9b	(sqrt.f64 y)
	43.1b	x
✓	39.1b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
✓	62.3b	(/.f64 1/2 (/.f64 x y))
✓	43.1b	(+.f64 (*.f64 (/.f64 1/2 x) y) x)
✓	39.5b	(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) x)
✓	39.1b	(neg.f64 x)
✓	39.1b	(-.f64 (*.f64 (/.f64 -1/2 x) y) x)

Compiler

Compiled 109 to 76 computations (30.3% saved)

regimes161.0ms (2.7%)

Counts

20 → 3

Calls

Call 1

Inputs
x
x
(neg.f64 x)
(*.f64 (/.f64 1/2 x) y)
(/.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 y x))
(+.f64 (*.f64 (/.f64 1/2 x) y) x)
(-.f64 (*.f64 (/.f64 -1/2 x) y) x)
(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
(+.f64 (/.f64 1/2 (/.f64 x y)) x)
(-.f64 (*.f64 (/.f64 y x) -1/2) x)
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 y x))) 1)
(+.f64 (-.f64 (+.f64 1 (*.f64 1/2 (/.f64 y x))) 1) x)
(-.f64 (-.f64 (+.f64 1 (*.f64 (/.f64 y x) -1/2)) 1) x)
(sqrt.f64 y)
(sqrt.f64 (+.f64 (*.f64 x x) y))
(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) x)
(fma.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x)))) (neg.f64 x))
(sqrt.f64 (fma.f64 x x y))

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

Calls

6 calls:

60.0ms	y
28.0ms	x
19.0ms	(+.f64 (*.f64 x x) y)
18.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
15.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.0b	3	`x`
17.5b	6	`y`
11.7b	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
11.7b	2	`(+.f64 (*.f64 x x) y)`
11.7b	2	`(*.f64 x x)`
11.7b	2	`(*.f64 x x)`

Compiler

Compiled 167 to 89 computations (46.7% saved)

bsearch151.0ms (2.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
133.0ms	3.330936254499464e+41	7.600769913657203e+45
18.0ms	-1.5720483880855185e+155	-5.087312645855571e+146

Compiler

Compiled 117 to 81 computations (30.8% saved)

regimes156.0ms (2.6%)

Counts

16 → 3

Calls

Call 1

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

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

Calls

2 calls:

122.0ms	y
27.0ms	x

Results

Error	Segments	Branch
4.4b	3	`x`
25.6b	8	`y`

Compiler

Compiled 102 to 57 computations (44.1% saved)

bsearch81.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
48.0ms	68.77666383520821	2340.1901509009426
32.0ms	-9.252132067005785e-39	-5.900500438794851e-40

Compiler

Compiled 208 to 152 computations (26.9% saved)

regimes153.0ms (2.6%)

Counts

15 → 2

Calls

Call 1

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

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

Calls

2 calls:

131.0ms	y
18.0ms	x

Results

Error	Segments	Branch
18.7b	2	`x`
31.5b	10	`y`

Compiler

Compiled 100 to 56 computations (44% saved)

bsearch167.0ms (2.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
167.0ms	-4.895299611719998e-308	8.577377730702204e-303

Compiler

Compiled 193 to 135 computations (30.1% saved)

regimes64.0ms (1.1%)

Counts

7 → 2

Calls

Call 1

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

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

Calls

2 calls:

50.0ms	y
12.0ms	x

Results

Error	Segments	Branch
18.8b	2	`x`
32.7b	8	`y`

Compiler

Compiled 34 to 20 computations (41.2% saved)

bsearch27.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
27.0ms	3.2505527960374563e-225	1.3762839120954544e-224

Compiler

Compiled 103 to 75 computations (27.2% saved)

regimes216.0ms (3.6%)

Counts

6 → 2

Calls

Call 1

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

Outputs
(neg.f64 x)
x

Calls

2 calls:

184.0ms	y
10.0ms	x

Results

Error	Segments	Branch
18.9b	2	`x`
32.7b	8	`y`

Compiler

Compiled 27 to 16 computations (40.7% saved)

bsearch49.0ms (0.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
49.0ms	-4.895299611719998e-308	8.577377730702204e-303

Compiler

Compiled 94 to 72 computations (23.4% saved)

regimes7.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
x
x

Outputs
x

Calls

2 calls:

3.0ms	y
3.0ms	x

Results

Error	Segments	Branch
43.1b	1	`x`
43.1b	1	`y`

Compiler

Compiled 10 to 6 computations (40% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	116
1	46	116
2	49	116
3	50	116

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 x -157204838808551850565492779938527722996974316197934892228530657837673465151747337608729310053544729233070561236616558931883027895976411719519607723860688896) (neg.f64 x) (if (<=.f64 x 339999999999999998239466770371832927223808) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -3766261041232008704/6277101735386680763835789423207666416102355444464034512896) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (if (<=.f64 x 70) (sqrt.f64 y) (+.f64 (.f64 (/.f64 1/2 x) y) x)))
(if (<=.f64 x 6562878239105760/772103322247736428651791941524190166662432288223808740069966728315087660095197093551484618001698015194652854401843307157096133183997320086925557708514169730840749451738610692460887556999562135090788908685580234789131193097780962748024381086918485856402626253175196722230275782071039209488625822100242638638716536487936) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (+.f64 (.f64 (/.f64 1/2 x) y) x))
(if (<=.f64 x 90018194843878032/6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877376) (neg.f64 x) (+.f64 (*.f64 (/.f64 1/2 x) y) x))
(if (<=.f64 x 0) (neg.f64 x) x)
x

Outputs
(if (<=.f64 x -157204838808551850565492779938527722996974316197934892228530657837673465151747337608729310053544729233070561236616558931883027895976411719519607723860688896) (neg.f64 x) (if (<=.f64 x 339999999999999998239466770371832927223808) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -3766261041232008704/6277101735386680763835789423207666416102355444464034512896) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (if (<=.f64 x 70) (sqrt.f64 y) (+.f64 (.f64 (/.f64 1/2 x) y) x)))
(if (<=.f64 x -7355978596156267/12259964326927110866866776217202473468949912977468817408) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (if (<=.f64 x 70) (sqrt.f64 y) (+.f64 x (.f64 y (/.f64 1/2 x)))))
(if (<=.f64 x 6562878239105760/772103322247736428651791941524190166662432288223808740069966728315087660095197093551484618001698015194652854401843307157096133183997320086925557708514169730840749451738610692460887556999562135090788908685580234789131193097780962748024381086918485856402626253175196722230275782071039209488625822100242638638716536487936) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (+.f64 (.f64 (/.f64 1/2 x) y) x))
(if (<=.f64 x 205089944972055/24128228820241763395368498172630942708201009006994023127186460259846489377974909173483894312553062974832901700057603348659254161999916252716423678391067804088773420366831584139402736156236316721587153396424382337160349784305655085875761908966202683012582070411724897569696118189719975296519556940632582457459891765248) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (+.f64 x (.f64 y (/.f64 1/2 x))))
(if (<=.f64 x 90018194843878032/6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877376) (neg.f64 x) (+.f64 (*.f64 (/.f64 1/2 x) y) x))
(if (<=.f64 x 5626137177742377/416750902054990892129990736920078612321547395144744260024766113235252327363602004470089512554472143171433119412089577527868050103382460317522709753270676877880947348719625909903942392869488376545560313508492912623855671752342278830697742336) (neg.f64 x) (+.f64 x (*.f64 y (/.f64 1/2 x))))
(if (<=.f64 x 0) (neg.f64 x) x)
x

Compiler

Compiled 92 to 60 computations (34.8% saved)

soundness93.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

759×	`times-frac_binary64`
599×	`associate-/l*_binary64`
502×	`unswap-sqr_binary64`
498×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	454
1	161	416
2	444	416
3	1586	414
4	5763	414
0	6	7
1	8	7

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 24 to 16 computations (33.3% saved)

end130.0ms (2.2%)

Compiler: Compiled 82 to 48 computations (41.5% saved)