Details

analyze162.0ms (3.1%)

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)

sample1.2s (23.4%)

Results

1.2s	8256×	body	256	valid
39.0ms	349×	body	256	invalid

preprocess16.0ms (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)

simplify61.0ms (1.2%)

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

25.3b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	25.3b	(sqrt.f64 (fma.f64 x x y))
▶	25.3b	(sqrt.f64 (+.f64 (*.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)
✓	23.5b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 18 to 5 computations (72.2% saved)

series7.0ms (0.1%)

Counts

2 → 40

Calls

12 calls:

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

rewrite137.0ms (2.6%)

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))))))

simplify55.0ms (1%)

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
✓	23.5b	(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	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))

rewrite76.0ms (1.4%)

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))))))))

simplify62.0ms (1.2%)

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 (0.6%)

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

prune24.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	128	7	135
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	129	8	137

Error

Counts

137 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	40.3b	x
▶	40.5b	(neg.f64 x)
	40.8b	(fma.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x)))) (neg.f64 x))
▶	40.5b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
▶	40.3b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
▶	44.7b	(sqrt.f64 y)
✓	25.3b	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	25.6b	(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)

Compiler

Compiled 117 to 77 computations (34.2% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)
✓	24.2b	(pow.f64 (fma.f64 x x y) 1/4)

Compiler

Compiled 24 to 11 computations (54.2% saved)

series17.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)
2.0ms	x	@	0	(pow.f64 (fma.f64 x x y) 1/4)
2.0ms	y	@	inf	(pow.f64 (fma.f64 x x y) 1/4)
2.0ms	x	@	inf	(pow.f64 (fma.f64 x x y) 1/4)
1.0ms	y	@	0	(pow.f64 (fma.f64 x x y) 1/4)

rewrite58.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

652×	`pow1_binary64`
605×	`add-log-exp_binary64`
605×	`log1p-expm1-u_binary64`
605×	`expm1-log1p-u_binary64`
590×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	171	14
2	1809	14

Stop Event

1×	node limit

Counts

2 → 38

Calls

Call 1

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

Outputs

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

simplify98.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

852×	`times-frac_binary64`
486×	`associate-/l*_binary64`
478×	`+-commutative_binary64`
411×	`associate-/r*_binary64`
364×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	2022
1	857	1885
2	3158	1746
3	7936	1744

Stop Event

1×	node limit

Counts

86 → 113

Calls

Call 1

Inputs
(pow.f64 y 1/4)
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (pow.f64 y 1/4))
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (+.f64 (pow.f64 y 1/4) (.f64 -3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 4)))))
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (+.f64 (pow.f64 y 1/4) (+.f64 (.f64 7/128 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (pow.f64 x 6))) (.f64 -3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 4))))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (sqrt.f64 x) (.f64 1/4 (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (sqrt.f64 x) (+.f64 (.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 (+.f64 (.f64 1/384 (pow.f64 y 3)) (+.f64 (.f64 1/12 (pow.f64 y 3)) (*.f64 -1/32 (pow.f64 y 3)))) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 x))
(+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 -1) y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 (sqrt.f64 -1) (sqrt.f64 x)))
(+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 -1) y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (.f64 (.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2)))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (.f64 (sqrt.f64 -1) (sqrt.f64 x))))
(+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 -1) y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (.f64 (.f64 (+.f64 (.f64 1/384 (pow.f64 y 3)) (+.f64 (.f64 1/12 (pow.f64 y 3)) (.f64 -1/32 (pow.f64 y 3)))) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (.f64 (.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2)))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 x)))))
(*.f64 (pow.f64 1 1/4) (sqrt.f64 x))
(+.f64 (.f64 (pow.f64 1 1/4) (sqrt.f64 x)) (.f64 1/4 (.f64 (pow.f64 1 1/4) (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (.f64 (pow.f64 1 1/4) (sqrt.f64 x)) (+.f64 (.f64 1/4 (.f64 (pow.f64 1 1/4) (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (.f64 -3/32 (.f64 (pow.f64 1 1/4) (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))
(+.f64 (.f64 (pow.f64 1 1/4) (sqrt.f64 x)) (+.f64 (.f64 1/4 (.f64 (pow.f64 1 1/4) (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (.f64 7/128 (.f64 (pow.f64 1 1/4) (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))))) (.f64 -3/32 (.f64 (pow.f64 1 1/4) (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))))))
(pow.f64 y 1/4)
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (pow.f64 y 1/4))
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (+.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (*.f64 1/32 (pow.f64 x 4)))) (pow.f64 y 1/4)))
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (+.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (+.f64 (.f64 -1/32 (pow.f64 x 6)) (+.f64 (.f64 1/12 (pow.f64 x 6)) (.f64 1/384 (pow.f64 x 6))))) (+.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (*.f64 1/32 (pow.f64 x 4)))) (pow.f64 y 1/4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1))))
(+.f64 (.f64 1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 x 2)) y)) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1))))) (pow.f64 y 2)) (+.f64 (.f64 1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 x 2)) y)) (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1))))))
(+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 (.f64 -1/12 (pow.f64 x 6)) (+.f64 (.f64 1/32 (pow.f64 x 6)) (.f64 -1/384 (pow.f64 x 6)))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1))))) (pow.f64 y 3))) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1))))) (pow.f64 y 2)) (+.f64 (.f64 1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 x 2)) y)) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))))))
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (+.f64 (.f64 (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (pow.f64 x 4)) (sqrt.f64 y)))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (+.f64 (.f64 (+.f64 (.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))))) (pow.f64 x 6)) (+.f64 (.f64 (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (pow.f64 x 4)) (sqrt.f64 y))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (pow.f64 y 2))) (pow.f64 x 3))) x)))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 1/2 (/.f64 (.f64 y (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2)))) (pow.f64 x 5))) (+.f64 (.f64 1/192 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (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 (.f64 -2 (/.f64 (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2))) (pow.f64 x 3))) (.f64 -1/16 (/.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 -1/192 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 -1/2 (/.f64 (.f64 y (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2)))) (pow.f64 x 5))) (+.f64 (.f64 -1 x) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2))) (pow.f64 x 3))) (+.f64 (.f64 -1/6 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (*.f64 -1/16 (/.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)))
(sqrt.f64 y)
(+.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 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (+.f64 (sqrt.f64 y) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))))))))
(+.f64 (.f64 1/16 (.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))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (+.f64 (.f64 -1/32 (pow.f64 x 6)) (+.f64 (.f64 1/12 (pow.f64 x 6)) (.f64 1/384 (pow.f64 x 6)))))) (+.f64 (sqrt.f64 y) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (pow.f64 x 2)))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))))))))))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (pow.f64 x 2)) y)))
(+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (pow.f64 x 2)) y)))))
(+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 2 (.f64 (+.f64 (.f64 1/32 (pow.f64 x 6)) (+.f64 (.f64 -1/384 (pow.f64 x 6)) (.f64 -1/12 (pow.f64 x 6)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2))) (.f64 -1/2 (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (.f64 (pow.f64 x 2) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2))))) (pow.f64 y 3))) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (pow.f64 x 2)) y))))))

Outputs
(pow.f64 y 1/4)
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (pow.f64 y 1/4))
(fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (pow.f64 y 1/4))
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (+.f64 (pow.f64 y 1/4) (.f64 -3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 4)))))
(+.f64 (fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (pow.f64 y 1/4)) (.f64 -3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 4))))
(fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (fma.f64 -3/32 (*.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 4)) (pow.f64 y 1/4)))
(fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (*.f64 -3/32 (pow.f64 x 4)) (pow.f64 y 1/4)))
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (+.f64 (pow.f64 y 1/4) (+.f64 (.f64 7/128 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (pow.f64 x 6))) (.f64 -3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 4))))))
(+.f64 (fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (pow.f64 y 1/4)) (fma.f64 7/128 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (pow.f64 x 6)) (.f64 -3/32 (*.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 4)))))
(fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (.f64 (pow.f64 x 6) 7/128) (fma.f64 -3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 4)) (pow.f64 y 1/4))))
(fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (.f64 (pow.f64 x 6) 7/128) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (.f64 -3/32 (pow.f64 x 4)) (pow.f64 y 1/4))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 1/4 (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x))
(+.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (sqrt.f64 x) (.f64 1/4 (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 (.f64 (.f64 y y) -3/32) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (+.f64 (sqrt.f64 x) (.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 (.f64 -3/32 (.f64 y y)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/4 (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x)))
(fma.f64 (.f64 y (.f64 y -3/32)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/4 (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x)))
(+.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (sqrt.f64 x) (+.f64 (.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 (+.f64 (.f64 1/384 (pow.f64 y 3)) (+.f64 (.f64 1/12 (pow.f64 y 3)) (*.f64 -1/32 (pow.f64 y 3)))) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))))))
(fma.f64 (.f64 (.f64 y y) -3/32) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (+.f64 (sqrt.f64 x) (fma.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 (fma.f64 1/384 (pow.f64 y 3) (*.f64 (pow.f64 y 3) 5/96)) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))))))
(+.f64 (fma.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 (.f64 (pow.f64 y 3) 7/128) (sqrt.f64 (/.f64 1 (pow.f64 x 11))))) (fma.f64 (.f64 -3/32 (*.f64 y y)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 x)))
(+.f64 (.f64 (.f64 (pow.f64 y 3) 7/128) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (fma.f64 (.f64 y (.f64 y -3/32)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/4 (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 -1))
(+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 -1) y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 (sqrt.f64 -1) (sqrt.f64 x)))
(fma.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 y (sqrt.f64 -1))) (*.f64 (sqrt.f64 x) (sqrt.f64 -1)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 -1) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 (*.f64 y 1/4) (sqrt.f64 -1))))
(.f64 (sqrt.f64 -1) (fma.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x)))
(+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 -1) y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (.f64 (.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2)))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (.f64 (sqrt.f64 -1) (sqrt.f64 x))))
(fma.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 y (sqrt.f64 -1))) (fma.f64 (.f64 (.f64 (.f64 y y) -3/32) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (.f64 (sqrt.f64 x) (sqrt.f64 -1))))
(fma.f64 (.f64 (.f64 y 1/4) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 (sqrt.f64 -1) (fma.f64 (.f64 -3/32 (*.f64 y y)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 x))))
(.f64 (sqrt.f64 -1) (fma.f64 (.f64 y (.f64 y -3/32)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x))))
(+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 -1) y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (.f64 (.f64 (+.f64 (.f64 1/384 (pow.f64 y 3)) (+.f64 (.f64 1/12 (pow.f64 y 3)) (.f64 -1/32 (pow.f64 y 3)))) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (.f64 (.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2)))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 x)))))
(fma.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 y (sqrt.f64 -1))) (fma.f64 (.f64 (fma.f64 1/384 (pow.f64 y 3) (.f64 (pow.f64 y 3) 5/96)) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 x 11))) (fma.f64 (.f64 (.f64 (.f64 y y) -3/32) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (.f64 (sqrt.f64 x) (sqrt.f64 -1)))))
(fma.f64 1/4 (.f64 y (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 (.f64 (pow.f64 y 3) 7/128) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 11))) (sqrt.f64 -1)) (.f64 (sqrt.f64 -1) (fma.f64 (.f64 -3/32 (*.f64 y y)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 x)))))
(+.f64 (.f64 (sqrt.f64 -1) (fma.f64 (.f64 y (.f64 y -3/32)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 x))) (.f64 (sqrt.f64 -1) (fma.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 (*.f64 (pow.f64 y 3) 7/128) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))))))
(*.f64 (pow.f64 1 1/4) (sqrt.f64 x))
(sqrt.f64 x)
(+.f64 (.f64 (pow.f64 1 1/4) (sqrt.f64 x)) (.f64 1/4 (.f64 (pow.f64 1 1/4) (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (sqrt.f64 x) (.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 1/4 (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x))
(+.f64 (.f64 (pow.f64 1 1/4) (sqrt.f64 x)) (+.f64 (.f64 1/4 (.f64 (pow.f64 1 1/4) (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (.f64 -3/32 (.f64 (pow.f64 1 1/4) (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))
(fma.f64 (.f64 (.f64 y y) -3/32) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (+.f64 (sqrt.f64 x) (.f64 1/4 (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 (.f64 -3/32 (.f64 y y)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/4 (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x)))
(fma.f64 (.f64 y (.f64 y -3/32)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/4 (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x)))
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(pow.f64 y 1/4)
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (pow.f64 y 1/4))
(fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (pow.f64 y 1/4))
(+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (pow.f64 x 2))) (+.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (*.f64 1/32 (pow.f64 x 4)))) (pow.f64 y 1/4)))
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(fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (*.f64 -3/32 (pow.f64 x 4)) (pow.f64 y 1/4)))
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(+.f64 (fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (pow.f64 y 1/4)) (fma.f64 7/128 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (pow.f64 x 6)) (.f64 -3/32 (*.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 4)))))
(fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (.f64 (pow.f64 x 6) 7/128) (fma.f64 -3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 4)) (pow.f64 y 1/4))))
(fma.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) (.f64 x x)) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (.f64 (pow.f64 x 6) 7/128) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (.f64 -3/32 (pow.f64 x 4)) (pow.f64 y 1/4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1))))
(pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1)))
(pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))
(*.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4))
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(fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) (/.f64 y (*.f64 x x))) (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))))
(fma.f64 1/4 (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) y) (.f64 x x)) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))))
(fma.f64 1/4 (.f64 (/.f64 (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) y) (.f64 x x)) (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1))))) (pow.f64 y 2)) (+.f64 (.f64 1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 x 2)) y)) (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1))))))
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(fma.f64 -1 (/.f64 (fma.f64 1/32 (pow.f64 x 6) (.f64 (pow.f64 x 6) -11/128)) (/.f64 (pow.f64 y 3) (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))))) (+.f64 (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) (/.f64 y (.f64 x x))) (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1)))) (/.f64 (.f64 (pow.f64 x 4) -3/32) (/.f64 (.f64 y y) (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1)))))))
(-.f64 (+.f64 (fma.f64 1/4 (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) y) (.f64 x x)) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (.f64 (/.f64 (.f64 -3/32 (pow.f64 x 4)) y) (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) y))) (.f64 (/.f64 (.f64 (pow.f64 x 6) -7/128) (pow.f64 y 3)) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))))
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(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 (.f64 x x) (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y))
(fma.f64 1/2 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 y)))) (sqrt.f64 y))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (+.f64 (.f64 (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (pow.f64 x 4)) (sqrt.f64 y)))
(fma.f64 1/2 (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 y))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8) (pow.f64 x 4) (sqrt.f64 y)))
(fma.f64 1/2 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 y)))) (fma.f64 (pow.f64 x 4) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (sqrt.f64 y)))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (+.f64 (.f64 (+.f64 (.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))))) (pow.f64 x 6)) (+.f64 (.f64 (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (pow.f64 x 4)) (sqrt.f64 y))))
(fma.f64 1/2 (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 y))) (fma.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) 1/16) (pow.f64 x 6) (fma.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8) (pow.f64 x 4) (sqrt.f64 y))))
(fma.f64 1/2 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 y)))) (fma.f64 (pow.f64 x 6) (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (fma.f64 (pow.f64 x 4) (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (sqrt.f64 y))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(fma.f64 1/2 (/.f64 y x) x)
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 -1/8 (pow.f64 y 2)) (*.f64 1/32 (pow.f64 y 2))) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (.f64 y y) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 y x) (fma.f64 2 (/.f64 (.f64 (*.f64 y y) -3/32) (pow.f64 x 3)) x)))
(fma.f64 1/16 (/.f64 y (/.f64 (pow.f64 x 3) y)) (fma.f64 1/2 (/.f64 y x) (fma.f64 2 (/.f64 (.f64 -3/32 (.f64 y y)) (pow.f64 x 3)) x)))
(fma.f64 1/16 (.f64 (/.f64 y (pow.f64 x 3)) y) (fma.f64 1/2 (/.f64 y x) (fma.f64 2 (/.f64 -3/32 (/.f64 (pow.f64 x 3) (.f64 y y))) x)))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 1/2 (/.f64 (.f64 y (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2)))) (pow.f64 x 5))) (+.f64 (.f64 1/192 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 -1/8 (pow.f64 y 2)) (.f64 1/32 (pow.f64 y 2))) (pow.f64 x 3))) x)))))))
(fma.f64 1/16 (/.f64 (.f64 y y) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 y x) (fma.f64 1/2 (/.f64 (.f64 y (.f64 (.f64 y y) -3/32)) (pow.f64 x 5)) (fma.f64 1/192 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/6 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 2 (/.f64 (.f64 (.f64 y y) -3/32) (pow.f64 x 3)) x)))))))
(fma.f64 1/16 (/.f64 y (/.f64 (pow.f64 x 3) y)) (fma.f64 1/2 (/.f64 y x) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 y 3) -3/32) (pow.f64 x 5)) (+.f64 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (fma.f64 2 (/.f64 (.f64 -3/32 (.f64 y y)) (pow.f64 x 3)) x)) (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) 11/64)))))
(fma.f64 1/16 (.f64 (/.f64 y (pow.f64 x 3)) y) (fma.f64 1/2 (/.f64 y x) (fma.f64 1/2 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -3/32) (+.f64 (fma.f64 2 (/.f64 -3/32 (/.f64 (pow.f64 x 3) (.f64 y y))) x) (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) 7/64)))))
(*.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)
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(fma.f64 -1/2 (/.f64 y x) (fma.f64 -1 x (fma.f64 -2 (/.f64 (.f64 (.f64 y y) -3/32) (pow.f64 x 3)) (/.f64 (.f64 -1/16 (.f64 y y)) (pow.f64 x 3)))))
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(fma.f64 -1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/192 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/2 (/.f64 (.f64 y (.f64 (.f64 y y) -3/32)) (pow.f64 x 5)) (fma.f64 -1 x (fma.f64 -2 (/.f64 (.f64 (.f64 y y) -3/32) (pow.f64 x 3)) (fma.f64 -1/6 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (/.f64 (.f64 -1/16 (*.f64 y y)) (pow.f64 x 3)))))))))
(fma.f64 (/.f64 y x) -1/2 (+.f64 (fma.f64 (/.f64 (.f64 (pow.f64 y 3) -3/32) (pow.f64 x 5)) -1/2 (-.f64 (fma.f64 (/.f64 (.f64 -3/32 (.f64 y y)) (pow.f64 x 3)) -2 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/6 (/.f64 -1/16 (/.f64 (pow.f64 x 3) (.f64 y y))))) x)) (*.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) 11/192)))
(fma.f64 (/.f64 y x) -1/2 (+.f64 (fma.f64 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -3/32) -1/2 (-.f64 (fma.f64 (/.f64 -3/32 (/.f64 (pow.f64 x 3) (.f64 y y))) -2 (fma.f64 (.f64 (/.f64 y (pow.f64 x 3)) y) -1/16 (/.f64 (pow.f64 y 3) (/.f64 (pow.f64 x 5) -1/6)))) x)) (/.f64 (.f64 (pow.f64 y 3) 11/192) (pow.f64 x 5))))
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 (/.f64 y (pow.f64 x 3)) y) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x)))
(fma.f64 1/16 (/.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 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (*.f64 (/.f64 y (pow.f64 x 3)) y) x)))
(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 (.f64 x x) (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y))
(fma.f64 1/2 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 y)))) (sqrt.f64 y))
(+.f64 (.f64 1/16 (.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))) (+.f64 (sqrt.f64 y) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))))))))
(fma.f64 1/16 (.f64 (pow.f64 x 4) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (fma.f64 1/2 (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 y))) (+.f64 (sqrt.f64 y) (.f64 2 (.f64 (.f64 (pow.f64 x 4) -3/32) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))))))
(fma.f64 1/16 (.f64 (pow.f64 x 4) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (fma.f64 1/2 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 y)))) (fma.f64 2 (.f64 (pow.f64 x 4) (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (sqrt.f64 y))))
(+.f64 (fma.f64 1/2 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 y)))) (sqrt.f64 y)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (+.f64 (.f64 2 (.f64 -3/32 (pow.f64 x 4))) (.f64 1/16 (pow.f64 x 4)))))
(+.f64 (.f64 1/16 (.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))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (+.f64 (.f64 -1/32 (pow.f64 x 6)) (+.f64 (.f64 1/12 (pow.f64 x 6)) (.f64 1/384 (pow.f64 x 6)))))) (+.f64 (sqrt.f64 y) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (pow.f64 x 2)))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))))))))))
(fma.f64 1/16 (.f64 (pow.f64 x 4) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (fma.f64 1/2 (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 y))) (fma.f64 2 (.f64 (fma.f64 -1/32 (pow.f64 x 6) (.f64 (pow.f64 x 6) 11/128)) (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (+.f64 (sqrt.f64 y) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 (.f64 x x) (.f64 (pow.f64 x 4) -3/32))) (.f64 2 (.f64 (.f64 (pow.f64 x 4) -3/32) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))))))))
(fma.f64 1/16 (.f64 (pow.f64 x 4) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (fma.f64 1/2 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 y)))) (+.f64 (fma.f64 2 (.f64 (pow.f64 x 4) (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 (pow.f64 x 6) -3/32)))) (fma.f64 2 (.f64 (.f64 (pow.f64 x 6) 7/128) (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (sqrt.f64 y)))))
(fma.f64 1/16 (.f64 (pow.f64 x 4) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (fma.f64 1/2 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 y)))) (+.f64 (.f64 (.f64 -3/32 (pow.f64 x 4)) (+.f64 (.f64 2 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (.f64 x x)))) (fma.f64 2 (.f64 (*.f64 (pow.f64 x 6) 7/128) (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (sqrt.f64 y)))))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)
(pow.f64 (*.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (pow.f64 x 2)) y)))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2) (.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2) (/.f64 y (.f64 x x)))))
(fma.f64 1/2 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) y) (.f64 x x)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2))
(fma.f64 1/2 (.f64 (/.f64 (.f64 x x) y) (pow.f64 (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2)) (pow.f64 (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2))
(+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (pow.f64 x 2)) y)))))
(fma.f64 1/16 (/.f64 (pow.f64 x 4) (/.f64 (.f64 y y) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2))) (+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2) (fma.f64 2 (/.f64 (.f64 (pow.f64 x 4) -3/32) (/.f64 (.f64 y y) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2))) (.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2) (/.f64 y (*.f64 x x)))))))
(+.f64 (fma.f64 2 (.f64 (/.f64 (.f64 -3/32 (pow.f64 x 4)) y) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) y)) (.f64 1/2 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) y) (.f64 x x)))) (fma.f64 1/16 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) y) (/.f64 (pow.f64 x 4) y)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)))
(+.f64 (fma.f64 2 (.f64 (/.f64 (pow.f64 x 4) (/.f64 y -3/32)) (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2) y)) (.f64 1/2 (.f64 (/.f64 (.f64 x x) y) (pow.f64 (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2)))) (fma.f64 1/16 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2) y) (/.f64 (pow.f64 x 4) y)) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2)))
(+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 2 (.f64 (+.f64 (.f64 1/32 (pow.f64 x 6)) (+.f64 (.f64 -1/384 (pow.f64 x 6)) (.f64 -1/12 (pow.f64 x 6)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2))) (.f64 -1/2 (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (.f64 (pow.f64 x 2) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2))))) (pow.f64 y 3))) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2)) (pow.f64 y 2))) (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) 2) (pow.f64 x 2)) y))))))
(fma.f64 1/16 (/.f64 (pow.f64 x 4) (/.f64 (.f64 y y) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2))) (+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2) (fma.f64 -1 (/.f64 (fma.f64 2 (.f64 (fma.f64 1/32 (pow.f64 x 6) (.f64 (pow.f64 x 6) -11/128)) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2)) (.f64 -1/2 (.f64 (.f64 (pow.f64 x 4) -3/32) (.f64 (.f64 x x) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2))))) (pow.f64 y 3)) (fma.f64 2 (/.f64 (.f64 (pow.f64 x 4) -3/32) (/.f64 (.f64 y y) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2))) (.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) 2) (/.f64 y (.f64 x x))))))))
(+.f64 (-.f64 (fma.f64 2 (.f64 (/.f64 (.f64 -3/32 (pow.f64 x 4)) y) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) y)) (.f64 1/2 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) y) (.f64 x x)))) (/.f64 (fma.f64 2 (.f64 (.f64 (pow.f64 x 6) -7/128) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)) (.f64 -1/2 (.f64 (.f64 (pow.f64 x 6) -3/32) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)))) (pow.f64 y 3))) (fma.f64 1/16 (*.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) y) (/.f64 (pow.f64 x 4) y)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)))
(+.f64 (-.f64 (fma.f64 2 (.f64 (/.f64 (pow.f64 x 4) (/.f64 y -3/32)) (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2) y)) (.f64 1/2 (.f64 (/.f64 (.f64 x x) y) (pow.f64 (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2)))) (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2) (+.f64 (.f64 2 (.f64 (pow.f64 x 6) -7/128)) (.f64 -1/2 (.f64 (pow.f64 x 6) -3/32)))) (pow.f64 y 3))) (fma.f64 1/16 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2) y) (/.f64 (pow.f64 x 4) y)) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 y) -1/4) (pow.f64 -1 1/4)) 2)))

localize3.0ms (0%)

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

localize26.0ms (0.5%)

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

localize7.0ms (0.1%)

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

localize2.0ms (0%)

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

eval184.0ms (3.5%)

Compiler: Compiled 3159 to 2366 computations (25.1% saved)

prune33.0ms (0.6%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	1	2
Picked	0	1	1
Done	0	5	5
Total	113	8	121

Error

Counts

121 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	40.3b	x
▶	40.8b	(fma.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x)))) (neg.f64 x))
✓	40.5b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	40.3b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	44.7b	(sqrt.f64 y)
✓	40.5b	(neg.f64 x)
✓	25.3b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	25.6b	(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize59.0ms (1.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(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))
✓	0.2b	(/.f64 1/8 (/.f64 x (/.f64 y x)))

Compiler

Compiled 47 to 18 computations (61.7% saved)

series49.0ms (0.9%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
30.0ms	x	@	0	(fma.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x)))) (neg.f64 x))
4.0ms	y	@	0	(fma.f64 (/.f64 y x) (+.f64 -1/2 (/.f64 1/8 (/.f64 x (/.f64 y x)))) (neg.f64 x))
2.0ms	x	@	0	(/.f64 1/8 (/.f64 x (/.f64 y x)))
1.0ms	y	@	inf	(/.f64 1/8 (/.f64 x (/.f64 y x)))
1.0ms	y	@	0	(/.f64 1/8 (/.f64 x (/.f64 y x)))

rewrite186.0ms (3.5%)

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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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))))))

simplify145.0ms (2.8%)

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)

eval131.0ms (2.5%)

Compiler: Compiled 4853 to 2132 computations (56.1% saved)

prune103.0ms (2%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	1	1
Picked	1	0	1
Done	0	6	6
Total	189	8	197

Error

Counts

197 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	40.3b	x
▶	40.8b	(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) x)
✓	40.5b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	40.3b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	44.7b	(sqrt.f64 y)
✓	40.5b	(neg.f64 x)
✓	25.3b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	25.6b	(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)

Compiler

Compiled 63 to 42 computations (33.3% saved)

localize16.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2))
✓	0.2b	(fma.f64 1/8 (/.f64 y (*.f64 x x)) -1/2)
✓	9.2b	(/.f64 y (*.f64 x x))

Compiler

Compiled 51 to 19 computations (62.7% saved)

series9.0ms (0.2%)

Counts

3 → 72

Calls

18 calls:

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

rewrite124.0ms (2.4%)

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	35
1	215	35
2	2809	35

Stop Event

1×	node limit

Counts

3 → 145

Calls

Call 1

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

simplify141.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1147×	`associate-/l/_binary64`
645×	`associate-/r/_binary64`
591×	`unswap-sqr_binary64`
407×	`sqr-pow_binary64`
313×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	819
1	48	819
2	108	819
3	334	765
4	1975	765
5	2698	765
6	3646	765
7	3833	765
8	4062	765
9	4339	765
10	7126	765

Stop Event

1×	node limit

Counts

217 → 158

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

eval143.0ms (2.7%)

Compiler: Compiled 2961 to 1801 computations (39.2% saved)

prune26.0ms (0.5%)

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	1	1
Picked	0	1	1
Done	0	6	6
Total	157	9	166

Error

Counts

166 → 9

Alt Table

Click to see full alt table

Status	Error	Program
	40.3b	x
	40.5b	(-.f64 (*.f64 y (/.f64 -1/2 x)) x)
✓	40.8b	(-.f64 (.f64 (/.f64 y x) (fma.f64 1/8 (/.f64 y (.f64 x x)) -1/2)) x)
✓	40.5b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	40.3b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	44.7b	(sqrt.f64 y)
✓	40.5b	(neg.f64 x)
✓	25.3b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	25.6b	(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)

Compiler

Compiled 72 to 48 computations (33.3% saved)

regimes187.0ms (3.6%)

Counts

12 → 3

Calls

Call 1

Inputs
x
x
(neg.f64 x)
(-.f64 (*.f64 y (/.f64 -1/2 x)) x)
(-.f64 (*.f64 (/.f64 y x) -1/2) x)
(+.f64 (*.f64 1/2 (/.f64 y x)) 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))
(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)

Outputs
(neg.f64 x)
(sqrt.f64 (fma.f64 x x y))
x

Calls

6 calls:

74.0ms	(+.f64 (*.f64 x x) y)
51.0ms	y
20.0ms	x
13.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
12.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.0b	3	`x`
20.0b	6	`y`
11.2b	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
11.2b	2	`(+.f64 (*.f64 x x) y)`
11.2b	2	`(*.f64 x x)`
11.2b	2	`(*.f64 x x)`

Compiler

Compiled 108 to 55 computations (49.1% saved)

bsearch70.0ms (1.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
53.0ms	1.4461216610068415e+141	4.073819549367646e+143
17.0ms	-1.7544275060164714e+154	-3.0076749459931755e+151

Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes451.0ms (8.6%)

Counts

10 → 3

Calls

Call 1

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

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

Calls

6 calls:

204.0ms	x
127.0ms	y
52.0ms	(*.f64 x x)
26.0ms	(+.f64 (*.f64 x x) y)
24.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

Results

Error	Segments	Branch
0.0b	3	`x`
20.0b	6	`y`
11.2b	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
11.2b	2	`(+.f64 (*.f64 x x) y)`
11.2b	2	`(*.f64 x x)`
11.2b	2	`(*.f64 x x)`

Compiler

Compiled 95 to 49 computations (48.4% saved)

bsearch99.0ms (1.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
63.0ms	1.4461216610068415e+141	4.073819549367646e+143
36.0ms	-1.7544275060164714e+154	-3.0076749459931755e+151

Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes112.0ms (2.1%)

Counts

7 → 3

Calls

Call 1

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

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

Calls

2 calls:

75.0ms	y
33.0ms	x

Results

Error	Segments	Branch
5.9b	3	`x`
27.1b	5	`y`

Compiler

Compiled 35 to 19 computations (45.7% saved)

bsearch382.0ms (7.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
199.0ms	4.008285978463555e-36	9.965324625791255e-21
183.0ms	-1.8290758091167849e-28	-5.9912199893643025e-31

Compiler

Compiled 283 to 207 computations (26.9% saved)

regimes40.0ms (0.8%)

Counts

6 → 2

Calls

Call 1

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

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

Calls

2 calls:

28.0ms	y
10.0ms	x

Results

Error	Segments	Branch
17.3b	2	`x`
34.6b	5	`y`

Compiler

Compiled 33 to 18 computations (45.5% saved)

bsearch28.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
28.0ms	-1.9028900314516054e-232	-4.8603220366534336e-234

Compiler

Compiled 153 to 107 computations (30.1% saved)

regimes78.0ms (1.5%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

65.0ms	y
11.0ms	x

Results

Error	Segments	Branch
17.4b	2	`x`
34.6b	5	`y`

Compiler

Compiled 26 to 15 computations (42.3% saved)

bsearch30.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
29.0ms	-1.9028900314516054e-232	-4.8603220366534336e-234

Compiler

Compiled 111 to 79 computations (28.8% saved)

regimes28.0ms (0.5%)

Counts

3 → 2

Calls

Call 1

Inputs
x
x
(neg.f64 x)

Outputs
(neg.f64 x)
x

Calls

2 calls:

20.0ms	y
7.0ms	x

Results

Error	Segments	Branch
17.4b	2	`x`
34.6b	5	`y`

Compiler

Compiled 12 to 7 computations (41.7% saved)

bsearch88.0ms (1.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
88.0ms	-8.127404055929888e-287	1.259221632089287e-302

Compiler

Compiled 112 to 86 computations (23.2% saved)

regimes18.0ms (0.3%)

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:

7.0ms	y
7.0ms	x

Results

Error	Segments	Branch
40.3b	1	`x`
40.3b	1	`y`

Compiler

Compiled 10 to 6 computations (40% saved)

simplify16.0ms (0.3%)

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	40	137
1	48	137
2	51	137
3	52	137

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 x -17544275060164713894306688303999904308694043034964030746747844514761268194827159750574352039749001188476558872411106367070798218777215600517420031550685184) (neg.f64 x) (if (<=.f64 x 1446121661006841454771711796042547343108706322033818959215399592987633476742054403222233718848700167038308020931795079235764251347040321142784) (sqrt.f64 (fma.f64 x x y)) x))
(if (<=.f64 x -17544275060164713894306688303999904308694043034964030746747844514761268194827159750574352039749001188476558872411106367070798218777215600517420031550685184) (neg.f64 x) (if (<=.f64 x 1446121661006841454771711796042547343108706322033818959215399592987633476742054403222233718848700167038308020931795079235764251347040321142784) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -6850788924988607/11417981541647679048466287755595961091061972992) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (if (<=.f64 x 6135968474170063/1496577676626844588240573268701473812127674924007424) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x)))
(if (<=.f64 x -1328464781374571/6991919901971426075297554671307333615898862102580725715195666431228287110681861367027657291461090911970058473930419853533788296083269867358507086435928852446414275954096487329654980776728266302794199220759703429559553357814144917874843453883416576) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (+.f64 (.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x -1328464781374571/6991919901971426075297554671307333615898862102580725715195666431228287110681861367027657291461090911970058473930419853533788296083269867358507086435928852446414275954096487329654980776728266302794199220759703429559553357814144917874843453883416576) (-.f64 (*.f64 y (/.f64 -1/2 x)) x) x)
(if (<=.f64 x 0) (neg.f64 x) x)
x

Outputs
(if (<=.f64 x -17544275060164713894306688303999904308694043034964030746747844514761268194827159750574352039749001188476558872411106367070798218777215600517420031550685184) (neg.f64 x) (if (<=.f64 x 1446121661006841454771711796042547343108706322033818959215399592987633476742054403222233718848700167038308020931795079235764251347040321142784) (sqrt.f64 (fma.f64 x x y)) x))
(if (<=.f64 x -17544275060164713894306688303999904308694043034964030746747844514761268194827159750574352039749001188476558872411106367070798218777215600517420031550685184) (neg.f64 x) (if (<=.f64 x 1446121661006841454771711796042547343108706322033818959215399592987633476742054403222233718848700167038308020931795079235764251347040321142784) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -17544275060164713894306688303999904308694043034964030746747844514761268194827159750574352039749001188476558872411106367070798218777215600517420031550685184) (neg.f64 x) (if (<=.f64 x 1446121661006841454771711796042547343108706322033818959215399592987633476742054403222233718848700167038308020931795079235764251347040321142784) (sqrt.f64 (+.f64 y (*.f64 x x))) x))
(if (<=.f64 x -6850788924988607/11417981541647679048466287755595961091061972992) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (if (<=.f64 x 6135968474170063/1496577676626844588240573268701473812127674924007424) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x)))
(if (<=.f64 x -6850788924988607/11417981541647679048466287755595961091061972992) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (if (<=.f64 x 6135968474170063/1496577676626844588240573268701473812127674924007424) (sqrt.f64 y) (+.f64 x (.f64 1/2 (/.f64 y x)))))
(if (<=.f64 x -1328464781374571/6991919901971426075297554671307333615898862102580725715195666431228287110681861367027657291461090911970058473930419853533788296083269867358507086435928852446414275954096487329654980776728266302794199220759703429559553357814144917874843453883416576) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (+.f64 (.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x -1328464781374571/6991919901971426075297554671307333615898862102580725715195666431228287110681861367027657291461090911970058473930419853533788296083269867358507086435928852446414275954096487329654980776728266302794199220759703429559553357814144917874843453883416576) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (+.f64 x (.f64 1/2 (/.f64 y x))))
(if (<=.f64 x -1328464781374571/6991919901971426075297554671307333615898862102580725715195666431228287110681861367027657291461090911970058473930419853533788296083269867358507086435928852446414275954096487329654980776728266302794199220759703429559553357814144917874843453883416576) (-.f64 (*.f64 y (/.f64 -1/2 x)) x) x)
(if (<=.f64 x 0) (neg.f64 x) x)
x

Compiler

Compiled 109 to 70 computations (35.8% saved)

soundness101.0ms (1.9%)

Algorithm

3×	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
0	6	7
1	8	7

Stop Event

1×	saturated
1×	saturated
1×	node limit

Compiler

Compiled 39 to 25 computations (35.9% saved)

end59.0ms (1.1%)

Compiler: Compiled 97 to 55 computations (43.3% saved)

Details

analyze162.0ms (3.1%)

sample1.2s (23.4%)

preprocess16.0ms (0.3%)

simplify61.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series7.0ms (0.1%)

rewrite137.0ms (2.6%)

simplify55.0ms (1%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite76.0ms (1.4%)

simplify62.0ms (1.2%)

eval33.0ms (0.6%)

prune24.0ms (0.5%)

localize16.0ms (0.3%)

series17.0ms (0.3%)

rewrite58.0ms (1.1%)

simplify98.0ms (1.9%)

localize3.0ms (0%)

localize26.0ms (0.5%)

localize7.0ms (0.1%)

localize2.0ms (0%)

eval184.0ms (3.5%)

prune33.0ms (0.6%)

localize59.0ms (1.1%)

series49.0ms (0.9%)

rewrite186.0ms (3.5%)

simplify145.0ms (2.8%)

eval131.0ms (2.5%)

prune103.0ms (2%)

localize16.0ms (0.3%)

series9.0ms (0.2%)

rewrite124.0ms (2.4%)

simplify141.0ms (2.7%)

eval143.0ms (2.7%)

prune26.0ms (0.5%)

regimes187.0ms (3.6%)

bsearch70.0ms (1.3%)

regimes451.0ms (8.6%)

bsearch99.0ms (1.9%)

regimes112.0ms (2.1%)

bsearch382.0ms (7.3%)

regimes40.0ms (0.8%)

bsearch28.0ms (0.5%)

regimes78.0ms (1.5%)

bsearch30.0ms (0.6%)

regimes28.0ms (0.5%)

bsearch88.0ms (1.7%)

regimes18.0ms (0.3%)

simplify16.0ms (0.3%)

soundness101.0ms (1.9%)

end59.0ms (1.1%)

Profiling