Details

analyze99.0ms (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)

sample1.6s (48.3%)

Results

1.5s	8256×	body	256	valid
27.0ms	336×	body	256	invalid

preprocess18.0ms (0.6%)

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)

simplify8.0ms (0.3%)

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))

eval1.0ms (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

21.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.0b	(sqrt.f64 (fma.f64 x x y))
▶	21.0b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 15 to 9 computations (40% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	19.6b	(sqrt.f64 (+.f64 (*.f64 x x) y))
	0.0b	(+.f64 (*.f64 x x) y)
✓	0.0b	(+.f64 (*.f64 x x) y)
✓	19.6b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 18 to 5 computations (72.2% saved)

series7.0ms (0.2%)

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	y	@	0	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite49.0ms (1.5%)

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	1746	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 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 expm1.f64 (log1p.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 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))))) (#(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 expm1.f64 (log1p.f64 (fma.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 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 expm1.f64 (log1p.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 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))))) (#(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 expm1.f64 (log1p.f64 (fma.f64 x x y)))))))

simplify49.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

759×	`times-frac_binary64`
595×	`associate-/l*_binary64`
504×	`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	1576	414
4	5621	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 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)))
(+.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 y (/.f64 (pow.f64 x 3) y)) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 (*.f64 y 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 y (/.f64 (pow.f64 x 3) y)) x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 -1 x))
(fma.f64 -1/2 (/.f64 y x) (neg.f64 x))
(-.f64 (*.f64 (/.f64 y x) -1/2) x)
(-.f64 (*.f64 y (/.f64 -1/2 x)) 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 y) (pow.f64 x 3)) 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 (.f64 y y) (pow.f64 x 3)) 1/8) x)))
(fma.f64 (/.f64 y x) -1/2 (-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) 1/8 (.f64 (/.f64 -1/16 (pow.f64 x 5)) (pow.f64 y 3))) 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))
(+.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 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 y (/.f64 (pow.f64 x 3) y)) 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)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	19.6b	(sqrt.f64 (fma.f64 x x y))
✓	19.6b	(sqrt.f64 (fma.f64 x x y))

Compiler

Compiled 13 to 4 computations (69.2% saved)

series2.0ms (0.1%)

Counts

1 → 16

Calls

6 calls:

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

rewrite40.0ms (1.2%)

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 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 expm1.f64 (log1p.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 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 expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))))))

simplify47.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

759×	`times-frac_binary64`
596×	`associate-/l*_binary64`
504×	`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	1568	309
4	5603	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 (.f64 1/16 (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 5))) (.f64 1/16 (pow.f64 x 6)) (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 (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))))
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))
(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 (/.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))
(fma.f64 (/.f64 y x) -1/2 (neg.f64 x))
(-.f64 (*.f64 y (/.f64 -1/2 x)) 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 1/8 y) y) (pow.f64 x 3)) 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 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) 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 1/8 y) y) (pow.f64 x 3)) x)))
(fma.f64 (/.f64 y x) -1/2 (fma.f64 (.f64 (/.f64 y (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 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x))
(fma.f64 (pow.f64 y 3) (/.f64 -1/16 (pow.f64 x 5)) (-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) 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 (/.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))
(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 (/.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)))

eval41.0ms (1.3%)

Compiler: Compiled 1630 to 811 computations (50.2% saved)

prune26.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	127	8	135
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	128	9	137

Error

Counts

137 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	41.8b	(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 -1 x))
▶	41.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
	42.2b	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)
▶	22.5b	(hypot.f64 x (sqrt.f64 y))
▶	41.8b	(-.f64 (*.f64 y (/.f64 -1/2 x)) x)
	41.2b	x
▶	41.7b	(neg.f64 x)
	42.3b	(sqrt.f64 y)
✓	21.0b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 131 to 87 computations (33.6% saved)

localize6.0ms (0.2%)

Compiler: Compiled 10 to 4 computations (60% saved)

localize3.0ms (0.1%)

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

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 20 to 12 computations (40% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite43.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`pow1_binary64`
571×	`add-log-exp_binary64`
570×	`log1p-expm1-u_binary64`
570×	`expm1-log1p-u_binary64`
560×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1556	7

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

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

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

44 → 22

Calls

Call 1

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

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

localize10.0ms (0.3%)

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

localize13.0ms (0.4%)

Compiler: Compiled 26 to 14 computations (46.2% saved)

eval9.0ms (0.3%)

Compiler: Compiled 204 to 132 computations (35.3% saved)

prune8.0ms (0.2%)

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	3	3
Picked	1	0	1
Done	0	5	5
Total	21	10	31

Error

Counts

31 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	41.8b	(-.f64 (/.f64 1 (/.f64 x (*.f64 y -1/2))) x)
✓	41.8b	(-.f64 (*.f64 y (/.f64 -1/2 x)) x)
▶	42.2b	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)
✓	22.5b	(hypot.f64 x (sqrt.f64 y))
✓	41.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
	41.2b	x
✓	41.7b	(neg.f64 x)
▶	42.3b	(sqrt.f64 y)
▶	41.8b	(-.f64 (*.f64 -1/2 (/.f64 y x)) x)
✓	21.0b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize8.0ms (0.2%)

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

localize3.0ms (0.1%)

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

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 56 to 28 computations (50% saved)

series20.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
13.0ms	x	@	0	(*.f64 (/.f64 y x) (/.f64 1/8 x))
1.0ms	y	@	0	(*.f64 (/.f64 y x) (/.f64 1/8 x))
1.0ms	y	@	inf	(*.f64 (/.f64 y x) (/.f64 1/8 x))
1.0ms	y	@	inf	(.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2))
1.0ms	y	@	0	(.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2))

rewrite72.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

596×	`log-prod_binary64`
396×	`prod-diff_binary64`
300×	`pow2_binary64`
236×	`log-div_binary64`
211×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	236	27
2	3460	27

Stop Event

1×	node limit

Counts

2 → 139

Calls

Call 1

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

Outputs

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

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

simplify101.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1155×	`associate-/l/_binary64`
672×	`associate-/r/_binary64`
591×	`unswap-sqr_binary64`
421×	`sqr-pow_binary64`
313×	`times-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	660
1	43	660
2	102	660
3	326	642
4	1932	606
5	2663	606
6	3610	606
7	3797	606
8	4026	606
9	4301	606
10	7160	606

Stop Event

1×	node limit

Counts

187 → 146

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

localize15.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.5b	(/.f64 1 (/.f64 x (*.f64 y -1/2)))
✓	0.5b	(/.f64 1 (/.f64 x (*.f64 y -1/2)))

Compiler

Compiled 30 to 20 computations (33.3% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite49.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

843×	`pow1_binary64`
783×	`add-log-exp_binary64`
783×	`log1p-expm1-u_binary64`
783×	`expm1-log1p-u_binary64`
766×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	168	7
2	2162	7

Stop Event

1×	node limit

Counts

1 → 45

Calls

Call 1

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

Outputs

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

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

69 → 46

Calls

Call 1

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

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

eval75.0ms (2.3%)

Compiler: Compiled 3562 to 2051 computations (42.4% saved)

prune31.0ms (1%)

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	0	1	1
Picked	0	1	1
Done	0	8	8
Total	191	11	202

Error

Counts

202 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	41.8b	(-.f64 (/.f64 1 (/.f64 x (*.f64 y -1/2))) x)
✓	41.8b	(-.f64 (*.f64 y (/.f64 -1/2 x)) x)
✓	42.2b	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)
✓	22.5b	(hypot.f64 x (sqrt.f64 y))
▶	41.8b	(-.f64 (.f64 -1 (/.f64 1 (.f64 (neg.f64 x) (/.f64 -2 y)))) x)
✓	41.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
	41.2b	x
✓	41.7b	(neg.f64 x)
✓	42.3b	(sqrt.f64 y)
✓	41.8b	(-.f64 (*.f64 -1/2 (/.f64 y x)) x)
✓	21.0b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 94 to 64 computations (31.9% saved)

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(/.f64 1 (*.f64 (neg.f64 x) (/.f64 -2 y)))
	0.2b	(*.f64 (neg.f64 x) (/.f64 -2 y))
✓	0.2b	(*.f64 (neg.f64 x) (/.f64 -2 y))
✓	0.5b	(/.f64 1 (*.f64 (neg.f64 x) (/.f64 -2 y)))

Compiler

Compiled 48 to 31 computations (35.4% saved)

series5.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

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

rewrite49.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

794×	`pow1_binary64`
737×	`add-log-exp_binary64`
735×	`log1p-expm1-u_binary64`
735×	`expm1-log1p-u_binary64`
722×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	192	14
2	2442	14

Stop Event

1×	node limit

Counts

2 → 57

Calls

Call 1

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

Outputs

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

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

simplify20.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
2×	`associate-*r/_binary64`
2×	`associate-*l/_binary64`
2×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	336
1	15	336
2	21	336
3	29	336
4	31	336

Stop Event

1×

saturated

Counts

105 → 61

Calls

Call 1

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

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

eval20.0ms (0.6%)

Compiler: Compiled 814 to 610 computations (25.1% saved)

prune16.0ms (0.5%)

Pruning

14 alts after pruning (5 fresh and 9 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	0	1	1
Picked	1	0	1
Done	0	9	9
Total	58	14	72

Error

Counts

72 → 14

Alt Table

Click to see full alt table

Status	Error	Program
	42.0b	(-.f64 (.f64 -1 (/.f64 1 (/.f64 (.f64 x (/.f64 -2 y)) 1))) x)
✓	22.5b	(hypot.f64 x (sqrt.f64 y))
	41.8b	(-.f64 (.f64 -1 (/.f64 1 (.f64 x (/.f64 2 y)))) x)
✓	41.8b	(-.f64 (/.f64 1 (/.f64 x (*.f64 y -1/2))) x)
✓	41.8b	(-.f64 (*.f64 y (/.f64 -1/2 x)) x)
	45.0b	(-.f64 (.f64 -1 (/.f64 1 (-.f64 (+.f64 1 (.f64 x (/.f64 -2 y))) 1))) x)
✓	41.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	42.2b	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)
	42.0b	(-.f64 (.f64 -1 (.f64 (/.f64 (/.f64 1 x) -2) y)) x)
	41.2b	x
✓	41.7b	(neg.f64 x)
✓	42.3b	(sqrt.f64 y)
✓	41.8b	(-.f64 (*.f64 -1/2 (/.f64 y x)) x)
✓	21.0b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 138 to 99 computations (28.3% saved)

regimes112.0ms (3.4%)

Counts

14 → 3

Calls

Call 1

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

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

Calls

6 calls:

26.0ms	x
25.0ms	y
17.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
15.0ms	(+.f64 (*.f64 x x) y)
12.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.0b	3	`x`
8.0b	3	`y`
10.5b	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
10.5b	2	`(+.f64 (*.f64 x x) y)`
10.5b	2	`(*.f64 x x)`
10.5b	2	`(*.f64 x x)`

Compiler

Compiled 143 to 89 computations (37.8% saved)

bsearch168.0ms (5.2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
144.0ms	1.2972857537778287e+77	4.7815405159678237e+83
21.0ms	-1.5541455371231858e+159	-4.463332571114178e+153

Compiler

Compiled 130 to 90 computations (30.8% saved)

regimes76.0ms (2.3%)

Counts

12 → 3

Calls

Call 1

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

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

Calls

2 calls:

49.0ms	y
21.0ms	x

Results

Error	Segments	Branch
5.6b	3	`x`
26.0b	6	`y`

Compiler

Compiled 108 to 70 computations (35.2% saved)

bsearch101.0ms (3.1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
49.0ms	1.7583871378880635e-67	6.610261936369603e-62
52.0ms	-7.974042488299587e-81	-2.9939890801132226e-87

Compiler

Compiled 283 to 207 computations (26.9% saved)

regimes46.0ms (1.4%)

Counts

11 → 2

Calls

Call 1

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

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

Calls

2 calls:

30.0ms	y
13.0ms	x

Results

Error	Segments	Branch
19.7b	2	`x`
35.9b	4	`y`

Compiler

Compiled 106 to 69 computations (34.9% saved)

bsearch14.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
14.0ms	1.9106561409245813e-254	1.0793106991915228e-253

Compiler

Compiled 103 to 75 computations (27.2% saved)

regimes24.0ms (0.7%)

Accuracy

Total -43.6b remaining (-220.9%)

Threshold costs -43.6b (-220.9%)

Counts

3 → 2

Calls

Call 1

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

Outputs
(neg.f64 x)
x

Calls

2 calls:

16.0ms	y
7.0ms	x

Results

Error	Segments	Branch
19.7b	2	`x`
35.9b	4	`y`

Compiler

Compiled 18 to 11 computations (38.9% saved)

bsearch22.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
22.0ms	-5.193554807866894e-303	5.312329990866099e-304

Compiler

Compiled 103 to 79 computations (23.3% saved)

simplify4.0ms (0.1%)

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	34	90
1	42	90
2	45	90
3	46	90

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x -1554145537123185758908088897679758451418343397331869382848477833268731500503401588412638201074716681092219294537035470602688033593264439869618119401923109978112) (neg.f64 x) (if (<=.f64 x 130000000000000009331693572985691597674199002984591404980029211519262914510848) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -6719234226533413/2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776) (-.f64 (.f64 -1/2 (/.f64 y x)) x) (if (<=.f64 x 5463756259384863/30354201441027016733116592294117482916287606860189680019559568902170379456331382784) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x)))
(if (<=.f64 x 55999220300380520/528294531135665246352339784916516606518847326036121522127960709026673902556724859474417255887657187894674394993257128678882347559502685537250538978462939576908386683999005084168731517676426441053024232908211188404148028292751561738838396898767036476489538580897737998336) (neg.f64 x) (+.f64 (*.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x 0) (neg.f64 x) x)
x

Outputs
(if (<=.f64 x -1554145537123185758908088897679758451418343397331869382848477833268731500503401588412638201074716681092219294537035470602688033593264439869618119401923109978112) (neg.f64 x) (if (<=.f64 x 130000000000000009331693572985691597674199002984591404980029211519262914510848) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -6719234226533413/2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776) (-.f64 (.f64 -1/2 (/.f64 y x)) x) (if (<=.f64 x 5463756259384863/30354201441027016733116592294117482916287606860189680019559568902170379456331382784) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x)))
(if (<=.f64 x -6719234226533413/2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776) (-.f64 (.f64 -1/2 (/.f64 y x)) x) (if (<=.f64 x 5463756259384863/30354201441027016733116592294117482916287606860189680019559568902170379456331382784) (sqrt.f64 y) (+.f64 x (.f64 (/.f64 y x) 1/2))))
(if (<=.f64 x 55999220300380520/528294531135665246352339784916516606518847326036121522127960709026673902556724859474417255887657187894674394993257128678882347559502685537250538978462939576908386683999005084168731517676426441053024232908211188404148028292751561738838396898767036476489538580897737998336) (neg.f64 x) (+.f64 (*.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x 6999902537547565/66036816391958155794042473114564575814855915754515190265995088628334237819590607434302156985957148486834299374157141084860293444937835692156317372307867447113548335499875635521091439709553305131628029113526398550518503536593945217354799612345879559561192322612217249792) (neg.f64 x) (+.f64 x (*.f64 (/.f64 y x) 1/2)))
(if (<=.f64 x 0) (neg.f64 x) x)
x

end46.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 136 to 81 computations (40.4% saved)

Details

analyze99.0ms (3.1%)

sample1.6s (48.3%)

preprocess18.0ms (0.6%)

simplify8.0ms (0.3%)

eval1.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.2%)

series7.0ms (0.2%)

rewrite49.0ms (1.5%)

simplify49.0ms (1.5%)

localize7.0ms (0.2%)

series2.0ms (0.1%)

rewrite40.0ms (1.2%)

simplify47.0ms (1.5%)

eval41.0ms (1.3%)

prune26.0ms (0.8%)

localize6.0ms (0.2%)

localize3.0ms (0.1%)

localize10.0ms (0.3%)

series4.0ms (0.1%)

rewrite43.0ms (1.3%)

simplify13.0ms (0.4%)

localize10.0ms (0.3%)

localize13.0ms (0.4%)

eval9.0ms (0.3%)

prune8.0ms (0.2%)

localize8.0ms (0.2%)

localize3.0ms (0.1%)

localize20.0ms (0.6%)

series20.0ms (0.6%)

rewrite72.0ms (2.2%)

simplify101.0ms (3.1%)

localize15.0ms (0.5%)

series2.0ms (0.1%)

rewrite49.0ms (1.5%)

simplify13.0ms (0.4%)

eval75.0ms (2.3%)

prune31.0ms (1%)

localize20.0ms (0.6%)

series5.0ms (0.2%)

rewrite49.0ms (1.5%)

simplify20.0ms (0.6%)

eval20.0ms (0.6%)

prune16.0ms (0.5%)

regimes112.0ms (3.4%)

bsearch168.0ms (5.2%)

regimes76.0ms (2.3%)

bsearch101.0ms (3.1%)

regimes46.0ms (1.4%)

bsearch14.0ms (0.4%)

regimes24.0ms (0.7%)

bsearch22.0ms (0.7%)

simplify4.0ms (0.1%)

end46.0ms (1.4%)

Profiling