Details

analyze112.0ms (3.5%)

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%	74.9%	0.1%	6
40.6%	59.3%	0.1%	7
53.1%	46.8%	0.1%	8
66.3%	33.6%	0.1%	9
74.1%	25.8%	0.1%	10
82.1%	17.8%	0.1%	11
86.4%	13.5%	0.1%	12

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.2s (37.5%)

Results

1.2s	8255×	body	256	valid
0.0ms	1×	body	2048	valid

preprocess116.0ms (3.6%)

Algorithm

2×	egg-herbie

Rules

1208×	`fma-neg_binary64`
549×	`fma-def_binary64`
520×	`div-sub_binary64`
492×	`associate-/r/_binary64`
385×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	28	32
2	43	28
3	65	28
4	95	28
5	165	28
6	292	28
7	557	28
8	1175	28
9	1912	28
10	3084	28
11	5520	28
12	6482	28
13	6660	28
14	6760	28
15	6760	28
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify144.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

1478×	`fma-neg_binary64`
989×	`div-sub_binary64`
824×	`associate-/l/_binary64`
519×	`fma-def_binary64`
450×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	28	14
3	41	14
4	60	14
5	96	14
6	172	14
7	254	14
8	497	14
9	1056	14
10	1771	14
11	3878	14
12	6393	14
13	6950	14
14	7116	14
15	7146	14
16	7152	14
17	7152	14
18	7775	14
19	7887	14
20	7887	14

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 23 to 16 computations (30.4% 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

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(+.f64 x (/.f64 1 (fma.f64 x -1/2 (/.f64 -1 y))))
▶	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))

Compiler

Compiled 25 to 18 computations (28% saved)

localize15.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x -1/2 (/.f64 -1 y))
✓	0.1b	(/.f64 1 (fma.f64 x -1/2 (/.f64 -1 y)))

Compiler

Compiled 34 to 24 computations (29.4% saved)

series6.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

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

rewrite61.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

777×	`pow1_binary64`
715×	`add-log-exp_binary64`
714×	`log1p-expm1-u_binary64`
714×	`expm1-log1p-u_binary64`
701×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	179	19
2	1975	19

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

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

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

Outputs

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

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

simplify62.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
668×	`distribute-rgt-neg-in_binary64`
567×	`distribute-lft-neg-in_binary64`
414×	`distribute-neg-frac_binary64`
414×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	754
1	146	718
2	429	714
3	1735	706
4	5854	706

Stop Event

1×	node limit

Counts

94 → 66

Calls

Call 1

Inputs
(*.f64 -1 y)
(+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (*.f64 -1 y))
(+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (*.f64 -1 y)))
(+.f64 (.f64 1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (*.f64 -1 y))))
(/.f64 -2 x)
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (*.f64 2 (/.f64 1 x)))
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2))))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(/.f64 -2 x)
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (*.f64 2 (/.f64 1 x)))
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2))))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(*.f64 -1 y)
(+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (*.f64 -1 y))
(+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (*.f64 -1 y)))
(+.f64 (.f64 1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (*.f64 -1 y))))
(/.f64 -2 x)
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (*.f64 2 (/.f64 1 x)))
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2))))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(/.f64 -2 x)
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (*.f64 2 (/.f64 1 x)))
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2))))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(/.f64 -1 y)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(/.f64 -1 y)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))

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

localize22.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 x y) 2)
✓	7.5b	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))

Compiler

Compiled 41 to 22 computations (46.3% saved)

series15.0ms (0.5%)

Counts

2 → 48

Calls

12 calls:

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

rewrite104.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

460×	`log-prod_binary64`
347×	`exp-prod_binary64`
283×	`pow-prod-down_binary64`
265×	`prod-diff_binary64`
245×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	198	18
2	2651	18

Stop Event

1×	node limit

Counts

2 → 104

Calls

Call 1

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

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

Outputs

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

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

simplify84.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-def_binary64`
675×	`fma-neg_binary64`
673×	`cancel-sign-sub-inv_binary64`
526×	`distribute-neg-frac_binary64`
414×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	714
1	142	706
2	429	702
3	1719	690
4	5293	690

Stop Event

1×	node limit

Counts

152 → 118

Calls

Call 1

Inputs
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.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
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x)))
(fma.f64 -1/2 (.f64 y (.f64 y x)) y)
(fma.f64 x (.f64 y (.f64 y -1/2)) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x))))
(fma.f64 1/4 (.f64 x (.f64 x (pow.f64 y 3))) (fma.f64 -1/2 (.f64 y (.f64 y x)) y))
(fma.f64 -1/2 (.f64 y (.f64 y x)) (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) y))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 1/4 (*.f64 x (pow.f64 y 3)))) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) (.f64 -1/2 (.f64 (.f64 y y) x)))))
(+.f64 (fma.f64 1/4 (.f64 x (.f64 x (pow.f64 y 3))) (fma.f64 -1/2 (.f64 y (.f64 y x)) y)) (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 y (.f64 y x)) (fma.f64 -1/8 (*.f64 (pow.f64 y 4) (pow.f64 x 3)) y)))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 1/4 (.f64 x (pow.f64 y 3)))) (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) y))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 -4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (.f64 x x))) (/.f64 8 (.f64 y (*.f64 y (pow.f64 x 3)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3))) (/.f64 -4 (.f64 y (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (-.f64 (/.f64 2 x) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (/.f64 4 (.f64 y (*.f64 x x)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3))))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3))) (-.f64 (/.f64 -4 (.f64 y (.f64 x x))) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 -4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (.f64 x x))) (/.f64 8 (.f64 y (*.f64 y (pow.f64 x 3)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3))) (/.f64 -4 (.f64 y (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (-.f64 (/.f64 2 x) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (/.f64 4 (.f64 y (*.f64 x x)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3))))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3))) (-.f64 (/.f64 -4 (.f64 y (.f64 x x))) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x)))
(fma.f64 -1/2 (.f64 y (.f64 y x)) y)
(fma.f64 x (.f64 y (.f64 y -1/2)) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x))))
(fma.f64 1/4 (.f64 x (.f64 x (pow.f64 y 3))) (fma.f64 -1/2 (.f64 y (.f64 y x)) y))
(fma.f64 -1/2 (.f64 y (.f64 y x)) (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) y))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 1/4 (*.f64 x (pow.f64 y 3)))) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) (.f64 -1/2 (.f64 (.f64 y y) x)))))
(+.f64 (fma.f64 1/4 (.f64 x (.f64 x (pow.f64 y 3))) (fma.f64 -1/2 (.f64 y (.f64 y x)) y)) (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 y (.f64 y x)) (fma.f64 -1/8 (*.f64 (pow.f64 y 4) (pow.f64 x 3)) y)))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 1/4 (.f64 x (pow.f64 y 3)))) (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) y))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 -4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (.f64 x x))) (/.f64 8 (.f64 y (*.f64 y (pow.f64 x 3)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3))) (/.f64 -4 (.f64 y (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (-.f64 (/.f64 2 x) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (/.f64 4 (.f64 y (*.f64 x x)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3))))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3))) (-.f64 (/.f64 -4 (.f64 y (.f64 x x))) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 -4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (.f64 x x))) (/.f64 8 (.f64 y (*.f64 y (pow.f64 x 3)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3))) (/.f64 -4 (.f64 y (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (-.f64 (/.f64 2 x) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (/.f64 4 (.f64 y (*.f64 x x)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3))))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3))) (-.f64 (/.f64 -4 (.f64 y (.f64 x x))) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))

eval98.0ms (3%)

Compiler: Compiled 3010 to 2108 computations (30% saved)

prune43.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	180	4	184
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	181	5	186

Error

0.0b

Counts

186 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(+.f64 x (/.f64 1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y))))
▶	0.1b	(-.f64 x (/.f64 y (+.f64 1 (pow.f64 (cbrt.f64 (.f64 y (.f64 x 1/2))) 3))))
▶	23.2b	(-.f64 x (/.f64 2 x))
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
▶	17.2b	(-.f64 x y)

Compiler

Compiled 54 to 39 computations (27.8% saved)

localize27.0ms (0.8%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
✓	0.1b	(/.f64 1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y)))

Compiler

Compiled 39 to 28 computations (28.2% saved)

series9.0ms (0.3%)

Counts

2 → 30

Calls

12 calls:

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

rewrite96.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

964×	`pow1_binary64`
895×	`add-log-exp_binary64`
895×	`log1p-expm1-u_binary64`
895×	`expm1-log1p-u_binary64`
98×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	195	19
2	2513	19

Stop Event

1×	node limit

Counts

2 → 66

Calls

Call 1

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

Outputs

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

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

simplify86.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
663×	`distribute-rgt-neg-in_binary64`
565×	`distribute-lft-neg-in_binary64`
415×	`distribute-neg-frac_binary64`
414×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	574
1	142	574
2	420	570
3	1718	562
4	5795	562

Stop Event

1×	node limit

Counts

96 → 84

Calls

Call 1

Inputs
(*.f64 -1 y)
(+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (*.f64 -1 y))
(+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (*.f64 -1 y)))
(+.f64 (.f64 1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (*.f64 -1 y))))
(/.f64 -2 x)
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (*.f64 2 (/.f64 1 x)))
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2))))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(/.f64 -2 x)
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (*.f64 2 (/.f64 1 x)))
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2))))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(*.f64 -1 y)
(+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (*.f64 -1 y))
(+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (*.f64 -1 y)))
(+.f64 (.f64 1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (*.f64 -1 y))))
(/.f64 -2 x)
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (*.f64 2 (/.f64 1 x)))
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2))))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(/.f64 -2 x)
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (*.f64 2 (/.f64 1 x)))
(-.f64 (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (.f64 y (pow.f64 x 2))))) (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (*.f64 2 (/.f64 1 x))))
(/.f64 -1 y)
(*.f64 -1/2 x)
(*.f64 -1/2 x)
(/.f64 -1 y)
(*.f64 -1/2 x)
(*.f64 -1/2 x)

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

localize5.0ms (0.2%)

Compiler: Compiled 7 to 3 computations (57.1% saved)

localize10.0ms (0.3%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

localize50.0ms (1.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 y (.f64 x 1/2))) 3)
✓	7.5b	(/.f64 y (+.f64 1 (pow.f64 (cbrt.f64 (.f64 y (.f64 x 1/2))) 3)))
✓	14.6b	(cbrt.f64 (.f64 y (.f64 x 1/2)))

Compiler

Compiled 65 to 47 computations (27.7% saved)

series27.0ms (0.8%)

Counts

3 → 6

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(pow.f64 (cbrt.f64 (.f64 y (.f64 x 1/2))) 3)
2.0ms	y	@	-inf	(/.f64 y (+.f64 1 (pow.f64 (cbrt.f64 (.f64 y (.f64 x 1/2))) 3)))
2.0ms	x	@	-inf	(cbrt.f64 (.f64 y (.f64 x 1/2)))
2.0ms	y	@	0	(/.f64 y (+.f64 1 (pow.f64 (cbrt.f64 (.f64 y (.f64 x 1/2))) 3)))
2.0ms	y	@	0	(cbrt.f64 (.f64 y (.f64 x 1/2)))

rewrite115.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

928×	`prod-diff_binary64`
544×	`log-prod_binary64`
381×	`fma-def_binary64`
283×	`pow2_binary64`
195×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	259	27
2	3001	27

Stop Event

1×	node limit

Counts

3 → 113

Calls

Call 1

Inputs
(cbrt.f64 (.f64 y (.f64 x 1/2)))
(/.f64 y (+.f64 1 (pow.f64 (cbrt.f64 (.f64 y (.f64 x 1/2))) 3)))
(pow.f64 (cbrt.f64 (.f64 y (.f64 x 1/2))) 3)

Outputs

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

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/2 (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) y)) 2)) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) y))) (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) y))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 x (*.f64 1/2 y) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/2) y)))) (#(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 1 (*.f64 1/2 (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x))) 2) (cbrt.f64 (*.f64 1/2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/4)) (*.f64 (cbrt.f64 (*.f64 x 1/2)) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (*.f64 x 1/2)) (pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x)))) 2) (*.f64 (cbrt.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 (sqrt.f64 (*.f64 x 1/2)) (*.f64 (sqrt.f64 (*.f64 x 1/2)) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (*.f64 x 1/2)))))) (#(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 (pow.f64 (*.f64 1/2 (*.f64 y x)) 1/6) (*.f64 (pow.f64 (*.f64 1/2 (*.f64 y x)) 1/6) (pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (cbrt.f64 (*.f64 (*.f64 x x) 1/4))) (cbrt.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (sqrt.f64 (*.f64 x 1/2))) (sqrt.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x 1/2) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x 1/2) (sqrt.f64 y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x))) 2) 1) (cbrt.f64 (*.f64 1/2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x))) 2) (cbrt.f64 y)) (cbrt.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x)))) 2)) (cbrt.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x))) 2) (pow.f64 (*.f64 1/2 (*.f64 y x)) 1/6)) (pow.f64 (*.f64 1/2 (*.f64 y x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 1/2 (*.f64 y x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) y))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (*.f64 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 y x) 3) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (*.f64 1/2 (*.f64 y x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/2 (*.f64 y x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x (*.f64 1/2 y) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x (*.f64 1/2 y) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 x (*.f64 1/2 y) 1)) (cbrt.f64 (pow.f64 (fma.f64 x (*.f64 1/2 y) 1) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x (*.f64 1/2 y) 1) 2)) (cbrt.f64 (fma.f64 x (*.f64 1/2 y) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x (*.f64 1/2 y) 1)) (sqrt.f64 (fma.f64 x (*.f64 1/2 y) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 (*.f64 y x) 3) 1/8 1) (/.f64 1 (fma.f64 (*.f64 1/2 (*.f64 y x)) (fma.f64 1/2 (*.f64 y x) -1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (*.f64 1/2 (*.f64 y x)) 2)) (/.f64 1 (-.f64 1 (*.f64 1/2 (*.f64 y x)))) -1)))))

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	6

Stop Event

1×

saturated

Counts

119 → 114

Calls

Call 1

Inputs
y
y
y
y
y
y

Outputs
y
y
y
y
y
y

eval112.0ms (3.4%)

Compiler: Compiled 3422 to 2364 computations (30.9% saved)

prune46.0ms (1.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	198	5	203

Error

0.0b

Counts

203 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y))))
✓	0.1b	(-.f64 x (/.f64 y (+.f64 1 (pow.f64 (cbrt.f64 (.f64 y (.f64 x 1/2))) 3))))
✓	23.2b	(-.f64 x (/.f64 2 x))
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
✓	17.2b	(-.f64 x y)

Compiler

Compiled 54 to 39 computations (27.8% saved)

regimes30.0ms (0.9%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
9.0ms	y
8.0ms	x

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))`

Compiler

Compiled 75 to 51 computations (32% saved)

regimes34.0ms (1%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

26.0ms	y
6.0ms	x

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`

Compiler

Compiled 27 to 18 computations (33.3% saved)

regimes186.0ms (5.7%)

Accuracy

Total -34.3b remaining (-687.9%)

Threshold costs -34.3b (-687.9%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

168.0ms	x
15.0ms	y

Results

Error	Segments	Branch
7.1b	3	`x`
5.0b	3	`y`

Compiler

Compiled 16 to 10 computations (37.5% saved)

bsearch78.0ms (2.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
48.0ms	7.311240477678702e+125	5.442935445952627e+129
30.0ms	-2.555489753483215e+105	-3.768947900436278e+102

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	66
1	40	66
2	59	66
3	67	66
4	71	66

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
(+.f64 x (/.f64 1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y))))
(if (<=.f64 y -2555489753483215224182715441191640616188263760224286004705176019693357190010578681050586604441217636761600) (-.f64 x (/.f64 2 x)) (if (<=.f64 y 731124047767870166823165564739759513065183449471097802737749120347865980396104245945739694777395665471156384315199045448499200) (-.f64 x y) (-.f64 x (/.f64 2 x))))
(-.f64 x y)

Outputs
(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
(+.f64 x (/.f64 1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y))))
(+.f64 x (/.f64 1 (-.f64 (*.f64 x -1/2) (/.f64 1 y))))
(+.f64 x (/.f64 1 (+.f64 (*.f64 x -1/2) (/.f64 -1 y))))
(if (<=.f64 y -2555489753483215224182715441191640616188263760224286004705176019693357190010578681050586604441217636761600) (-.f64 x (/.f64 2 x)) (if (<=.f64 y 731124047767870166823165564739759513065183449471097802737749120347865980396104245945739694777395665471156384315199045448499200) (-.f64 x y) (-.f64 x (/.f64 2 x))))
(if (<=.f64 y -2555489753483215224182715441191640616188263760224286004705176019693357190010578681050586604441217636761600) (+.f64 x (/.f64 -2 x)) (if (<=.f64 y 731124047767870166823165564739759513065183449471097802737749120347865980396104245945739694777395665471156384315199045448499200) (-.f64 x y) (+.f64 x (/.f64 -2 x))))
(-.f64 x y)

Compiler

Compiled 54 to 37 computations (31.5% saved)

soundness0.0ms (0%)

end206.0ms (6.4%)

Compiler: Compiled 48 to 30 computations (37.5% saved)

Details

analyze112.0ms (3.5%)

sample1.2s (37.5%)

preprocess116.0ms (3.6%)

simplify144.0ms (4.4%)

eval1.0ms (0%)

prune1.0ms (0%)

localize15.0ms (0.5%)

series6.0ms (0.2%)

rewrite61.0ms (1.9%)

simplify62.0ms (1.9%)

localize22.0ms (0.7%)

series15.0ms (0.5%)

rewrite104.0ms (3.2%)

simplify84.0ms (2.6%)

eval98.0ms (3%)

prune43.0ms (1.3%)

localize27.0ms (0.8%)

series9.0ms (0.3%)

rewrite96.0ms (3%)

simplify86.0ms (2.7%)

localize5.0ms (0.2%)

localize10.0ms (0.3%)

localize50.0ms (1.5%)

series27.0ms (0.8%)

rewrite115.0ms (3.5%)

simplify13.0ms (0.4%)

eval112.0ms (3.4%)

prune46.0ms (1.4%)

regimes30.0ms (0.9%)

regimes34.0ms (1%)

regimes186.0ms (5.7%)

bsearch78.0ms (2.4%)

simplify10.0ms (0.3%)

soundness0.0ms (0%)

end206.0ms (6.4%)

Profiling